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A unified approach to the analysis of the nonstationary vibrations of piezoelectric ceramic plane layers, cylinders, and spheres taking into account the functional inhomogeneity and viscoelasticity of the material is proposed. The standard model of vibration damping and the Kelvin–Voigt viscoelastic model are considered. The proposed approach makes it possible to study the transition of the transducer to a static state or to a steady-state vibration mode under nonstationary perturbations. The effect of functional inhomogeneity on the nonstationary vibrations of a piezoelectric element is analyzed. The damping of the vibrations and viscoelastic axisymmetric vibrations of a radially polarized cylinder under electrical and mechanical perturbation using the Heaviside function is calculated. The dynamics of damping is analyzed, and the obtained results are compared with the static solution to validate the results. The generation of voltage by a piezoceramic cylinder under mechanical axisymmetric loading is also studied taking into account the viscoelastic properties of the material. It was found that the time to reach the steady-state mode for mechanical and electrical loads is almost the same. [ABSTRACT FROM AUTHOR]

The problem of analysis of creep strains in thin-walled tubular elements made of linearly viscoelastic materials under uniaxial tension, pure torsion, and combined tension with torsion is solved and experimentally validated. The analysis is based on the use of viscoelasticity models in the form of proportionality of deviators. The creep kernels are represented by fractional-exponential functions. The longitudinal, transversal, shear, and volume creep strains are calculated. [ABSTRACT FROM AUTHOR]

The influence of ionizing radiation on the mechanical behavior of rubber-like materials is studied using the theory of viscoelasticity with Volterra's integral operators. Experimental results on the effect of ionizing radiation on the dynamic shear modulus, dissipation coefficient, life, and fracture mechanism of rubber elements under the combined action of radiation and cyclic loading are presented. [ABSTRACT FROM AUTHOR]

A technique of solving problems of linear viscoelasticity is presented. Some basics are given on the application of continued fractions to solve some problems for viscoelastic anisotropic bodies with slowly growing cracks. It is shown, using examples, that the operator continued fraction technique can be effectively used for solving complex problems of fracture mechanics for modern anisotropic composite materials. [ABSTRACT FROM AUTHOR]

The dynamical stress field in a sandwich plate-strip is mathematically modeled using the piecewise-homogeneous body model and the three-dimensional linearized theory of electro-elastic waves in initially stressed bodies. The plate consists of a piezoelectric core perfectly bonded to elastic layers with initial stress, rests on a rigid foundation, and is subject to harmonic force. It is assumed that the piezoelectric material is poled perpendicularly to the free surface of the body. The governing system of partial differential equations of motion is solved by the finite-element method. The numerical results are presented, illustrating the effect of certain relationships of the problem of the propagation of stresses and electric displacements at the interfaces between the elastic layers and the piezoelectric core and between the plate-strip and the rigid foundation. The effect of the initial stress parameter and a change in the thickness of the piezoelectric core on the frequency response of the plate-strip is studied. [ABSTRACT FROM AUTHOR]

The opening of a mode I crack in a polymeric composite with viscoelastic properties subject to tensile loads is solved within the framework of nonlinear fracture mechanics. The modeling of the viscoelastic properties of the composite and crack is analyzed. Techniques for studying the deformation of a cracked composite and determining safe loads under which the crack is at rest are proposed. The efficiency of the techniques is evaluated by comparing the computed results with experimental data for polymeric composites used in modern aircraft. [ABSTRACT FROM AUTHOR]

The Laplace-Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state. The hereditary creep kernel characterizing the behavior of the viscoelastic Poisson’s ratio with time is identified. The calculation of shear creep strains and transverse creep under uniaxial loading with allowance for the time-dependent Poisson’s ratio are experimentally validated. [ABSTRACT FROM AUTHOR]

The forced resonant vibrations and vibrational heating of viscoelastic plates with actuators are modeled considering geometrical nonlinearity and transverse shear. An approximate analytical solution of the problem is obtained for a hinged rectangular plate by the Bubnov-Galerkin method. The effect of geometrical nonlinearity and shear deformations on the efficiency of active damping of vibrations with piezoelectric actuators is analyzed. [ABSTRACT FROM AUTHOR]

