Search

This paper elaborates on the wave propagation characteristics of a smart sandwich plate consisting of smart piezo composite layers on a plate's upper and lower borders via an auxetic core. This study's equation of motion was derived using a refined version of the Shear-deformation theory at a higher order, or HSDT. Additionally, detecting the properties of the auxetic core and piezoelectric composite layers employs a micromechanical model. The fundamental equations of the smart sandwich plates were formulated utilizing the Hamiltonian principle and Maxwell's law. Then, the governing equations of a sandwich plate are solved using an exponential form and an analytical method. Furthermore, the phase velocity of the intelligent sandwich plate is provided based on the layer thicknesses of the auxetic core and thicknesses of intelligent piezoelectric composite layers. In addition, each figure calculates and presents the weight of the Winkler–Pasternak coefficient, the viscoelastic substances factor, the source of the outside electricity, and the volume percent of reinforcement in the matrix on the phase velocity. [ABSTRACT FROM AUTHOR]

It is clear that there is a relationship between time and space in nanostructures that are always attacked by waves with wavelengths within the intrinsic characteristic length of the nanostructure. Also, the viscoelastic behavior of nanostructures is affected by this relationship between nonlocal time and nonlocal space. It is worth noting that the conventional tempo-spatially decoupled nonlocal viscoelasticity does not give accurate results regarding the viscoelastic response of these structures. Hence, herein and for the first time, a novel fractional nonlocal time–space strain gradient viscoelasticity is implemented to be able to give a correct answer in addressing the dispersion of elastic waves inside functionally graded material (FGM) viscoelastic nanoplates. The constructive equations of this theory are based on the theory of nonlocal strain gradient elasticity. The properties of the FGM studied in this research are obtained by the power-law model, and the kinematic relations are extracted based on the refined higher-order plate theory. Subsequently, motion equations are written using Hamilton's principle and solved analytically. The results of this work reveal that an increase in the nonlocal parameter can reduce the loss factor in a remarkable way due to the coupling between the nonlocalities in the spatial and temporal domains. [ABSTRACT FROM AUTHOR]

There is a correlation between nonlocal time and space in the nanostructures which are attacked by waves whose length lies in the range of the nanostructure's intrinsic characteristic lengths. This temporal–spatial coupling affects the viscoelastic behaviors of the nanostructures. In such a case, the conventional tempo-spatially decoupled nonlocal viscoelasticity is not able to provide accurate dynamic responses. To resolve this problem, the present paper focuses on the development of a novel fractional nonlocal time–space strain gradient viscoelasticity and shows its application in the wave propagation analysis of functionally graded material (FGM) nanobeams. The fractional constitutive equations are derived on the basis of the combination of the well-known nonlocal strain gradient elasticity and fractional nonlocal time–space hypotheses. The motion equations of the beam-type elements are presented on the basis of the refined higher-order beam theory and Hamilton's principle. With this newly developed nonlocal theory, the governing equations of the nanobeam are extracted. Afterward, an analytical wave solution will be utilized to achieve the loss factor of the problem. The results of this work reveal that an increase in the nonlocal parameter can reduce the loss factor in a remarkable way due to the coupling between the nonlocalities in the spatial and temporal domains. [ABSTRACT FROM AUTHOR]

This research is concerned with the analysis of wave propagation of multi-scale hybrid composite beams subjected to various types of thermal loading. Carbon fiber (CF) and carbon nanotube (CNT) are assumed as reinforcements that are distributed in the matrix. The homogenization process is performed exerting the Halpin–Tsai model and the rule of mixture. Different types of temperature rise, namely, uniform, linear and sinusoidal temperature rise are presumed to present a more trustworthy thermal analysis. The beam is rested on Winkler–Pasternak foundation. A refined trigonometric shear deformable beam theory is used to compute the kinetic relations without any external shear correction coefficient. Governing equations are derived implementing Hamilton's principle and then solved analytically. Eventually, the effects of different parameters, such as CNT's weight fraction, the volume fraction of CF, elastic foundation, different types of temperature rise, etc., on wave frequency and phase velocity. are provided numerically in the framework of a set of illustrations. [ABSTRACT FROM AUTHOR]

