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In this paper, the coupled linear theory of thermoviscoelasticity for porous materials is considered in which the coupled phenomenon of the following four mechanical principles is proposed: the deformation of the skeleton of a porous solid, the volume fraction concept of the pore network, Darcy's law for the flow of a fluid through a porous medium, and Fourier's law of thermal conduction. The governing systems of equations of motion and steady vibrations are proposed. The fundamental solution of the system of steady vibration equations is presented explicitly by means of elementary functions, and its basic properties are established. By virtue of Green's identity the uniqueness theorems for the classical solutions of the basic internal and external boundary value problems (BVPs) of steady vibrations are proved. Then, the surface and volume potentials are presented and their basic properties are given. Finally, the existence theorems for classical solutions of the above-mentioned BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. [ABSTRACT FROM AUTHOR]

At present, structural analysis of polymer composite materials is a highly relevant issue. The complexity of taking into account the viscoelastic stress–strain dependence and the time-dependent distribution of stress–strain state parameters over the volume occupied by a solid is a limiting factor. The relevance and demand for new efficient methods of mathematical modeling of creep and relaxation processes in viscoelastic structures are obvious. The aim of this work is to verify and validate the method for solving boundary value problems of a linear viscoelastic solid. The proposed approach is based on the formulation of the generalized principle of correspondence between elastic and viscoelastic problems, according to which a viscoelastic solution can be obtained by replacing elastic constants by some time functions, which are hereinafter called time-effective moduli. The results derived from the theoretical validation and the solution of several problems suggest that the proposed method can be used for solving problems on the stress–strain state of viscoelastic structures. [ABSTRACT FROM AUTHOR]

The article touches upon an unsteady rectilinear motion of a submarine in a liquid under an ice cover. The ice cover is modeled as a viscoelastic plate. The viscoelastic properties of the ice are described using the Kelvin–Voigt model. The fluid is assumed to be inviscid and incompressible, and its motion is potential. Free surface fluid flow past system of one source and several sinks is used to simulate the motion of Joubert submarine. The solution of this problem is constructed analytically using the Fourier and Laplace transforms. Numerical results for the wave resistance and lift force acting on Joubert submarine are presented for different ice thicknesses, length-to-diameter ratio of a submarine, and the speed of the uniform motion. It is demonstrated that the use of a viscoelastic model for an ice cover results in a significant decrease in the maximum values of wave resistance and lift coefficients compared to the scenario of using an elastic plate model. The results indicate that when a submarine moves at realistic speeds (Fr < 0.7) under a thick ice cover (thicker than a meter), the wave resistance is less than for the same submarine moving under a free surface. The lift force for moving at these speeds under a thick ice cover is directed upwards. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of a Rayleigh-type wave is explored in a half-space of an incompressible nematic elastomer with a uniform director aligned orthogonal to the surface. The nematic elastomer is idealized so as to fit within the framework of linear viscoelasticity theory. The governing equations of nematic elastomers are subjected to the Tiersten-type impedance boundary conditions. An explicit secular equation of the Rayleigh wave is obtained which depends upon the non-dimensional anisotropy parameter, impedance parameters, frequency, rubber relaxation time, director rotation times, and the dynamic soft elasticity of nematic elastomers. The numerical computations of the Rayleigh wave speed are restricted for the case of ideal nematic rubbers. The Rayleigh wave speed is illustrated graphically to observe the effects of non-dimensional anisotropy parameter, frequency, impedance parameters, rubber relaxation time, and director rotation times. [ABSTRACT FROM AUTHOR]

The flexural wave propagation in a micro-beam mounted on viscoelastic foundation is considered in the present work. The mechanical behavior of the micro-beam is modeled by nonlocal strain gradient elasticity with the size-effects taken into account. The constraint is modeled by the Pasternak foundation with the rheology behavior modeled by fractional-order viscoelasticity. The main concerns are the dispersion and attenuation feature of five kinds of possible flexural waves derived from the governing equations of the presented micro-beam model. The influences of the nonlocal effects, strain gradient effects and the fractional-order viscoelastic effects are investigated by a parameter study in the numerical examples. This research is helpful for the design of micro-sensor, micro-actuator and energy-harvest devices in micro electric-mechanic system (MEMS). [ABSTRACT FROM AUTHOR]

The present work is mainly stimulated by the definition of the general fractional-order derivative operator (GFODO) involving the Miller–Ross kernel in the sense of the Liouville–Sonine type. The novel emphasis is the introduction of the GFODO within the Miller–Ross kernel into the Maxwell model and Kelvin–Voigt model, thereby constructing viscoelastic constitutive models with the property of inheritance and memorability. It is noteworthy that the fractional viscoelasticity can capture the strain response within a wide range of strain rates. The procedure used in our paper to calculate the creep compliance of the proposed model is the Laplace transform, and then comparisons between the general fractional-order models and the classical integer-order models are presented. In summing up, it may be stated that the general fractional-order Kelvin–Voigt model exhibits a very different behavior compared to the classical Kelvin–Voigt model and it can describe the whole creep process including the accelerated creep stage. [ABSTRACT FROM AUTHOR]

To gain a complete view on the unique spatial attenuation phenomenon arising from the periodicity and the material viscoelasticity of the two-dimensional phononic crystals with finite out-of-plane extension, this paper presents a theoretical study of the viscoelastic phononic crystal slabs to investigate the wave transmission characteristics in terms of the dispersion relations for the propagating, evanescent, and complex modes. A numerical approach based on the theory of three-dimensional elasticity is proposed to eliminate the restrictions of plane analysis and to obtain the complex band diagrams using the wave expansion functions combined with the finite discretization technique. This formulation allows one to perform the simulations associated with the nonlinear frequency-dependent viscoelastic property which is accurately described by a generalized Maxwell model in this work. Numerical results are presented to show the validity of the established model and to reveal the dissipation mechanisms inside and outside the band gaps as well as to investigate the effects induced by the material viscoelasticity on the attenuation diagrams. Furthermore, the influences of the out-of-plane extension, the geometrical size and the shape of the etcfhed holes are detailed discussed to obtain thorough understandings of such a finite solid viscoelastic periodic lattice which is indispensable to practical applications. [ABSTRACT FROM AUTHOR]