The long-term fracture of a plate made of an isotropic linear viscoelastic nanocomposite with a mode I crack is studied. A technique for experimental determination of the viscoelastic characteristics of a nanocomposite is employed. The efficiency of the approach proposed is validated considering data obtained in experiments with real composites. It is shown that the shape of kinetic curves and plate durability significantly depend on the fracture parameters and the concentration of nanoinclusions. [ABSTRACT FROM AUTHOR]

An algorithm for solving the problem of slow growth of a mode I crack with a zone of partial contact of the faces is proposed. The algorithm is based on a crack model with a cohesive zone, an iterative method of finding a solution for the elastic opening displacement, and elasto-viscoelastic analogy, which makes it possible to describe the time-dependent opening displacement in Boltzmann-Volterra form. A deformation criterion with a constant critical opening displacement and cohesive strength during quasistatic crack growth is used. The algorithm was numerically illustrated for tensile loading at infinity and two concentrated forces symmetric about the crack line that cause the crack faces to contact. When the crack propagates, the contact zone disappears and its dynamic growth begins. [ABSTRACT FROM AUTHOR]

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed. [ABSTRACT FROM AUTHOR]

The transverse bending vibrations of an axially accelerating viscoelastic beam are studied. The material of the beam is constituted by the standard viscoelastic model. The method of multiple scales is applied to determine the steady-state response of the beam. The numerical examples illustrate the asymptotic solution. [ABSTRACT FROM AUTHOR]

Relations between the shear and bulk creep kernels of an isotropic linear viscoelastic material in combined stress state and the longitudinal and shear creep kernels constructed from data of creep tests under uniaxial tension and pure torsion are formulated. The constitutive equations of viscoelasticity for the combined stress state are chosen in the form of a superposition of the equation for shear strains and the equation for bulk strains. The hereditary kernels are described by Rabotnov's fractional-exponential functions. The creep strains of thin-walled pipes under a combination of tension and torsion or tension and internal pressure are calculated [ABSTRACT FROM AUTHOR]

The concept of complex characteristics is used to formulate the coupled nonlinear boundary-value thermoelectroviscoelastic problem of the forced harmonic vibrations and self-heating of inelastic three-dimensional bodies of revolution taking into account the nonlinearity due to the dependence of the mechanical and electrical characteristics on temperature. An iteration method is used to reduce this nonlinear problem to a linear electroviscoelastic problem and a linear heat-conduction problem with a known heat source, which are solved using the finite-element method. This approach is used to solve a coupled nonlinear thermoelectroviscoelastic problem of the forced harmonic vibrations and self-heating of a hinged sandwich cylindrical panel. The numerical data obtained are analyzed, and the effect of nonlinearity on the amplitude-frequency and temperature-frequency responses is studied [ABSTRACT FROM AUTHOR]

A method for solving the problem of electromagnetoviscoelasticity for multiply connected plates is proposed. The small-parameter method is used to reduce this problem to a recursive sequence of problems of electromagnetoelasticity, which are solved by using complex potentials. A procedure is developed to determine, using complex potentials, approximations of the basic characteristics (stresses, electromagnetic-field strength, electromagnetic-flux density) of the electromagnetoelastic state at any time after application of a load. A plate with an elliptic hole is considered as an example. The variation in the electromagnetoelastic state of the multiply connected plate with time is studied [ABSTRACT FROM AUTHOR]

The propagation coefficient associated with the wave dispersion and attenuation in viscoelastic bars is calculated experimentally. The phase velocity and the attenuation coefficient in relation to the frequency are obtained from a series of impact tests on a PMMA Hopkinson pressure bar using ball bearing projectiles of different diameters. A wave dispersion correction technique is applied using the fast Fourier transforms of the longitudinal strains associated with the incident and reflected waves [ABSTRACT FROM AUTHOR]

