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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]

This is the first research on the smart control and frequency analysis of a cylindrical sandwich nanoshell in the framework of the numerical-based generalized differential quadrature method (2D-GDQM). The current sandwich smart nanostructure is made of a honeycomb core and piezoelectric face sheets as sensor and actuator (PFSA). For modeling the size-dependent nanoshell, nonlocal stress-strain gradient theory (NSGT) is presented. Also, this nanostructure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. Also, the current structure rotates around its axial direction. The stresses and strains are obtained using the higher-order shear deformation theory (HSDT). The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. Governing equations and boundary conditions of the cylindrical sandwich nanoshell are obtained by implementing Hamilton's principle. The results show that the geometry of honeycomb core, PD controller, velocity of fluid flow, length to radius ratio (L/R), and applied voltage and have a significant influence on the frequency characteristics of a cylindrical sandwich nanoshell. Another important consequence is that applying the PD controller leads to an increase in the critical velocity of fluid flow in the smart nanostructure. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear vibrational behaviors of doubly-curved functionally graded piezoelectric (FGP) microshells in thermal environments have been studied. The doubly-curved microshell has been modeled by using modified couple stress and thin shell theories. The microshell has two material constituents which are piezoelectric materials and their gradation is described using power-law functions. Temperature fields are considered to be uniform, linear, and nonlinear. A closed-form of nonlinear vibration frequency has been obtained by analytically solving the governing equations using the Harmonic balance method. It will be demonstrated that nonlinear vibrational frequency of doubly-curved microshell relies on couple stress influence, material gradation, curvature radius, center deflection, and electrical field. [ABSTRACT FROM AUTHOR]

The goal of the present research is an investigation of the smart control and wave propagation examination of a graphene nanoplatelets reinforced (GPLRC) cylindrical micro-shell covered with piezoelectric layers as the sensor and actuator (PLSA) in the framework of an analytical method. The stress and strain components are given based on the first-order shear deformable theory (FSDT), and for accessing the size effects, the nonlocal strain gradient theory is used for obtaining the correct results. The material properties of the GPLRC micro-shell are modeled via modified Halpin–Tsai and the rule of the mixture. The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. The governing equations of the electrically micro-shell are derived via Hamilton's principle. This work concludes that the PD controller, wave number, applied voltage, and weight fraction of graphene nanoplatelets (GPL) have a significant influence on the wave propagation of the GPLRC cylindrical micro-shell. The remarkable result is that consideration of the PD controller leads to expand the stable area and improve the dynamic behaviors of the smart system. [ABSTRACT FROM AUTHOR]

This composition presents a multi-phase-lags thermos-elasticity model for the thermos-elastic wave propagation reaction of a composite hollow circular cylinder with the interface layer LEMV/CFRP (Linear Elastic Material with void/Carbon Fiber Reinforced Polymer) using new modified couple stress theory. Three partial differential equations of the modified couple stress and multiphase lag model of composite hollow cylinder are derived for axisymmetric mode and solved exactly using linear theory of elasticity. The frequency equations are achieved for the traction free outer surface with continuity conditions at the interfaces. The influences of changing wave number and thickness on the field quantities like frequency, temperature, displacements, are investigated. Some comparisons are tabulated and presented graphically to estimate the effects of various thermos-elasticity theories and coupled stress parameter. [ABSTRACT FROM AUTHOR]

The purpose of present investigation is to study propagation of flexural wave in porous metal foam beams resting on Winkler–Pasternak foundation based upon refined higher-order shear deformable beam theory. Moreover, different types of porosity distribution through the thickness direction are probed namely; uniform, symmetric and asymmetric. The Hamiltonian approach is implemented to catch motion equations of porous metal foam beams. Then, the obtained governing equations of porous metal foam are solved analytically. The influences of different parameters such as various types of porosity distribution, porosity coefficient, slenderness ratio, wave number and elastic foundation coefficients on the variation of wave frequency, escape frequency and phase velocity are covered and presented within the framework of a group of figures which can be observed in detail. [ABSTRACT FROM AUTHOR]