Strain/stress-controlled loading, loading–unloading, loading-relaxation (or creep), and corresponding cyclic tests are essential for characterizing the viscoelastic materials' rate-dependent stress–strain relationship. A three-parameter model is proposed based on the basic definition of fractional derivative viscoelasticity and time-varying viscosity. This model is applied to many complex loading conditions. The solutions for three monocyclic loading conditions are given and then further generalized to arbitrary linear loading conditions, which are assumed to be first-order functions of time. The generalized solution for the arbitrary linear loading path is validated by modelling the mechanical response of cyclic loading–unloading and loading–relaxation (or creep) tests. Four sets of experimental data for polymer materials are employed to demonstrate the proposed fractional derivative model's efficiency. The results show that it can accurately model strain/ stress-controlled response under various loading conditions using only three parameters. The model is then implemented in numerical software to explore its capacity further, and the simulation results show that it also succeeds in simulating cyclic loading–unloading tests. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of the material properties on the deceleration dynamics of a deformable cylinder rolling with slipping on a half-space of the same material. The interaction of the cylinder and the half-space is described by the 2D quasistatic contact problem of viscoelasticity (Goryacheva: J Appl Math Mech 37(5):877–885, 1973; Contact mechanics in tribology. Kluwer, Dordrecht 1998) which includes as limiting cases the absolutely rigid and elastic materials. Full dynamical analysis of the problem including the phase portrait, the dependence of the deceleration distance on the mechanical properties of the contacting bodies and on the friction coefficient is provided. The qualitative features of deceleration are justified by asymptotic analysis. [ABSTRACT FROM AUTHOR]

In this work, by constructing the equivalent viscoelasticity between a fractional Zener model and a time-varying viscosity Zener model, we obtain the time-varying viscosity of creep and relaxation response. The derived time-varying viscosity can well interpret the physical meaning of the evolution of material from Hooke body to Newtonian fluid body. With the relaxation time gradually becoming larger, the viscosity of creep is closer to the viscosity of relaxation. The relaxation modulus and creep compliance of a time-varying viscosity Zener model obtained by inserted viscosity of creep and relaxation approximate that of a fractional Zener model. And the variation of fractional order is accompanied by the transformation of viscoelasticity. Based on the importance of relaxation time, a variable-order function related to relaxation time is proposed, and it can well interpret the physical meaning of evolution of viscoelasticity. Then, it also can reveal a process where the viscosity is consumed to resist deformation in rheology. The viscosity increases with an increase in time and a decrease in the fractional order. Finally, based on the variable-order function, a variable-order fractional viscoelastic Zener model is proposed, and it is in well agreement with experimental data. [ABSTRACT FROM AUTHOR]

A novel thermodynamic framework for the continuum mechanical response of nonlinear solids is described. Large deformations, nonlinear hyperelasticity, viscoelasticity, and property changes due to evolution of damage in the material are all encompassed by the general theory. The deformation gradient is decomposed in Gram–Schmidt fashion into the product of an orthogonal matrix and an upper triangular matrix, where the latter can be populated by six independent strain attributes. Strain attributes, in turn, are used as fundamental independent variables in the thermodynamic potentials, rather than the usual scalar invariants of deformation tensors as invoked in more conventional approaches. A complementary set of internal variables also enters the thermodynamic potentials to enable history and rate dependence, i.e., viscoelasticity, and irreversible stiffness degradation, i.e., damage. Governing equations and thermodynamic restrictions imposed by the entropy production inequality are derived. Mechanical, thermodynamic, and kinetic relations are presented for material symmetries that reduce to cubic or isotropic thermoelasticity in the small strain limit, restricted to isotropic damage. Representative models and example problems demonstrate utility and flexibility of this theory for depicting nonlinear hyperelasticity, viscoelasticity, and/or damage from cracks or voids, with physically measurable parameters. [ABSTRACT FROM AUTHOR]

In this work, based on Eringen's theory of nonlocal anisotropic elasticity, the three-dimensional nonlocal anisotropic elasticity of generalized Helmholtz type is developed. The derivation of a new three-dimensional nonlocal anisotropic kernel, which is the Green function of the three-dimensional anisotropic Helmholtz equation, enables to capture anisotropic length scale effects by means of a length scale tensor, which is a symmetric tensor of rank two. The derived nonlocal kernel function possesses up to six internal characteristic lengths on the Ångström-scale. The presented theory of nonlocal elasticity possesses the appropriate property to be a generalized continuum theory of Ångström-mechanics, since the range of its validity and applicability is up to the Ångström-scale. The connection between the theory of nonlocal anisotropic elasticity and lattice theory is established. The tensor function of nonlocal elastic moduli as well as the nonlocal kernel function is given in terms of the Hessian matrix in the lattice approach. In the framework of the considered theory, the modeling of dislocations in anisotropic materials taking into consideration anisotropic dislocation core effects is presented. Important dislocation key formulas, namely the anisotropic Peach–Koehler stress formula, the Peach–Koehler force and the anisotropic Blin's formula, are derived. A major tool used in deriving the expression of anisotropic Blin's formula is Kirchner's so-called F -tensor, which is here generalized toward nonlocal anisotropic elasticity. The main feature and advantage of the derived fields, compared with the corresponding ones in classical anisotropic elasticity, is that they are free of singularities. Numerical applications to straight dislocations in bcc Fe are given, revealing the ability and advantage of the considered theory to describe adequately nonsingular anisotropic stress and self-energy fields capturing the effects of anisotropy on the Ångström-scale. [ABSTRACT FROM AUTHOR]