The high mechanical properties of auxetic materials with negative Poisson's ratio make them suitable for a variety of applications. This article investigated how the auxetic layer affects wave propagation and its effective characteristics in cylindrical sandwich shells. An analytical solution is established to describe wave propagation through wave frequency and wave velocity according to first-order shear deformable shell theory. Moreover, the Hamilton principle was applied. Then, the governing equation was solved by utilizing an analytical method. Different parameters such as auxetic cell angle inclined and dimensions on wave behavior were investigated. The final step is to conduct a numerical investigation. The results are reported in the form of several figures and analyze how each parameter influences wave propagation. [ABSTRACT FROM AUTHOR]

In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSDT) is implemented to take into account the influence of the shear deformation on the motion equations of the system. Then, the governing equations are achieved on the basis of the energy-based Hamilton's principle. Finally, the derived equations will be solved analytically for the purpose of extracting the natural frequency of the continuous system. A set of numerical examples are provided to cover the effects of various parameters on the wave dispersion characteristics of the plate. It can be declared that the hybrid nanocomposite system can achieve higher wave frequencies compared with other types of composite structures. Additionally, it is found that the selection of the lay-ups and length-to-diameter ratio plays a significant role in the determination of the sandwich plate's acoustic response. [ABSTRACT FROM AUTHOR]

In this article, wave propagation of the sandwich composite beam with tunable electro-rheological (ER) fluid core is investigated. The sandwich composite beam is made of three layers consisting of the basic layer, ER fluid core, and the limiter layer. ER fluid core embedded withindoors the basic and limiter layers. The upper and lower layers are constructed of the elastic materials. Hamilton's principle is utilized for deriving the governing equations of motion. Using an analytical solution, the wave frequency and the phase velocity can be gathered by solving eigenvalue problem. Moreover, the effect of different parameters such as electric field, core-to-top layer thickness ratio, and thickness of ER core is investigated on the wave dispersion characteristics. [ABSTRACT FROM AUTHOR]

This paper investigates the wave propagation behavior of a high-speed rotating laminated nanocomposite cylindrical shell. The small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the cylindrical laminated composite nanoshell in a thermal environment were obtained using Hamilton's principle and solved by the analytical method. For the first time in this study, the wave propagation behavior of a high-speed rotating nanocomposite cylindrical shell is studied based on classic, strain gradient, nonlocal and nonlocal strain gradient theories (4 continuum theories) with considering the calibrated values of the nonlocal constant and material length scale parameter. The results show that wave number, angular velocity, and different types of laminated composites have an important role in the phase velocity of the nanocomposite structure using mentioned continuum mechanics theories. Another significant result is that in the higher values of angular velocity, three layers of laminated composite has the highest phase velocity in comparison with the other layers. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques. [ABSTRACT FROM AUTHOR]

This investigation deals with wave propagation analysis of porous metal foam resting on the Kerr substrate in the thermal environment within the framework of the refined higher-order plate theory. Different types of temperature rise are studied namely; uniform, linear and sinusoidal temperature rise. The pores are distributed through the thickness symmetrically and asymmetrically. The principle of Hamilton is employed in order to reach motion equations of porous metal foam plates. Next, governing equations of porous metal foam are derived for a refined inverse cotangential shear deformation plate and then solved analytically. The effects of various parameters including porosity coefficient, various types of porosity distribution, different types of temperature rise, length to thickness ratio, shape function, wave number and linear and shear layers of Kerr substrate on the variation of wave frequency and phase velocity of metal foam plate are covered and presented within the framework of a group of figures which can be observed in detail. [ABSTRACT FROM AUTHOR]

In this article, wave propagation behavior of a size-dependent spinning graphene nanoplatelet-reinforced composite (GNPRC) cylindrical nanoshell with porosity is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT), this accurate theory employs exact length scale parameter and nonlocal constant. The governing equations of GNPRC cylindrical nanoshell coupled with piezoelectric actuator (PIAC) are evolved by minimum potential energy principle and solved by the analytical method. For the first time in the current study, wave propagation-porosity behavior of a GNPRC cylindrical nanoshell coupled with PIAC is examined based on NSGT. The results show that, as the angular velocity increases, the difference between the minimum and maximum values of the phase velocity decreases. Another important result of this paper is that, by increasing the radius, extremum values of phase velocity occur in the lower values of the wave number. Finally, the influences of porosity, angular velocity, wave number and different graphene platelet distribution patterns on the phase velocity are investigated using the mentioned continuum mechanics theory. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques. [ABSTRACT FROM AUTHOR]