Theoretical and experimental studies on the deformation and delayed fracture of viscoelastic bodies due to slow subcritical crack growth are reviewed. The focus of this review is on studies of subcritical growth of cracks with well-developed fracture process zones, the conditions that lead to their critical development, and all stages of slow crack growth from initiation to the onset of catastrophic growth. Models, criteria, and methods used to study the delayed fracture of viscoelastic bodies with through and internal cracks are analyzed. Experimental studies of the fracture process zones in polymers using physical and mechanical methods as well as theoretical studies of these zones using fracture mesomechanics models that take into account the structural and rheological features of polymers are reviewed. Particular attention is given to crack growth in anisotropic media, the effect of the aging of viscoelastic materials on their delayed fracture, safe external loads that do not cause cracks to propagate, the mechanism of multiple-flaw fracture of viscoelastic bodies with several cracks and, especially, processes causing cracks to coalesce into a main crack, which may result in a break of the body. Methods and results of solving two- and three-dimensional problems of the mechanics of delayed fracture of aging and non-aging viscoelastic bodies with cracks under constant and variable external loads, wedging, and biaxial loads are given [ABSTRACT FROM AUTHOR]

The dynamic stability of viscoelastic plates of variable stiffness is analyzed. The deflections are described by partial integro-differential equations of motion. The Bubnov-Galerkin method based on monomial and polynomial approximation of deflections is used to reduce the problem to ordinary integro-differential equations with time as an independent variable. These equations are solved numerically using a singular kernel. A numerical problem-solving algorithm based on this method is described. A number of new mechanical effects are revealed [ABSTRACT FROM AUTHOR]

A numerical method for solving problems of the linear viascoelasticity of an anisotropic body is proposed. The method does not require deriving explicit analytical expressions for the creep and relaxation kernels. The approximate solution of the integral equations is based on using experimental data preliminarily smoothed with filling in data gaps. The results of numerical analysis of the viscoelastic stress state of an orthotropic plate with an elliptic hole are presented [ABSTRACT FROM AUTHOR]

The stress-strain state of an unbounded linear viscoelastic isotropic body weakened by collinear cracks of equal length and subjected to a time-independent load normal to the cracks is studied. The expression for the crack opening displacement in the nonlinear range that is derived based on the Leonov-Panasyuk-Dugdale model is used to deduce the equations of subcritical crack growth. A numerical algorithm for solving them is presented. The solutions of the equations describing subcritical crack growth are analyzed in determining the duration of the initial crack growth period. The numerical results are presented as graphs and tables [ABSTRACT FROM AUTHOR]

The coupled problem of the forced axially symmetric vibrations and self-heating of clamped and hinged flexible circular plates with viscoelastic piezoelectric layers as sensors and actuators is solved. The mechanical and electric excitation of vibrations and the damping of mechanical vibrations by applying the appropriate potential difference to the electrodes of the actuators are studied. The effect of geometrical nonlinearity on the frequency-dependence of the deflection, self-heating temperature, and sensor voltage of a plate under harmonic electromechanical loading at principal bending resonance is analyzed [ABSTRACT FROM AUTHOR]

A method to solve a thermoviscoelastic problem for multiply connected anisotropic plates is proposed. The perturbation method is used to reduce the problem to a recurrent sequence of thermoelastic problems that are solved using generalized complex potentials. By expanding the unknown functions into Faber-Laurent series and satisfying the boundary conditions using the generalized least-squares method, the problem for a plate with elliptic rigid inclusions is reduced to a system of algebraic equations. The thermostressed state of a plate with one or two inclusions is numerically analyzed depending on time and geometry [ABSTRACT FROM AUTHOR]

It is proved that fractional exponential hereditary kernels of nonlinear viscoelasticity can be used to evaluate creep strains and stress relaxation. A nonlinear theory of viscoelasticity with time-independent nonlinearity described as a nonlinear curve of instantaneous elastoplastic deformation is used. The calculated results are validated against experimental data on the viscoelastic deformation of laminated and unidirectional fibrous composites and their components under the conditions of constant stresses, complete unloading, incremental loading, pure torsion, and constant strains [ABSTRACT FROM AUTHOR]