In this communication, we propose a nonlocal fractional viscoelastic model of a nanobeam resting on the fractional viscoelastic foundation and under the influence of the longitudinal magnetic field and arbitrary number of attached nanoparticles. Size effects are taken into account using the differential form of the nonlocal constitutive relation together with the fractional Kelvin-Voigt model. The governing equation for the free vibration of a nanobeam is derived, where Maxwell’s equations are used in order to represent the effect of the longitudinal magnetic field. We propose an analytical solution of the problem based on the Laplace transform, Mellin-Fourier transforms, and residue theory. From the validation study, it is shown that the obtained complex roots of the characteristic equation, where the imaginary part is the damped frequency and the real part is the damping ratio, are approximated eigenvalues of the system. In the parametric study, several numerical examples are given to investigate the influence of different parameters on complex roots as well as different masses and numbers of nanoparticles on the damped vibration behavior of a nanobeam system. [ABSTRACT FROM AUTHOR]

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs) using first-order shear deformation theory and a stress function with full motion equations (not using Volmir’s assumptions). The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of the GPLRC layers. The plate is assumed to rest on a viscoelastic Pasternak medium and to be subjected to dynamic mechanical load in a thermal environment. Numerical results for the nonlinear dynamic response and vibration of functionally graded (FG) multilayer GPLRC plates are obtained by the Runge-Kutta method. The results show the influences of the GPL distribution pattern, weight fraction, geometry, foundation models, mechanical and temperature loads on the nonlinear dynamic response and vibration, natural frequencies and frequency-amplitude curves of FG multilayer GPLRC plates. [ABSTRACT FROM AUTHOR]

The approach of viscoelastic body constitutive equation fractionalization using rheological representation of the classical Burgers model and considering the Scott-Blair (fractional) elements instead of the dash-pot elements is adopted. The obtained fractional Burgers model is further generalized by considering arbitrary model parameters: multiplicative constants and orders of fractional differentiation. Thermodynamical consistency of the fractional Burgers model is analyzed, resulting in formulation of eight thermodynamically consistent fractional Burgers models. [ABSTRACT FROM AUTHOR]

The work in this paper is based on a non-classical continuum theory in the Lagrangian description for thermoviscoelastic solids without memory in which the conservation and balance laws are derived by incorporating internal rotations (iΘ) arising from the Jacobian of deformation (J), as well as Cosserat rotations (eΘ) at a material point. Such non-classical solids have additional energy storage due to rotations and additional dissipation due to rotation rates compared to classical continuum theories. Rotations iΘ are completely defined by J, whereas displacements u and Cosserat rotations eΘ are degrees of freedom at each material point. When iΘ and eΘ are resisted by the deforming matter, conjugate moments arise, which together with (iΘ,eΘ) and (iΘ.,eΘ.) result in additional work and rate of work. This paper utilizes thermodynamic framework for non-classical solids derived based on internal as well as Cosserat rotations and presents a thermodynamically consistent derivation of the constitutive theories that incorporate the aforementioned deformation physics. The constitutive theories are derived using the conditions resulting from the entropy inequality in conjunction with the representation theorem. [ABSTRACT FROM AUTHOR]

The interfacial adhesion and viscoelasticity of an additional mass layer have a significant influence on the resonant frequency of a quartz crystal microbalance (QCM), especially when the attached mass layer is thick. In this study, a detailed quantitative investigation is conducted on the influence of the interface parameter and viscosity coefficient on the resonant frequency and admittance of a QCM. The obtained explicit expression of free vibration of the QCM can be numerically solved using Muller’s method. The results obtained in this study show that the viscoelasticity of the mass layer and its bonding characteristics significantly affect the performances of the QCM, such as the resonance frequency, displacement, and stress distributions, and the peak and bandwidth of admittance. The non-proportional relation between the resonance frequency and thickness of the mass layer becomes obvious when the thickness of the mass layer is larger than 2% that of the quartz plate. Meanwhile, the error between the exact solution and Sauerbrey’s solution is enlarged as the interface parameter increases or the viscosity coefficient decreases. The proposed method will be more precise in solving the resonant frequency than Sauerbrey’s equation does and able to provide a guidance for determining the viscosity of an attached mass layer. The novel points in the article are as follows: (i) The effects of the imperfect interface and viscosity on the resonance frequency of a QCM at different layer thicknesses are investigated. (ii) The difference between effects of the imperfect interface and viscosity on the characteristics of the admittance is discussed in detail. [ABSTRACT FROM AUTHOR]

The problem of structural design of polymeric and composite viscoelastic materials is currently of great interest. The development of new methods of calculation of the stress-strain state of viscoelastic solids is also a current mathematical problem, because when solving boundary value problems one needs to consider the full history of exposure to loads and temperature on the structure. The article seeks to build an iterative algorithm for calculating the stress-strain state of viscoelastic structures, enabling a complete separation of time and space variables, thereby making it possible to determine the stresses and displacements at any time without regard to the loading history. It presents a modified theoretical basis of the iterative algorithm and provides analytical solutions of variational problems based on which the measure of the rate of convergence of the iterative process is determined. It also presents the conditions for the separation of space and time variables. The formulation of the iterative algorithm, convergence rate estimates, numerical computation results, and comparisons with exact solutions are provided in the tension plate problem example. [ABSTRACT FROM AUTHOR]

When the so-called eek effect emerges while shifting a vehicle shift gearbox, car drivers perceive audible noise and vibrations of drivetrain components. Some physical approaches have been provided in order to explain the effect as well as to search for countermeasures. In Jehle and Fidlin (ZAMM J Appl Math Mech 94(11):911-916 (2014), the interaction of sliding clutch disk and gears is addressed in a rigid body model. The clutch disk’s non-conservative follower forces in combination with geometric coupling in gears imply the action of non-symmetric restoring- and velocity-proportional forces. The desired motion of gearbox components can therefore undergo a mode-coupling flutter instability, out of which vibrations emerge with exponentially growing amplitudes. As the contacts in clutch and gears hold non-smooth transitions such as the possibility of sticking and opening, dynamic solutions are both limited and complex. In this contribution, first of all model details concerning the gear formulation are revised: rigid and viscoelastic normal contact are compared, which imply differences in the nature of the solution and method of stability analysis. Nevertheless the two approaches are shown to converge. Finally, the dynamics behind the loss of stability of the desired motion is investigated. [ABSTRACT FROM AUTHOR]