This study presents an investigation of the wave propagation of a rectangular sandwich composite plate with tunable magneto-rheological fluid core. The constituent parts of this rectangular sandwich composite plate are the base layer, magneto-rheological fluid core, and limiter layer. Magneto-rheological fluid core is embedded within the base and limiter layers. Also, the upper and lower layers are made of elastic materials. For obtaining the governing equations of motion, Hamilton's principle and classical plate theory are used. After that, applying an analytical solution, the wave frequency and phase velocity of the propagated waves can be gained by solving eigenvalue problem. By investigating the effect of the magnetic field, the results emphasize that the magnetic field intensity is the most important factor for changing the value of the wave frequency and phase velocity. Besides, results show by enhancing the core-to-top layer thickness ratio, the wave frequencies reduce because magneto-rheological fluid core is softer in comparison to elastic layers. Therefore, magneto-rheological fluid layer operates similar to a damper. At the end, the influence of the thickness of magneto-rheological fluid core on the phase velocity is also discussed. [ABSTRACT FROM AUTHOR]

Herein, the thermo-magneto-elastic wave dispersion answers of rotary functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler–Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters. [ABSTRACT FROM AUTHOR]

This research presents the agglomeration effect of reinforcements on wave propagation analysis of multi-scale hybrid nanocomposite shell based on first-order shear deformable theory (FSDT) of shell for the first time. The nanocomposite shell is consist of carbon fiber (CF) as macro reinforcement, carbon nanotubes (CNTs) as nanoreinforcement and epoxy as an initial matrix. Eshelby-Mori-Tanaka method and rule of mixture are implemented in order to predict the equivalent mechanical properties of nanocomposite shell. To derive the motion equation of shell, FSDT is applied and governing equations are attained by employing Hamilton's principle. Dispersion solution is calculated by solving eigenvalue problem and also analytical method is utilized to solve the governing equations and finally wave frequency and phase velocity of nanocomposite shell can be achieved. In detail, several illustrations are presented which influence various parameters such as longitudinal and circumferential wave number, the volume fraction of CF, volume fraction of CNTs inside the cluster and so on are investigated. Communicated by Chandrika Prakash Vyasarayani. [ABSTRACT FROM AUTHOR]

This article investigates wave propagation behavior of a multi-phase nanocrystalline nanobeam subjected to a longitudinal magnetic field in the framework of nonlocal couple stress and surface elasticity theories. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, couple stress and surface effects are omitted. Hamilton's principle is employed to derive the governing equations which are solved by applying an analytical method. The frequencies are compared with those of nonlocal and couple stress-based beams. It is showed that wave frequencies and phase velocities of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, magnetic field, surface effect and nonlocality. [ABSTRACT FROM AUTHOR]

This paper contains a nonlocal strain gradient-based theory to survey viscoelastic wave dispersion characteristics of axially loaded double-layered graphene sheets (DLGSs) resting on the viscoelastic substrate. Actually, a comprehensive size-dependent analysis is performed in which both amplifying and minimizing effects are covered. Also, the kinematic relations have been derived by the means of a one-variable classical plate theory. Besides, the final nonlocal governing equations can be developed using the Hamilton's principle. These equations will be finally solved utilizing an analytical solution to obtain wave frequency, phase velocity and escape frequency of DLGSs. Last section is allocated to study the effects of various terms including wave number, nonlocal parameter, length scale parameter, structural damping coefficient, Winkler coefficient, Pasternak coefficient, damping coefficient and axial load on the wave propagation behaviors of DLGSs. [ABSTRACT FROM AUTHOR]