The analytical and experimental procedures of the method for determining the parameters of the hereditary kernels in the modified Rabotnov's nonlinear viscoelastic model are outlined. The method is based on the similarity of the isochronous creep curves to the instantaneous-deformation curve. The parameters of the kernels are determined by fitting the discrete values of the kernels that are found by differentiating the average similarity function. The discrete values of the kernels in the domain of singularity are calculated using weight functions [ABSTRACT FROM AUTHOR]

The coupled problem of the forced axisymmetric vibrations and self-heating of electrothermoviscoelastic cylindrical shells with piezoceramic actuators under monoharmonic electromechanical loading is solved. The temperature dependence of the complex characteristics of the passive and piezoactive materials is taken into account. The coupled nonlinear problem of electrothermoelasticity is solved by using a time-marching method with discrete orthogonalization at each time step (to integrate the equations of elasticity) and an explicit finite-difference method (to solve the heat-conduction equations). An analysis is made of the effect of the boundary conditions at the shell ends, the dimensions of the piezoactuator, and the self-heating temperature on the actuator voltage and the effectiveness of active damping of the forced vibrations of the shell under uniform transverse monoharmonic pressure [ABSTRACT FROM AUTHOR]

The coupled problem of forced vibrations and self-heating of thermoviscoelectroelastic shells of revolution with piezoceramic sensor and actuator under monoharmonic loading is solved. The temperature dependence of the complex characteristics of the passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoelectroelasticity is solved by time-marching integration, using discrete orhogonalization to integrate the equations of elasticity and explicit finite differencing to solve the heat conduction equation. The effect of the dimensions of the sensor and actuator and self-heating on the sensor voltage and on the active damping of forced vibrations of a circular plate under uniform monoharmonic transverse pressure is studied [ABSTRACT FROM AUTHOR]

The paper presents a method to calculate the difference of principal stresses and strains in linear viscoelastic optically sensitive polymeric materials from a time-dependent fringe pattern. The governing equations are derived using the direct and inverse Laplace transforms [ABSTRACT FROM AUTHOR]

The time variation in the stresses around an elliptic hole in a composite plate is studied. Solutions that characterize the effect of the time dependence of the relaxation moduli of the composite components on stresses are obtained. The solutions in the time domain are obtained from the elastic-viscoelastic analogy and the corresponding elastic solutions for the effective moduli of the composite and the stress field around an elliptic hole in an anisotropic plate. The inverse Laplace transformation is carried out by an effective numerical method [ABSTRACT FROM AUTHOR]

n approach to the active damping of the forced resonant vibrations of orthotropic thermoviscoelastic plates with distributed sensors and actuators is proposed. The mechanical load is assumed unknown and is determined from the sensors' indications. The problem of active damping of an isotropic thermoviscoelastic rectangular plate with hinged edges is solved as an example. A formula for the voltage to be applied to the actuator to damp the forced vibrations in the first mode is derived. The effect of the dimensions of the sensor and actuator and the dissipative properties of the materials on the effectiveness of active damping is studied [ABSTRACT FROM AUTHOR]

The paper proposes an approach to solving boundary-value problems for linear viscoelastic orthotropic bodies based on the method of operator continued fractions and the boundary-element method. A problem-solving algorithm and a procedure to estimate the possible error are outlined. The solution for a viscoelastic orthotropic plate with a rigid circular inclusion under uniaxial tension is obtained as an example and compared with available ones [ABSTRACT FROM AUTHOR]

The flutter of a viscoelastic plate in a supersonic gas flow is studied. A technique and algorithm for numerical solution of nonlinear integro-differential equations with weakly singular kernels are elaborated. The critical flutter speed of viscoelastic plates is determined [ABSTRACT FROM AUTHOR]

The paper discusses the active damping of the resonant flexural vibrations of a clamped thermoviscoelastic rectangular plate with distributed piezoelectric sensors and actuators. The thermoviscoelastic behavior of the passive and active materials is described using the concept of complex characteristics. The interaction of the mechanical and thermal fields is taken into account. The Bubnov-Galerkin method is used. The effect of self-heating, the dimensions of the piezoelectric inclusions, and the feedback factor on the effectiveness of active damping of the resonance vibrations of the plate is studied [ABSTRACT FROM AUTHOR]