The present article deals with the viscoelastic modeling and dynamic responses of the carbon nanotubes (CNTs)-based carbon fiber-reinforced polymer (CNTs-CFRP) composite spherical shell panels where CNTs are reinforced in the polymer matrix phase. The Mori-Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of CNTs-based polymer matrix phase. Further, the strength of material method has been employed to formulate the viscoelastic material behavior of the homogenized hybrid CNTs-CFRP composite materials. An eight-noded shell element with five degrees of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP composite materials. Frequencyand temperature-dependent material properties of such hybrid composite materials have been obtained and analyzed. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters on thematerial properties and such dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such CNTs-based proposed composite materials. [ABSTRACT FROM AUTHOR]

Experimental data are reported on polycarbonate in tensile tests with a constant strain rate and relaxation tests in a wide range of temperatures. It is demonstrated that the growth of temperature results in a decrease in Young's modulus and a strong increase in the relaxation rate. Constitutive equations are developed for the non-isothermal linear viscoelastic response of glassy polymers when the rates of heating/cooling and stress relaxation are comparable. A good agreement is demonstrated between the observations in relaxation tests on polycarbonate, poly(methyl methacrylate), polystyrene, and epoxy resin, and results of simulation. The model is applied to the numerical analysis of creep flow under non-isothermal multi-step thermal programs. [ABSTRACT FROM AUTHOR]

This article presents vibration characteristics of a piezoelectric viscoelastic nanoplate under various boundary conditions embedded in a visco-Pasternak's medium using nonlocal plate theory. The piezo-hygrothermal effects are all included. The hygrothermal piezoelectric nanoplate is made of orthotropic viscoelastic material. Also, the visco-Pasternak's medium is modeled according to a Kelvin-Voigt foundation. A Two-variable sinusoidal shear deformation plate theory is presented. The imaginary and real parts of the eigenfrequency of piezoelectric viscoelastic nanoplates which are associated with viscoelastic foundation, nonlocal parameter, as well as the viscoelastic structural damping coefficient, are obtained. The effects of other parameters such as aspect ratio, side-to-thickness ratio, temperature change, and moisture concentration are all investigated. The predicted results are compared with the corresponding ones in the literature to check their validation. Additional results are presented and suitable discussions are made. [ABSTRACT FROM AUTHOR]

A non-classical model for an orthotropic Kirchhoff plate embedded in a viscoelastic medium is developed by using an extended version of the modified couple stress theory and a three-parameter foundation model. The equations of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton's principle. The new plate model contains three material length scale parameters to capture the microstructure effect, one damping coefficient to account for the viscoelastic damping effect, and two foundation moduli to represent the foundation effect. The current non-classical orthotropic plate model includes the isotropic plate model incorporating the microstructure effect and the classical elasticity-based orthotropic plate model as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported orthotropic plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate predicted by the current model is smaller than that predicted by the classical model, and the difference is large when the plate thickness is small but diminishes as the thickness becomes large. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. In addition, the damping ratio predicted by the new plate model is lower than that predicted by the classical plate model, and the difference is diminishing as the plate thickness increases. These predicted trends of the size effect at the micron scale agree with those observed experimentally. Furthermore, it is quantitatively shown that the presence of the foundation enlarges the plate natural frequency. [ABSTRACT FROM AUTHOR]

The dynamic mechanical behavior of PBX1314 is examined by means of a micromechanical model. The basis for this work is Eshelby theory. The effective moduli derived by Weng and Tandon are used for the randomly oriented two-phase composites. The dynamic mechanical behavior of the PBX1314 is described as a function of aspect ratio and inclusion concentration. The viscoelastic behavior of the polymer binder is modeled using a generalized Maxwell model with a Prony series representation for the stress relaxation functions. Numerical inverse Laplace transform required by the model can be performed analytically. To demonstrate the utility and validity of the theory, we compare its predictions to several dynamic compressive experiments on the PBX1314. We also compare the predictions of the present model to the theoretical results derived by Mas and Clements. Their studies can be used to assess the properties of energetic composites, and this method is a useful tool for the design of energetic composites. [ABSTRACT FROM AUTHOR]

In the present paper, the linear theory of binary viscoelastic mixtures is considered. The basic properties of plane harmonic waves are established. Green's first identity for 3D bounded and unbounded domains is obtained. On the basis of this identity the uniqueness theorems of regular (classical) solutions of the boundary value problems (BVPs) of steady vibrations are proved. Then these theorems are established in the quasi-static case. Finally, the uniqueness theorems for the first internal and external BVPs of steady vibrations in general and quasi-static cases are proved under weak condition on the viscoelastic constants. [ABSTRACT FROM AUTHOR]

This paper concerns the vibration response under moving loads of Euler-Bernoulli uniform beams with translational supports and rotational joints, featuring Kelvin-Voigt viscoelastic behaviour. Using the theory of generalized functions to handle the discontinuities of the response variables at the support/joint locations, exact beam modes are obtained from a characteristic equation built as determinant of a $$4\times 4$$ matrix, for any number of supports/joints. Based on pertinent orthogonality conditions for the deflection modes, the response under moving loads is built in the time domain by modal superposition. Remarkably, all response variables are built in a closed analytical form, regardless of the number of supports/joints. [ABSTRACT FROM AUTHOR]