Herein, the agglomeration effect of nanoparticles on the wave dispersion of multi-scale hybrid nanocomposite beams is investigated. The constituent material consists of both macro- and nano-reinforcements which are dispersed in the polymer matrix. Homogenization is conducted according to the well-known micromechanical methods. Herein, the combination of the Eshelby–Mori–Tanaka model and the rule of the mixture is implemented in order to estimate the equivalent material properties of the nanocomposite beam. Also, a refined higher-order beam theory is used in order to calculate the kinetic relations free from utilizing an additional factor to account for the shear deformation. Furthermore, the governing equations are achieved by applying Hamilton's principle. Then, the governing equations are solved analytically to enrich the wave frequency. The effects of various parameters on the variation in wave frequency and phase velocity of the multi-scale hybrid nanocomposite beam are studied. The results of this study reveal that the mechanical responses of the system decrease whenever the nanotubes are inside the clusters. [ABSTRACT FROM AUTHOR]

In this study, the survey of the wave dispersion behaviors of sandwich composite nanoplates is carried out by considering the magnetostriction phenomenon. The nanoplate is assumed to be made up of a central magnetostrictive core in addition to two composite face sheets. The scale influences are covered based on the nonlocal strain gradient theory. Moreover, the equations of plate motion are derived according to the classical plate theory. Afterward, the magnetization effects are considered by introducing a feedback control system. Then, Hamilton’s principle is introduced to obtain the Euler–Lagrange equations of the magnetostrictive sandwich composite nanoplate. Also, by relating the achieved equations with those of the nonlocal strain gradient theory, the nonlocal governing equations of magnetostrictive sandwich composite nanoplate are developed. The wave frequency and phase velocity values are computed by the application of an analytical solution. Finally, the effects of participant coefficients are illustrated separately through certain figures. [ABSTRACT FROM AUTHOR]

In this research, it is tried to inquire the wave propagation problem of a double-layered graphene sheet (DLGS) undergoing thermal loading for the first time. Here, uniform and linear temperature distributions are included to enucleate the effect of each one in comparison with the other. A classical plate theory is employed to derive the kinematic relations of each layer of DLGS. On the other hand, the non-local elasticity theory is introduced to account for the nanoscale effects. In addition, attachment of graphene sheets to a fixed surface is modeled by a visco-Pasternak foundation and the interactions between two layers are simulated utilizing van der Waals (vdW) model. By the means of Hamilton’s principle, the non-local governing equations are derived. Also, in the framework of an analytical procedure, the wave frequency and phase velocity values are obtained. Eventually, a complex of various diagrams is organized to separately investigate the influence of each parameter on the wave frequency, phase velocity, and escape frequency of DLGSs. [ABSTRACT FROM AUTHOR]

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc. [ABSTRACT FROM AUTHOR]

In this article, wave propagation characteristics of protein lipid nanotubules are covered with respect to scale effects utilizing nonlocal strain gradient theory. The structure is supposed to be modeled as a simply supported beam and the kinematic relations are derived based on the classical beam theory (CBT). Implementing an energy based approach, the Euler-Lagrange equations of the lipid tubules are obtained. Moreover, the final governing equations are solved analytically to achieve the wave frequency and phase velocity of propagated waves. Influences of small size and wave number on the wave dispersion responses of lipid nanotubules are shown in detail in different diagrams for both phase velocity and wave frequency. Also, accuracy of introduced model is verified comparing responses of present model with those of former papers. [ABSTRACT FROM AUTHOR]

The coupled influences of shear deformation and angular velocity of a FG rotary nanobeam are going to be analyzed in the existence of external magnetic and electric fields. The effective material properties seem to be defined by the means of power law formulation. Moreover, the influences of small scale are included precisely in the framework of a nonlocal strain gradient theory. The magneto-electric potentials are supposed to vary through the thickness with a combination of linear and cosine approximations. Employing Hamilton’s principle, the nonlocal governing equations of magneto-electro-elastic functionally graded (MEE-FG) rotary size-dependent beams are derived in terms of displacement fields. Afterwards, the obtained governing equations are solved analytically to gather wave frequency, phase velocity, and escape frequency of the MEE-FG rotary nanobeam. The obtained results are validated with those of former researches. At the end, a numerical study is performed to show the influence of involved parameters on the wave propagation behaviors of MEE-FG rotary nanobeams. [ABSTRACT FROM PUBLISHER]

This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded nanoplate in thermal environments. The theory contains two scale parameters corresponding to nonlocal and strain gradient effects. A quasi-3D plate theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanoplate accounting for thickness stretching effect. These equations are solved analytically to find wave frequencies and phase velocities of functionally graded nanoplate. It is indicated that wave dispersion behavior of functionally graded nanoplates is significantly affected by temperature rise, nonlocality, length scale parameter, and material composition. [ABSTRACT FROM AUTHOR]