The relaxation moduli of a composite are determined. The relaxation of its components is described by various few-parameter kernels: Mittag-Leffler functions of different orders and Rzhanitsyn kernel. It is assumed that the composite components are made of model materials with volume relaxation. The Laplace transform and fractional rational approximation are used to develop an algorithm for reducing the relaxation functions of the composite to one class (series of decreasing exponents or exponents of fractional order). The relaxation moduli of a unidirectionally reinforced composite are determined as an example. [ABSTRACT FROM AUTHOR]

The basic equations for thin-walled thermoviscoelastic plates with distributed piezoelectric actuators under monoharmonic mechanical and electric loads are derived. The thermomechanical behavior of materials is described using the concept of complex characteristics. Variational methods of solving nonlinear problems of active damping of the bending vibrations of plates are considered. The effect of dissipative heating on the damping of the axisymmetric bending vibrations of a circular plate is examined as an example [ABSTRACT FROM AUTHOR]

The paper studies the stress rupture behavior of a reinforced viscoelastic composite through which a penny-shaped mode I crack propagates under a constant load. The composite has hexagonal symmetry and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled as a transversely isotropic homogeneous viscoelastic medium with effective characteristics. The crack is in the isotropy plane. The ring-shaped fracture process zone at the crack front is modeled by a modified Dugdale zone with time-dependent stresses. The viscoelastic properties of the matrix are characterized using a resolvent integral operator. Use is made of Volterra's principle, the method of operator continued fractions, and the theory of precritical crack growth in viscoelastic bodies. The problem is reduced to nonlinear integral equations. Numerical results are obtained for certain components of the composite, constant volume fractions, and different fracture strengths [ABSTRACT FROM AUTHOR]

The paper addresses the geometrically nonlinear problem of dynamic stability of a viscoelastic plate with concentrated masses. The Bubnov-Galerkin method based on polynomial approximation is used to reduce the problem to a system of nonlinear Volterra-type integro-differential equations with singular relaxation kernels. This system is solved by numerical method based on quadrature formulas. The critical loads are found and their dependence on the arrangement and number of concentrated masses is studied for a wide range of mechanical and geometrical parameters of the plate. The choice of a relaxation kernel for dynamic problems for viscoelastic thin-walled plate-like structures is justified. Results produced by different theories are compared [ABSTRACT FROM AUTHOR]

The paper deals with the coupled problem of flexural vibrations and dissipative heating of a viscoelastic ring plate with piezoceramic actuators under monoharmonic electromechanical loading. The temperature dependence of the complex characteristics of passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoviscoelasticity is solved by an iterative method. At each iteration, orthogonal discretization is used to integrate the equations of elasticity and an explicit finite-difference scheme is used to solve the heat-conduction equation with a nonlinear heat source. The effect of the dissipative heating temperature, boundary conditions, and the thickness and area of the actuator on the active damping of the forced vibrations of the plate under uniform transverse harmonic pressure is examined [ABSTRACT FROM AUTHOR]

Thermodynamic and statistical methods for setting up the constitutive equations describing the viscoelastoplastic deformation and hardening of materials are proposed. The thermodynamic method is based on the law of conservation of energy, the equations of entropy balance and entropy production in the presence of self-balanced internal microstresses characterized by conjugate hardening parameters. The general constitutive equations include the relationships between the thermodynamic flows and forces, which follow from nonnegative entropy production and satisfy the generalized Onsager’s principle, and the thermoelastic relations and the expression for entropy, which follow from the law of conservation of energy. Specific constitutive equations are derived by representing the dissipation rate as a sum of two terms responsible for kinematic and isotropic hardening and approximated by power and hyperbolic-sinus functions. The constitutive equations describing viscoelastoplastic deformation and hardening are derived based on stochastic microstructural concepts and on the linear thermoelasticity model and nonlinear Maxwell model for the spherical and deviatoric components of microstresses and microstrains, respectively. The problem of determining the effective properties and stress-strain state of a three-component material found using the Voigt-Reuss scheme leads to constitutive equations similar in form to those produced by the thermodynamic method [ABSTRACT FROM AUTHOR]