In this paper, surface and thermal effects on the vibration characteristics of viscoelastic functionally graded (FG) nanobeams embedded in a viscoelastic foundation are investigated based on nonlocal strain gradient elasticity theory and Euler-Bernoulli beam model. The present model contains two parameters to capture the size effects in which the stress is considered for not only the nonlocal stress field but also the strain gradients stress field. Gurtin-Murdoch elasticity theory is incorporated into the nonlocal strain gradient theory to develop a nonclassical beam model including the surface effects. The viscoelastic foundation consists of a Winkler-Pasternak layer together with a viscous layer of infinite parallel dashpots. A power-law model is adopted to describe a continuous variation of material properties of the FG nanobeam. The governing equations of nonlocal viscoelastic FG nanobeams are obtained using Hamilton's principle and solved implementing an analytical solution for simply supported and clamped-clamped boundary conditions. The results are validated with those available in the literature. The effects of linear, shear and viscous layers of foundation, structural damping coefficient, surface elasticity, nonlocal parameter, length scale parameter, temperature change, power-law exponent, and slenderness ratio on the frequencies of viscoelastic FG nanobeams are examined. [ABSTRACT FROM AUTHOR]

The present paper investigates the theory of propagation of Voigt-type viscoelastic Love waves in a functionally graded material layer over an anisotropic porous half-space. The complex dispersion equation of Love waves has been expanded into real and imaginary parts. An assumption of the dissipation factor has been applied. Some particular cases have also been deduced, and it is noticed that the dispersion equation is in well agreement with the classical Love wave equation. In addition, to study the effect of initially stressed parameter, inhomogeneity parameter and porosity on phase velocity and dissipation function, some significant observations have been made by detailed numerical calculations and illustrated graphically. The results of this paper may present a deeper insight into the nature of the propagation behavior in elastic inhomogeneous functionally graded materials and can provide theoretical guidance for the design and optimization to the field of earthquake engineering. [ABSTRACT FROM AUTHOR]

The phononic band structure of waves, which travel though composites, results from the geometric and mechanical properties of the materials and from the interaction of the different constituents. In this article, we study two different models to simulate imperfect bonding and their impact on the phononic bands: (a) imperfect bonding is simulated by introducing an artificial interphase constituent with properties which define the bonding quality; (b) imperfect bonding is described by conjugate conditions in the interface, in which the difference in the displacement is proportional to the interfacial stress. Viscoelastic behavior of the constituents has a crucial influence on the traveling signal, and the wave attenuates with increasing viscosity. We study the interaction of the different bonding conditions and the viscoelastic behavior as well as the impact of such interplay on the wave attenuation and dispersion characteristics of the material. [ABSTRACT FROM AUTHOR]

Thermo-electro-mechanical transient analysis of a sandwich nanoplate is studied in this paper. The sandwich nanoplate consists of a Kelvin-Voigt viscoelastic nanoplate and two integrated piezoelectric face sheets resting on a visco-Pasternak foundation. The sandwich nanoplate is subjected to thermal and mechanical loads, and the piezoelectric face sheets are subjected to an applied electric potential. Two-variable sinusoidal shear deformation plate theory is used for the description of the displacement components. The governing equations of motion are derived using Hamilton's principle by calculation of strain and kinetic energies and energy due to external forces. The natural frequencies of the sandwich nanoplate are calculated in terms of three parameters of foundation, structural viscoelastic damping parameter and excitation frequency. Also, bending results of the problem in terms of the parameters of the temperature loadings are presented. [ABSTRACT FROM AUTHOR]

This paper aims to study the vibration characteristics of viscoelastic double-walled carbon nanotubes embedded in a viscoelastic medium. In doing this, the governing equations of the system are derived by combining the Euler-Bernoulli beam theory, nonlocal viscoelastic model and Kelvin viscoelastic foundation model. Subsequently, the transfer function method is employed to solve the governing equations, which enables one to obtain the natural frequencies and the corresponding mode shapes in closed form for the DWCNTs with arbitrary boundary conditions. Here, the developed mechanics model is first compared with the existing techniques available in the literature, where excellent agreement is achieved. Also, a detailed parametric study is conducted to examine the effect of boundary conditions, nonlocal parameter, relaxation time, slenderness ratio, stiffness coefficient and damping coefficient on the vibration response of the DWCNTs. [ABSTRACT FROM AUTHOR]

In previous works, a model was developed for the transition of an epoxy liquid to a cured solid as a result of the continuous formation of solid epoxy networks by crosslinking. The model accounts for volume decrease during crosslinking, thermal expansion due to heat generation, deformation and stress generation. The networks were assumed to be linear thermo-elastic isotropic solids, material properties were deduced from the literature, and the model was used to determine the stresses generated by curing in a number of examples. The purpose of the present work is to revisit the ideas on which this model is based and incorporate them into a general framework within the context of continuum mechanics. This will show the assumptions that have been made in the existing model because of the lack of experimental results and also provide a proper framework for extending the model as new experimental results are obtained. Each network is now assumed to be a nonlinear thermo-viscoelastic solid with its own properties. The assumption of small deformations is introduced to lead to a simplified model that is linear in the strains. [ABSTRACT FROM AUTHOR]

Rotating elements supported on journal bearings are widely encountered structures in engineering practice. Most commonly, these are asymmetrically manufactured and loaded rigid rotors transmitting torque and carrying transverse as well as axial forces. Nowadays, despite high operational demands and high rotational velocities, such systems are still expected to exhibit stable working, even in the presence of small assembly deviations, light unbalance or external disturbances. The surrounding environment of a rotating machine may interact with it by kinematic excitation from vibrating foundation. This, in turn, may lead to hazardous response and the onset of irregular and chaotic motion of the rotor. The subject of the study is to find and analyze regions of the occurrence of such vibrations in the system of a rigid rotor supported in journal bearings. The bearings themselves are assumed to be non-perfectly mounted in the housing, i.e., their sleeves are inserted in rings possessing some viscoelastic properties. These properties are treated as variable parameters, and the aim is to move the regions of irregular and chaotic vibration outside the operational regime (angular velocity). The adjustability of the viscoelastic parameters may be realized by incorporation of smart materials such as piezoelectric or magnetorheological ones. The considered system is an asymmetric rigid rotor supported on two journal bearings subject to a steady kinematic excitation. The system is described by eight coupled nonlinear ordinary differential equations of motion. Results of the examinations prove that by selecting an appropriate magnitude of damping and stiffness of the bearing mountings, it is possible to enlarge the region of stable operation of the rotating system and thus secure its safety. This, however, does not mean the elimination of chaotic response at all, but only a shift of it outside the range of operational rotation speed. [ABSTRACT FROM AUTHOR]

