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In the current paper, analysis of torsional vibration behavior of non-circular nanorods made of auxetic honeycomb material is investigated for the first time. The triangular and elliptical cross-sections are selected to be analyzed. Moreover, one of the distinct properties of auxetic honeycomb materials is that they possess a negative Poisson's ratio, which can be effective on the design and analysis of structures. In order to capture a small size or scale effect, the constitutive relation of nanorods is modified based on Eringen's nonlocal elasticity theory (ENET). Hamilton's principle is employed to obtain the kinematic relation of nanoscale rods. The nonlocal derived governing equations of non-circular auxetic nanorods are solved by utilizing an analytical method with respect to different boundary conditions. In order to verify the correctness of obtained outcomes, the results are compared to previous investigations, and good agreement can be observable. The influences of various parameters such as both Clamped–Clamped (C–C) and Clamped-Free (C-F) boundary conditions, nonlocal parameters, inclined angles, and geometrical ratios are explored and illustrated in the framework of several figures, which can be seen in detail. [ABSTRACT FROM AUTHOR]

The current paper is devoted to investigate the free and forced vibrational responses of the multi-phase angle-ply laminated nanocomposite beam with focusing on the occurrence of resonance phenomenon. The influence of uniform thermal loading and three-parameter Kerr substrate which can affect the resonance behavior of the structure is surveyed. Utilizing a superior nanofiller with the name of Graphene Oxide (GO) together with the macro-scale Carbon Fibers (CFs) will constitute a novel multi-scale hybrid reinforcement for the polymer matrix. The combination of the Halpin–Tsai micromechanical model and extended rule of the mixture is implemented to estimate the effective properties of this multi-scale hybrid nanocomposite. Refined higher-order beam theory is employed to obtain the displacement fields and then with applying Hamilton's principle, the governing equations are derived and analytically solved via Galerkin's exact solution method. Also, the presented results are validated with reputed works in open literature. Furthermore, some tabulated and graphical results are provided to reveal the effects of various parameters such as fibers' orientation angle, weight and volume fractions of reinforcements, different boundary conditions, beam's slenderness ratio, Kerr substrate parameters, excitation frequency and temperature change on the dynamic behavior of the proposed structure. [ABSTRACT FROM AUTHOR]

The present article studies the two phase local/nonlocal deformation of magneto thermo electrical composite nano beam reinforced with graphene oxide powder (GOP). The controlling equation of motion and boundary conditions are derived via two phase elasticity in differential form conjunction with Hamilton's principle and Euler-Bernoulli beam model. The effect of a non-uniform magnetic and piezo electric field is incorporated with the governing equations by convoluting field quantities and displacement components. Then, Navier method is adopted to observe the influence of various boundary conditions on the dynamics of the beam. Comparison studies are performed to display the accuracy and efficiency of this analytical model. Further, the effects of magnetic field, GOP weight fraction, two phase parameter, external electric voltage, nonlocal parameter and temperature difference on the dimensionless frequency of GOP reinforced magneto piezo thermo elastic composite beams are thoroughly investigated and highlighted through tables and dispersion curves. [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]

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 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]

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]

This paper investigates the buckling problem of a multi-scale hybrid nanocomposite shell for the first time while the cylinder is supposed to be rested on an elastic substrate. The constituent material is considered to be made from a polymeric matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers' agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing the Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube-reinforced (CNTR) nanocomposite are coupled with those of carbon fibers (CFs) within the framework of a modified rule of the mixture. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the static form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin's method to obtain the buckling load of the structure for both simply supported and clamped boundary conditions. The results indicate on the fact that if the agglomeration effects are ignored, the designed nanocomposite system may fail under low static excitations. Also, it is better to avoid from the construction of a large number of small clusters to make the nanocomposite structure more powerful against buckling mode failure. [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]

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 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]

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]

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 article aims to investigate buckling characteristics of a functionally graded magneto-electro-thermo-elastic nanoshell based on nonlocal strain gradient theory (NSGT). Accounting for nonlocal and strain gradient size-dependency, NSGT has two scale coefficients. The nanoshell is subjected to external electric, magnetic, mechanical, and thermal fields. The temperature distributions are considered as uniform and linear thorough the nanoshell thickness. All material properties including elastic, piezoelectric, and magnetic properties are defined based on a power-law distribution type. Seven coupled governing equations are derived for the nanoshell based on Hamilton's rule and then solved applying Galerkin's approach. The dependency of the buckling behavior of the nanoshell on applied thermal load, temperature distribution, electric voltage, magnetic potential, material gradient index, scale parameters, and shear deformation will be explored. [ABSTRACT FROM AUTHOR]