In the current investigation, the influences of waviness and agglomeration factor of nanofillers on wave dispersion of embedded nanocomposite beams reinforced with multi-walled carbon nanotubes (MWCNTs) is investigated for the first time. These beams are supported on Winkler–Pasternak elastic foundation. The effective mechanical properties of nanocomposite beam are estimated by employing a blend of a new form of Halpin–Tsai micromechanical model and rule of mixture. The kinematic and kinetic relations of nanocomposite beam are computed based upon refined higher-order shear deformation theory. Moreover, the governing equations are derived by utilizing the Hamiltonian approach. Afterward, an analytical method is used in order to solve the obtained governing equations. Effects of the wide range of variants such as volume fraction of MWCNTs, slenderness ratio, waviness factor, random orientation factor, agglomeration factor and elastic foundation coefficient on the variation of wave frequency and phase velocity have been illustrated comparatively. Furthermore, the results are thoroughly discussed to obtain the highlights of each figure. [ABSTRACT FROM AUTHOR]

In the current work, wave propagation in simply supported (S-S) functionally graded (FG) beam is investigated while the beam is exposed to magneto-thermal environments and embedded on two-parameter elastic foundation. The mechanical properties of the structure are supposed to vary through the thickness via the exponential and power law function. The governing equations of the motion are derived by implementing Hamilton's principle on the basis of refined higher order beam theory which can capture the shear deformation effect. Two novel metal and ceramic with interesting properties named Osmium and Silicon Carbide (SiC) are used as materials of this structure. The thermal loadings are applied to the structure with various temperature changes namely uniform, linear and sinusoidal, through the thickness. Influences of the wide range of parameters such as magnetic field intensity, slenderness ratio, various thermal loadings, exponential- and power-law exponents and elastic foundation coefficient on the wave frequency and phase velocity of the FG beam have been illustrated comparatively and the results are thoroughly discussed to obtain the highlights of each figure. [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]

Free oscillation analysis of shells consisted of multi-scale hybrid nanocomposites is carried out with regard to the destroying effect of the nanofillers' agglomeration on the system's dynamics. The equivalent material properties of the hybrid nanocomposite are obtained in the framework of a bi-level micromechanical procedure. The influence of existence of agglomerated carbon nanotubes (CNTs) on the stiffness of the nanocomposite is included with the aid of the Eshelby-Mori-Tanaka method. Thereafter, the first-order shear deformation theory (FSDT) of the shells will be combined with the dynamic form of the principle of virtual work to reach the Euler-Lagrange equations of the problem. Next, the governing equations will be extracted from the Euler-Lagrange ones by using the constitutive equations of the nanocomposite. To obtain the natural frequencies of the system for shells with clamped and simply supported ends, the Galerkin's method is hired. The validity check reveals that the utilized methodology is powerful enough to predict the frequency behaviors of nanocomposite shells. According to the results, it can be inferred that the hybrid nanocomposite shells may be involved in resonance phenomenon in low-range frequencies if the impact of the CNTs' aggregation is neglected. Obviously, the volume fraction of the CNTs inside the inclusions plays a magnificent role in the determination of the system's dynamic behavior. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the wave propagation analysis of multi-scale hybrid nanocomposite plates by considering the influences of the aggregation of the nanoparticles. For the constituent materials of the plate, a polymeric matrix is supposed to have macro- and nano-reinforcements dispersed in it. The well-known micromechanical methods, such as Eshelby-Mori-Tanaka model and the rule of the mixture, are exerted to compute the effective material properties of the nanocomposite plate. Also, a refined higher-order shear deformation theory is implemented to obtain the motion relations. Besides, the governing equations are derived by employing the principle of Hamilton. Then, the analytic method is used to solve the obtained governing equations of structure and finally wave frequency and phase velocity are calculated. The effects of the various parameters on the variation of phase velocity and wave frequency of the multi-scale nanocomposite plates are examined. The presented results demonstrate that the mechanical response of the system can be decreased, while the nanotubes are covered by clusters. [ABSTRACT FROM AUTHOR]