Experimental pulse transmission in impulsively loaded, homogeneous, and dimer granular chains, optionally embedded in a viscoelastic matrix, is studied. All tested chains are composed of spherical elastic beads of common radius. Homogeneous chains were composed of granules with equal mass, whereas dimer chains had alternating 'heavy' and 'light' granules with different masses. These media are strongly nonlinear due to Hertzian interactions between adjacent beads under compressive loads, and separations and collisions between them in the absence of compression. A series of experimental tests was performed to study primary pulse transmission in the non-embedded chains, and assess the effect of the surrounding viscoelastic matrix on pulse transmission in the embedded ones. For the case of dimer chains, the effect of mass inhomogeneity on pulse attenuation caused by scattering at the interfaces between adjacent beads is studied. In total, two embedded dimer chains, as well as an embedded homogeneous one, were manufactured and tested, and a previous theoretical model is used to compare theoretical predictions to experimental measurements. Whereas one of the non-embedded dimer chains differs from the others in that its light beads are hollow and so its experimental responses are not captured well by our theoretical model, for the other embedded and non-embedded chains, the theoretical predictions match remarkably well with the experimental measurements, despite the complexity in the acoustics induced by the surrounding matrix, and the conceptual simplicity of the theoretical model. The results of this work contribute to the development of practical acoustic metamaterials incorporating embedded granular media. [ABSTRACT FROM AUTHOR]

In this paper, we study the propagation of the Rayleigh surface waves in a half-space filled by an exponentially functionally graded thermoviscoelastic material with voids. We take into consideration the dissipative character of the porous thermoviscoelastic models upon the propagation waves and study the damped in time wave solutions. The propagation condition is established in the form of an algebraic equation of tenth degree whose coefficients are complex numbers. The eigensolutions of the dynamical system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is expressed as a linear combination of the five analytical solutions, while the secular equation is established in an implicit form. The explicit secular equation is obtained for an isotropic and homogeneous thermoviscoelastic porous half-space, and some numerical simulations are given for a specific material. [ABSTRACT FROM AUTHOR]

Surface stresses have a remarkable effect on nanocontact response of layered viscoelastic solids, especially under specific loading patterns. In the framework of nonlinear viscoelastic contact mechanics, a numerical model is developed to investigate the quasistatic nanocontact response of elastically layered viscoelastic solids under different loading patterns. The developed model accounts for surface energy effects by adopting the complete Gurtin-Murdoch surface elasticity model. The Schapery's constitutive viscoelastic creep model is used for the stress, strain, and time relationships. The transient term in the creep compliance is expressed by Prony's series. Frictionless contact condition is assumed throughout the contact interface. The equilibrium contact configuration, in which the contact constraints are exactly satisfied without any need for an appropriate value for the penalty parameter, is obtained by using the Lagrange multiplier method in the framework of the Newton-Raphson procedure. The developed model is applied to study and analyze the quasistatic nanocontact response of two different problems under different loading patterns. Results show the significant effect of the type of loading pattern and its rate on the nanocontact response of elastically layered viscoelastic solids. [ABSTRACT FROM AUTHOR]

Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the well-known Newmark method taking into account fractional derivatives discretized via the Grünwald-Letnikov summation allows the analysis of structural systems using standard Finite Element technology. [ABSTRACT FROM AUTHOR]

Beck's type column on a Winkler type foundation is the subject of the present analysis. Instead of the Bernoulli-Euler model describing the rod, two generalized models will be adopted: Eringen's nonlocal model corresponding to nano-rods and a viscoelastic model of fractional Kelvin-Voigt type. The analysis shows that for a nano-rod the Herrmann-Smith paradox holds whilst for a viscoelastic rod it does not. [ABSTRACT FROM AUTHOR]

In this paper, the quasi-static stability of moderately thick skew viscoelastic composite plates subjected to in-plan forces is analyzed using the element-free Galerkin method. The study is based on the first-order shear deformation theory and the method of effective moduli. The shape functions are constructed using the moving least squares approximation and the essential boundary conditions are introduced into the formulation through the Lagrange multiplier method and the orthogonal transformation techniques. The method is programmed and several numerical examples are presented to demonstrate the scope and efficacy of the procedure. Also, local buckling of viscoelastic stepped plates is studied. [ABSTRACT FROM AUTHOR]