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress [ABSTRACT FROM AUTHOR]

The paper gives explicit expressions of the elastic T-stress components T I, T II, and T III for an elliptic crack in an unbounded body under uniform pressure and bending and expressions of all the T-stress components for parabolic and tunnel cracks under uniform loading. These formulas are derived by analyzing the asymptotic behavior of the stress components near the crack front using special harmonic functions. The dependence of the T-stresses on Poisson’s ratio, semiaxes and parametric angle of the elliptic crack is studied. The expressions of T I, T II, and T III for a penny-shaped crack under arbitrary uniform pressure and bending follow as a special case from the respective expressions for an elliptic crack [ABSTRACT FROM AUTHOR]

The vibrations and self-heating of a layered metal-polymer rectangular prism kinematically excited by a normally vibrating punch are analyzed numerically. The effect of reinforcement layers on the rate of variation in and the spatial distribution of the temperature field is examined. It is established that thin metallic layers in a polymer matrix change the dissipation mechanism from shear to bulk. The effect of contact stress concentration on the localization of temperature field is studied. It is established that the energy flux through the load application area decreases due to softening of the material. Several reinforcement effects are revealed. It is shown that they are determined by the value of the load parameter. The numerical results are in good agreement with experimental data on self-heating kinetics [ABSTRACT FROM AUTHOR]

The state-of-the-art in the investigation of nonlinear oscillations and evolution of deformable flexible systems in fluid is analyzed. Statements of problems and methods of solving them as well as results on the dynamics of flexible systems interacting with the ambient medium are briefly outlined. Important quantitative and qualitative results are presented, and conclusions of applied and fundamental importance are drawn [ABSTRACT FROM AUTHOR]

The subcritical growth of a mode I crack with nonsmall end zones in an aging viscoelastic plate under tensile loads applied at infinity is studied assuming that the fracture process zone is of constant length. The equations of incubation, transition, and major crack growth stages are obtained on the basis of the Volterra principle and critical crack opening criterion. The crack subcritical growth of a specific material is studied as an example [ABSTRACT FROM AUTHOR]

The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined [ABSTRACT FROM AUTHOR]

A method is proposed for studying the stress state of a viscoelastic multiply connected isotropic plate with aligned elastic inclusions. The viscoelastic state of a plate with a finite or infinite number of circular and linear inclusions is analyzed [ABSTRACT FROM AUTHOR]

The paper studies the subcritical stable growth of a penny-shaped mode I crack in an aging linear viscoelastic body with cylindrical anisotropy under tensile loads applied at infinity. The equations of quasistatic crack growth are derived using the Volterra principle for a modified Dugdale model and the critical crack opening displacement as a failure criterion. The kernel of the operator that describes the viscoelastic crack opening is found using operator-valued continued fractions. As an example, the subcritical stable growth of a crack in a specific material is studied numerically [ABSTRACT FROM AUTHOR]

A finite-element algorithm is proposed for the analysis of the thermoviscoelastoplastic stress-strain state of bodies under complex loading (thermal and mechanical). It is assumed that an arbitrary element of the body deforms along a rectilinear or slightly curved path. The three-dimensional stress-strain state of the body’s elements is determined using the iterative method of additional strains. The technique is tested by analyzing the three-dimensional viscoelastic stress-strain state of a hollow cylinder and the thermoplastic state of a disk [ABSTRACT FROM AUTHOR]

Nonlinear vibrations of viscoelastic orthotropic and isotropic shells are mathematically modeled using a geometrically nonlinear Timoshenko theory. Nonlinear problems are solved by using the Bubnov-Galerkin method and a numerical method based on quadrature formulas. Results obtained from different theories are compared and analyzed. For each problem, the Bubnov-Galerkin method is tested for convergence. The influence of the viscoelasticity and inhomogeneity of materials on the vibrations of plates is demonstrated [ABSTRACT FROM AUTHOR]

A dissipative-heating problem for an incompressible viscoelastic cylinder rolling over a rigid foundation is solved. The effect of tangential stresses on the dissipative-heating temperature is examined [ABSTRACT FROM AUTHOR]