The present paper is mainly focused on analyzing wave propagation of sigmoid functionally graded (SFG) piezoelectric nanobeams rested on an elastic foundation on the basis of the nonlocal elasticity theory. The small-scale influence is taken into account by employing Eringen's nonlocal elasticity theory (ENET). Zinc oxide and Lithium niobate are supposed to be constituent materials of the nanoscale structure. Although the common power-law formulation has been used to determine electromechanical properties of functionally graded piezoelectric in the reported investigations, the sigmoid power-law formulation is employed in order to characterize the distribution of electromechanical properties in the current paper. Hamilton's principle and the Euler–Bernoulli beam theory, which is also known by classic beam theory, are applied to derive nonlocal governing equations of piezoelectric nanobeam. Afterward, the obtained nonlocal governing equations are solved via the analytical method. Eventually, the effect of various parameters, such as wave number, nonlocal parameter, gradient index, slenderness ratio, elastic foundation coefficients, and electric voltage on the variation of wave frequency and phase velocity of SFG piezoelectric nanobeam, is examined and also, the obtained result is presented in a group of illustrations that can be found in detail. [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]

An analytical approach is developed in this paper to investigate the wave propagating in graphene oxide powder (GOP) reinforced nanocomposite plates under thermal loading. The plate is embedded on a two parameter elastic substrate to make this research more realistic. The structure is exposed to thermal loadings with various temperature rises such as sinusoidal temperature rise (STR), linear temperature rise (LTR) and uniform temperature rise (UTR). The governing differential equations are derived via incorporation of the Hamilton's principle and refined higher order plate theory then solved analytically to obtain the wave frequency and phase velocity of the GOP reinforced nanocomposite plate. The GOPs are dispersed in a polymeric matrix through the thickness of the plate by considering different functionally graded (FG) patterns. Moreover, the effective material properties of the structure are predicted on the basis of Halpin–Tsai micromechanical scheme. Furthermore, the accuracy of the present model is verified with previous works and also the influences of various parameters on the wave propagation behavior of the structure are covered too. The graphical results declare that wave propagation in GOP reinforced nanocomposite plates dramatically depends on these parameters. [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]

A comparative study of Love-type wave vibrations in a distinct piezoelectric (PE) material thin film with a highly and weakly dielectric interface with an elastic pre-stressed elastic plate is investigated analytically. Using the PZT-2, PZT-4, PZT-5H, LiNbO3 and BaTiO3 numerical data for the PE material, we achieved significant outcomes of PE and flexoelectric effect in the study. Dispersion equations are achieved analytically for both electrically open and short cases together with highly and weekly conducting interfaces in the transcendental complex form. Outcomes specify that microstructures having flexoelectricity has a significant influence on dispersion features. The existence of flexoelectricity shows that complex phase velocity with a positive imaginary part increases the phase velocity of considered waves with time. Numerical results are highlighted graphically and validated with existing results. The present study is a prior attempt to show the flexoelectricity influence with weekly and highly conducting interfaces and also to show that the outcomes are significant to obtain better surface acoustic wave device's performance. [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 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]

This article deals with the wave propagation analysis of single/double layered functionally graded (FG) size-dependent nanobeams in elastic medium and subjected to a longitudinal magnetic field employing nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants, and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also, presence of cut-off and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated. [ABSTRACT FROM AUTHOR]

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton’s principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated. [ABSTRACT FROM AUTHOR]

A comparative study of Love-type wave vibrations in a distinct piezoelectric (PE) material thin film with a highly and weakly dielectric interface with an elastic pre-stressed elastic plate is investigated analytically. Using the PZT-2, PZT-4, PZT-5H, LiNbO3 and BaTiO3 numerical data for the PE material, we achieved significant outcomes of PE and flexoelectric effect in the study. Dispersion equations are achieved analytically for both electrically open and short cases together with highly and weekly conducting interfaces in the transcendental complex form. Outcomes specify that microstructures having flexoelectricity has a significant influence on dispersion features. The existence of flexoelectricity shows that complex phase velocity with a positive imaginary part increases the phase velocity of considered waves with time. Numerical results are highlighted graphically and validated with existing results. The present study is a prior attempt to show the flexoelectricity influence with weekly and highly conducting interfaces and also to show that the outcomes are significant to obtain better surface acoustic wave device's performance. [ABSTRACT FROM AUTHOR]