This paper presents ordered rate constitutive theories in Lagrangian description for compressible as well as incompressible homogeneous, isotropic thermoviscoelastic solid matter with memory in which the material derivative of order m of the deviatoric stress tensor and heat vector are functions of temperature, temperature gradient, time derivatives of the conjugate strain tensor up to any desired order n, and the material derivatives of up to order m−1 of the stress tensor. The thermoviscoelastic solids described by these theories are called ordered thermoviscoelastic solids with memory due to the fact that the constitutive theories are dependent on orders m and n of the material derivatives of the conjugate stress and strain tensors. The highest orders of the material derivative of the conjugate stress and strain tensors define the order of the thermoviscoelastic solid. The constitutive theories derived here show that the material for which these theories are applicable have fading memory. As is well known, the second law of thermodynamics must form the basis for deriving constitutive theories for all deforming matter (to ensure thermodynamic equilibrium during evolution), since the other conservation and balance laws are independent of the constitution of the matter. The entropy inequality expressed in terms of Helmholtz free energy density $${\Phi}$$ does not provide a mechanism to derive a constitutive theory for the stress tensor when its argument tensors are stress and strain rates in addition to others. With the decomposition of the stress tensor into equilibrium and deviatoric stress tensors, the constitutive theory for the equilibrium stress tensor is deterministic from the entropy inequality. However, for the deviatoric stress tensor, the entropy inequality requires a set of inequalities to be satisfied but does not provide a mechanism for deriving a constitutive theory. In the present work, we utilize the theory of generators and invariants to derive rate constitutive theories for thermoviscoelastic solids with memory. This is based on axioms and principles of continuum mechanics. However, we keep in mind that these constitutive theories must satisfy the inequalities resulting from the second law of thermodynamics. The constitutive theories for heat vector q are derived: (i) strictly using conditions resulting from the entropy inequality; (ii) using the theory of generators and invariants with admissible argument tensors that are consistent with the stress tensor as well as the theories in which simplifying assumptions are employed which yield much simplified theories. It is shown that the rate theories presented here describe thermoviscoelastic solids with memory. Mechanisms of dissipation and memory are demonstrated and discussed, and the derivation of memory modulus is presented. It is shown that simplified forms of the general theories presented here result in constitutive models that may resemble currently used constitutive models but are not the same. The work presented here is not to be viewed as extension of the current constitutive models; rather, it is a general framework for rate constitutive theories for thermoviscoelastic solids with memory based on the physics and derivations that are consistent within the framework of continuum mechanics and thermodynamics. The purpose of the simplified theories presented in the paper is to illustrate possible simplest theories within the consistent framework presented here. [ABSTRACT FROM AUTHOR]

The Euler-Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler-Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler-Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a fractional constitutive law has to be considered. In this context, it has been provided that if the homogeneous beam correspondence principle also holds, then the study of a fractional visco-elastic Euler-Bernoulli beam may be derived from the elastic one. As mentioned before, when dealing with visco-elasticity the Timoshenko beam model is more appropriate than Euler-Bernoulli's one, and this paper provides important information to engineering designers, introducing exact linking relationships between elastic Euler-Bernoulli beam response and fractional visco-elastic Timoshenko beam response. Ready-to-use tables and a straightforward formulation have been provided leading to significant analysis cost savings and improved quality. [ABSTRACT FROM AUTHOR]

The Kelvin-Voigt and Zener viscoelasticity models have been studied using a stressed uniform bar. The presented results show that since a classic single element model and a real structure are governed by a first-order ordinary differential equation and a second/third-order partial differential equation, respectively, an ideal single element model will behave differently from a structure when acceleration has to be taken into account. When for a Zener viscoelasticity holds $${\tau_{\varepsilon} < \tau_{\sigma}}$$ , then it may cause no a creep relaxation due to a positive real part of an eigenvalue in vibration that may become unstable. This suggests that the Zener model is valid for a real material when, and only when, $${\tau_{\varepsilon} \geq \tau_{\sigma}}$$ . It has been found that the formulations of calculating Q parameters developed in literature from a single element model may need to be improved and that the initial response obtained from a classic single element model relaxes far more quickly than that of a stressed bar. [ABSTRACT FROM AUTHOR]

The viscoelastic behavior of hydrated soft biological tissue is strongly influenced by the mechanical interaction of its interstitial fluid with the solid phase. The classical uniaxial steady biphasic theory for soft tissue with high moisture content under confined compression is extended by replacing the Darcy steady flow assumption with an unsteady internal fluid flow model that involves an unsteady flow coefficient based on non-equilibrium thermodynamics. The finite deformation, non-equilibrium, unsteady biphasic viscoelastic analysis derived from conservation of linear momentum, which includes the mass terms neglected in some steady models, produces a nonlinear hyperbolic partial differential equation for the solid phase displacements, with a finite propagation velocity of the disturbance from the plunger in contrast to the instantaneous propagation of the classical parabolic steady description for cartilage. For confined compression of a small cylinder of hydrated soft biological tissue, the new hyperbolic equation is solved for the solid phase local displacements during both loading and relaxation as a function of time and position by a finite difference scheme of Shampine. A parametric study shows the influence of the unsteady coefficient on the predicted behavior, for both a linear elastic and a linear viscoelastic solid phase and for a constant permeability, by a comparison of the respective solid phase displacement distributions at the end of a constant rate plunger displacement at 0.001/s, 1/s and 1,000/s. Models assuming the Darcy relation predict physically realistic responses only for slow rates. The concavity of the stress-time curve for the solid phase at the plunger during a constant displacement of the plunger even at slow rates may be adjusted from softening to hardening by increasing the unsteady coefficient to increase the drag force exerted by the fluid on the solid phase. Because of unsteady fluid flow, overshoot of the solid phase displacement may occur initially during relaxation and also again near the end of the approach to equilibrium. A Zener standard linear viscoelastic solid phase slows the relaxation to equilibrium in comparison with a linear elastic solid phase. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical study on propagation of torsional surface waves in a homogeneous viscoelastic isotropic layer with Voigt type viscosity over an inhomogeneous isotropic infinite half space. The non-homogeneity in half space is assumed to arise due to exponential variation in shear modulus and density. A closed-form solution has been obtained for the displacement in the layer as well as for a infinite half space. The dispersion and absorption relations for an torsional wave under the assumed geometry have been found. Numerical results are presented for propagation characteristics in terms of a number of non-dimensionalized parameters and have been produced graphically. This study investigates the effect of various parameters, namely non-homogeneity parameter, internal friction, the layer width and complex wave number on dissipation function and phase velocity of the torsional wave. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close agreement. [ABSTRACT FROM AUTHOR]

A new approach to the derivation of the theory of thermoviscoelasticity is proposed. Neither the hypothesis of fading memory nor rheological models are used within the framework of this approach. The proposed approach is based on the mechanical model of a one-rotor gyrostat continuum. In special cases, the mathematical description of this model is proved to reduce to the equations of the coupled problem of thermoelasticity, the self-diffusion equation, and the equation describing the flow of a viscous incompressible fluid. In the context of this model, we consider the original treatment of the physical nature of the mechanism of thermal conduction and internal damping. The first part of the paper contains the aforesaid theoretical results. The second part of the paper is devoted to the determination of some parameters of the model. On the base of the proposed theory, we obtain the dependence of the acoustic wave attenuation factor on a signal frequency. This dependence is in close agreement with the classical dependence in the low-frequency range and agrees with the dependence obtained on the base of the phonon theory in the hypersonic frequency range. We discuss some ways of determining of the volume and shear viscosities and the heat flow relaxation timescale by using known values of the sound velocity and the acoustic wave attenuation factor. The obtained values of the heat flow relaxation timescale are compared with the values derived from the phonon theory. [ABSTRACT FROM AUTHOR]