The present article aims to clarify the effect of the nanoflow on the nonlinear dynamic instability of graphene sheets under parametric excitation. To achieve this aim, the graphene layer is added to a visco-Pasternak foundation then, the resulting nanostructure is subjected to the nanoflow and a parametric axial force, simultaneously. The nonlocal elasticity and the nonlinear von Karman theories and Hamilton's principle are combined in this article, which lead to the governing equation of motion. A class of nonlinear Mathieu–Hill equation is established to determine the bifurcations and the regions of the nonlinear dynamic instability. The main conclusion to be drawn is that nanoflow directly influences the amplitude response of the system. This investigation contains analysis of how the nanoflow affects the nonlinear instability of nanostructures including the graphene sheets which can be provided useful information for the next investigations in field of nano electromechanical system. [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 study, a cylindrical microshell stability reinforced by graphene nanoplatelets is investigated while an axial load is applied uniformly. In addition, viscoelastic foundation covers the composite nanostructure. Therefore, the impacts of the small scale parameter are studied while nonlocal strain gradient theory (NSGT) is considered. The present research deals for the first time with the consideration of viscoelastic, strain–stress size-dependent parameters along with taking into account of various boundary conditions (BCs), especially C-F ones put into effect on the proposed theory. The governing equations (G.Eqs) and BCs have been obtained utilizing energy method and solved with assistance of the generalized differential quadrature method (GDQM). Besides, for the validation of the results, the results of the current model are compared to the results acquired from analytical method. The results show that, viscoelastic foundation, patterns of GPL distribution, nonlocal parameter, length scale parameter, layers' numbers, boundary condition as well as GPL weight function have considerable impact on the stability of the GPLRC cylindrical microshell. Another significant result is that; for C-F B.Cs, at the higher value of the l / R parameter, the influence of the g GPL on the dimensionless buckling load of the structure is much more remarkable in comparison with the lower one which in results section is investigated in detail. The results of the present investigation would be informative for design and fabrication of the microactuators and microsensors. [ABSTRACT FROM AUTHOR]

In this paper, a sandwich composite plate with tunable magneto-rheological (MR) fluid core is utilized for analyzing the wave propagation. Sandwich composite plate is made of three layers consisting of the base layer, MR layer and the limiter layer. MR layer is embedded within the base and the limiter layers. Moreover, the upper and the lower layers are made of the elastic materials. This structure is also located on a viscoelastic substrate. At first, for achieving the governing equations of motion, Hamilton's principle and classical plate theory (CLPT) are utilized. Then, exerting 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 most important factor for changing the value of the wave dispersion characteristic. Besides, results indicate by enhancing the core-to-top layer thickness ratio, the wave frequency decreases because MR fluid core is softer in comparison to the elastic layers, Hence, MR fluid core operates similar damper. At the end, the effect of the other parameters such as thickness of MR layer, Winkler, Pasternak and damping coefficients are also discussed. [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]

The present article is proposed to capture the influences of carbon nanotubes' agglomeration on the natural frequency behaviors of multi-scale hybrid nanocomposite plates for the first time. The constituent material, which is a hybrid nanocomposite, is consisted of both macro- and nano-scale reinforcing fibers dispersed in a polymer matrix. The equivalent material properties are seemed to be calculated coupling the Eshelby-Mori-Tanaka model with the rule of the mixture to consider the effects of carbon nanotubes inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy-based approach is implemented to obtain the governing equations of the problem utilizing a refined higher-order plate theorem. Next, the derived equations will be solved in the framework of Galerkin's well-known analytical method to reach the fundamental frequency. It is worth mentioning that the influence of various boundary conditions is included. Once the validity of the presented results is proven, a set of numerical examples are presented to explain how each variant can affect the plate's natural frequency. Communicated by Wei-Chau Xie. [ABSTRACT FROM AUTHOR]

Application of a newly developed refined higher-order beam theory in the thermal buckling problem of a multiscale hybrid nanocomposite beam is shown here with respect to effect of nanofillers aggregation for the first time. In this research, a mixture of macro and nanoscale fillers will be utilized to be dispersed in an initial matrix to possess a multiscale hybrid nanocomposite. The equivalent material properties are seemed to be calculated coupling the Eshelby-Mori-Tanaka model with the rule of mixture to consider the effects of CNTs inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy based approach is implemented to obtain the governing equations of the problem utilizing a refined higher-order plate theorem. Next, the derived equations will be solved in the framework of Galerkin's well-known analytical method to reach the critical buckling load. It is worth mentioning that influence of various boundary conditions is included. Once the validity of presented results is proven, a set of numerical examples are presented to explain how each variant can affect the buckling behaviors of the structure. [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 article deals with the thermal vibration analysis of the graphene-oxide powder-reinforced (GOPR) nanocomposite plates, once the plate is embedded on the viscoelastic substrate. The structure is subjected to thermal loadings with various temperature rises such as sinusoidal temperature rise (STR), linear temperature rise (LTR), and uniform temperature rise (UTR). Damping behavior of the GOPR nanocomposite plates is investigated based on the variations of the natural frequencies. Four functionally graded (FG) patterns of GOPs' distribution are taken into account comparatively in order to find out the best model of reinforcing the structure. The homogenization of the materials is carried based on the Halpin-Tsai micromechanical scheme. The governing equations of the motion have been derived through the combination of refined higher-order shear deformation theory and Hamilton's principle. The accuracy of this modeling is validated with those reported in the open literature. Finally, the influences of different parameters on the natural frequencies of the embedded GOPR nanocomposite plates are investigated based on the damping coefficient of the viscoelastic substrate. The graphical results reveal that the free vibrational behavior of the structure is remarkably affected by the variations of these parameters. [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 develops a nonlocal strain gradient plate model for buckling analysis of graphene sheets under hygrothermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as moisture concentration rise, temperature rise, nonlocal parameter, length scale parameter, elastic foundation and geometrical parameters on buckling characteristics a graphene sheets are examined. [ABSTRACT FROM AUTHOR]