In the present article, wave dispersion behavior of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation subjected to thermal loading is investigated according to nonlocal strain gradient theory, in which the stress enumerates for both nonlocal stress field and the strain gradient stress field. Mori–Tanaka distribution model is considered to express the gradual variation of material properties across the thickness. The governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton’s principle according to Euler–Bernoulli beam theory. By applying an analytical solution, the dispersion relations of rotating FG nanobeam are obtained by solving an eigenvalue problem. Obviously, numerical results indicate that various parameters such as angular velocity, gradient index, temperature change, wave number, and nonlocality parameter have significant influences on the wave characteristics of rotating FG nanobeams. Hence, the results of this research can provide useful information for the next generation studies and accurate design of nanomachines including nanoscale molecular bearings and nanogears, etc. [ABSTRACT FROM AUTHOR]

This paper contains a nonlocal strain gradient theory to capture size effects in wave propagation analysis of compositionally graded smart nanoplates. Shear deformation influences are also covered employing a higher-order shear deformation plate theory. Furthermore, a power law function is used here to describe the material distribution across the thickness of functionally graded (FG) nanoplate. A combination of linear and cosine function is assumed to show the variations of electric and magnetic potentials through the thickness of nanoplate. The nonlocal governing equations of FG-MEE nanoplate have been derived utilizing Hamilton’s principle for MEEMs. Then, attained differential equations are solved by the means of an analytical solution incorporating with an exponential function. After that, wave frequency, phase velocity and escape frequency of FG-MEE nanoplates are derived for each natural mode. Influences of a large variety of parameters including wave number, nonlocal parameter, length scale parameter, electric voltage, magnetic potential and material distribution parameter has been illustrated separately and the results are exactly interpreted to obtain highlights of each figure. [ABSTRACT FROM AUTHOR]

Present manuscript undergoes with the investigation of the wave propagation features of smart magnetostrictive sandwich nanoplates (MSNPs) with regard to the influences of small scale in the context of the so-called nonlocal strain gradient theory (NSGT) of elasticity. The under observation continuous system, i.e. a thin-type one, is modeled via the Kirchhoff-Love theorem incorporated with the dynamic form of the principle of virtual work considering the impacts of both thermal and viscose losses on the dispersion characteristics of the nanostructure. Once the modified size-dependent constitutive equations are inserted into the motion equations, the final governing equations of the problem are attained. Thereafter, an analytical dispersion solution will be employed for the purpose of solving the dynamic problem to extract the wave response of the system. In order to examine the accuracy of the presented results, the natural frequencies obtained from this methodology are compared with those reported in the open literature. According to the presented illustrations, it can be declared that the magnetostriction can affect the dispersion responses of the smart nanoplate in low wave numbers. • The wave propagation features of smart magnetostrictive sandwich nanoplates (MSNPs) are studied using nonlocal strain gradient theory. • The magnetostriction can affect the dispersion responses of the smart nanoplate in low wave numbers. • The dispersion of MSNPs can be amplified by either increasing the length scale parameter or decreasing the nonlocal parameter. • Greater Winkler or Pasternak coefficients enhance the phase velocity values. • For low frequencies, the phase velocity of the system decreases with increasing temperature or damping coefficient. [ABSTRACT FROM AUTHOR]

In the present article, first-order shear deformation theory (FSDT) of the shell has been employed, for the first time, in order to analyze the propagation of the flexural waves in anisotropic fluid-conveying cylindrical shells. Four various anisotropic materials are utilized and their wave propagation behavior surveyed. Viscous fluid flow has been regarded to be laminar, fully developed, Newtonian, and axially symmetric. The Navier–Stokes equation can be utilized to explore the flow velocity effect. FSDT of the shell and Hamilton's principle have been employed in order to achieve governing equations of anisotropic fluid-conveying cylindrical shells and finally, the obtained governing equations have been solved via an analytical method. In addition, the influences of different variables such as flow velocity, radius to thickness ratio, and longitudinal and circumferential wave numbers have been investigated and indicated within the framework of a detailed set of figures. [ABSTRACT FROM AUTHOR]