We consider a thermoelastic model for phase transforming materials which can adequately describe the evolution with respect to the temperature of the hysteresis loop both in compression and tension tests. The specificity of this model is that the Grüneisen coefficient changes its sign. The model is augmented by considering a dissipative mechanism governed by a Maxwellian rate-type constitutive equation that can describe stress relaxation phenomena toward equilibrium between phases. Existence and uniqueness of traveling wave solutions are investigated. One derives that the admissibility condition induced by the Maxwellian rate-type approach, coupled or not with Fourier heat conduction law is related to the chord criterion with respect to the Hugoniot locus. We investigate the structure of profile layers, and we focus on their thermodynamic properties. The influence of the exothermic or endothermic character of phase transitions on the inner structure of interphase layers is captured. A phenomenon of temperature overshoot/undershoot with respect to the front state temperature and Hugoniot back state temperature inside an interphase layer is revealed. [ABSTRACT FROM AUTHOR]

This paper presents ordered rate constitutive theories in Lagrangian description for compressible as well as incompressible homogeneous, isotropic thermoviscoelastic solids without memory in which the deviatoric stress tensor and heat vector as dependent variables in the constitutive theories are functions of temperature, temperature gradient, and the material derivatives of the conjugate strain tensor up to a desired order. The thermoelastic solids described by these theories are called ordered thermoelastic solids due to the fact that the deviatoric stress tensor and heat vector are dependent on the material derivative of the conjugate strain tensor up to a desired order. The highest order of the material derivative of the strain tensor defines the order of the thermoelastic solid or the order of the rate constitutive theory. For thermodynamic equilibrium during the evolution, the constitutive theories must be derived using (or must satisfy) the second law of thermodynamics as conservation of mass, balance of momenta, and energy balance are independent of the constitution of the matter. In this study, we consider the entropy inequality resulting from the second law of thermodynamics in Helmholtz free energy density Φ and conjugate pairs: second Piola-Kirchhoff stress tensor σ and Green's strain tensor ɛ. It is shown that when Φ is a function of the material derivatives of ɛ, the entropy inequality necessitates decomposition of σ into equilibrium and deviatoric parts: $${_e{\mathbf{\sigma}}^{[0]}}$$ and $${_d{\mathbf{\sigma}}^{[0]}}$$. The equilibrium stress tensor is deterministic using the conditions resulting from the entropy inequality, but $${_d{\mathbf{\sigma}}^{[0]}}$$ is not. The entropy inequality only requires that work expended due to $${_d{\mathbf{\sigma}}^{[0]}}$$ be positive, but provides no mechanism for deriving a constitutive theory for it. In the present work, we use the theory of generators and invariants for deriving a constitutive theory for $${_d{\mathbf{\sigma}}^{[0]}}$$. The constitutive theories for the heat vector q are derived using (i) conditions resulting from the entropy inequality. In the simplest case, this yields Fourier heat conduction law, and (ii) the theory of generators and invariants with at least two alternate choices of the argument tensors for q. Merits and shortcomings of the resulting theories are discussed. It is shown that the rate theories presented here describe thermoviscoelastic solids without memory. Simplified cases of the general theory are considered to demonstrate that many of the currently used models for such solids (like Kelvin-Voigt model) resemble the theory presented here, but are quite different, and the theories provide a rationale for modeling the mechanism of dissipation in thermoelastic solids that is consistent with principles of continuum mechanics and thermodynamics. One-dimensional numerical studies using the proposed rate theories and comparisons with current theories are also presented. [ABSTRACT FROM AUTHOR]

The theory for the deformations of a spheroidal particle is of great scientific interest in numerous physical and biological problems ranging from fracture analysis of plain solids to the compression of biological cells in an atomic force microscope or during micropipette aspiration. Using a formulation in terms of Papkovich-Neuber potentials, we derive the deformations of a prolate, elastic spheroid under known axisymmetric loading. The internal stresses to which the object is subjected are deduced from Hooke's law of elasticity in prolate spheroidal coordinates. The generalisation to layered spheroids with viscoelastic properties is also discussed. Since for isotropic objects the surface displacements and stresses are directly related by the elastic modulus and Poisson's ratio alone, the presented, closed-form, analytical solutions may be applied to deduce these important elastic constants from standard stress-deformation experiments. We illustrate the versatility of the findings by analysing the surface displacements and stress states of spheroids with small and large aspect ratios in the presence of both normal and shear surface tractions. Of particular interest in this study is the influence of Poisson's ratio on the deformation of a near-spherical particle, for instance a soft cancer cell, which is subjected to surface stresses of the kind that can be found in optical traps, like the optical stretcher. [ABSTRACT FROM AUTHOR]

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material's properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions. [ABSTRACT FROM AUTHOR]

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical panels using piezoelectric-fiber- reinforced composite (PFRC) materials. The constraining layer of the ACLD treatment is considered to be made of the PFRC materials. The Golla-Hughes-McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type-nonlinear strain-displacement relations and a simple first-order shear deformation theory are used for deriving this electromechanical coupled problem. A three-dimensional finite element ( FE) model of smart composite panels integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin symmetric and antisymmetric laminated cylindrical panels in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of both symmetric and antisymmetric panels for suppressing the geometrically nonlinear transient vibrations of the panels. The effect of the shallowness angle of the panels on the control authority of the patches has also been investigated. [ABSTRACT FROM AUTHOR]