This paper develops a nonlocal strain gradient plate model for vibration analysis of double-layered graphene sheets under biaxial in-plane mechanical loads. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. In fact, frequency increment due to the strain gradient effect is neglected in all previous papers related to double-layer graphene sheets. Governing equations of a nonlocal strain gradient double-layer graphene sheet on elastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as in-plane loading, nonlocal parameter, length scale parameter, elastic foundation, interlayer stiffness and boundary conditions on vibration characteristics a double-layer graphene sheet are examined. [ABSTRACT FROM AUTHOR]

In this paper, free vibration behavior of functionally nanoplate resting on a Pasternak linear elastic foundation is investigated. The study is based on third-order shear deformation plate theory with small scale effects and von Karman nonlinearity, in conjunction with Gurtin–Murdoch surface continuum theory. It is assumed that functionally graded (FG) material distribution varies continuously in the thickness direction as a power law function and the effective material properties are calculated by the use of Mori–Tanaka homogenization scheme. The governing and boundary equations, derived using Hamilton's principle are solved through extending the generalized differential quadrature method. Finally, the effects of power-law distribution, nonlocal parameter, nondimensional thickness, aspect of the plate, and surface parameters on the natural frequencies of FG rectangular nanoplates for different boundary conditions are investigated. [ABSTRACT FROM AUTHOR]

In the present paper, nonlocal couple stress theory is developed to investigate free vibration characteristics of functionally graded (FG) nanobeams considering exact position of neutral axis. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher-order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton's principle and they are solved applying Galerkin's method, which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters, such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation, and various boundary conditions on natural frequencies of FG nanobeams in detail. [ABSTRACT FROM AUTHOR]

In this article, an analytical approach is presented to study the surface and flexoelectric effects on the buckling characteristics of an embedded piezoelectric sandwich nanobeam. According to the nonlocal elasticity theory, the flexoelectricity is believed to be authentic for size-dependent properties in nanostructures. The boundary conditions and the governing equations are derived by Hamilton's principle and are solved by Navier method. The results obtained from the present work show that the nonlocal term has an important reduction on the critical load and also the flexoelectricity shows an increasing influence on the buckling loads of the sandwich nanobeam, especially at lower thicknesses. [ABSTRACT FROM AUTHOR]

Thermoelectric-mechanical vibration behavior of functionally graded piezoelectric (FGP) nanobeams is first investigated in this article, based on the nonlocal theory and third-order parabolic beam theory by presenting a Navier-type solution. Electro-thermo-mechanical properties of a nanobeam are supposed to change continuously throughout the thickness based on the power-law model. To capture the small-size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for the third-order, shear deformable, piezoelectric, FG nanobeams are obtained and they are solved applying an analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of FGP nanobeams. The influences of several parameters, including external electric voltage, power-law exponent, nonlocal parameter, and mode number on the natural frequencies of the size-dependent FGP nanobeams are discussed in detail. The results should be relevant to the design and application of the piezoelectric nanodevices. [ABSTRACT FROM AUTHOR]

In this research, vibration characteristics of axially functionally graded nanobeams resting on variable elastic foundation are investigated based on nonlocal strain gradient theory. This nonclassical nanobeam model contains a length scale parameter to explore the influence of strain gradients and also a nonlocal parameter to study the long-range interactions between the particles. The present model can degenerate into the classical models if the material length scale parameter and the nonlocal stress field parameter are both taken to be zero. Elastic foundation consists of two layers: a Winkler layer with variable stiffness and a Pasternak layer with constant stiffness. Linear, parabolic and sinusoidal variations of Winkler foundation in longitudinal direction are considered. Material properties are graded axially via a power-law distribution scheme. Hamilton's principle is employed to derive the governing equations that are solved applying a Galerkin-based solution for different boundary edges. Comparison study is also performed to verify the present formulation with those of previous papers. Results are presented to investigate the influences of the nonlocal and length scale parameters, various material compositions, elastic foundation parameters, type of foundation and various boundary conditions on the vibration frequencies of AFG nanobeams in detail. [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]

This article is concerned with the thermo-mechanical vibration behavior of flexoelectric nanoplates under uniform and linear temperature distributions. Flexoelectric nanoplates have higher natural frequencies than conventional piezoelectric nanoplates, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric nanoplates for the first time. Hamilton's principle is employed to derive the governing equations and the related boundary conditions, which are solved applying the Galerkin-based solution. A comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameters, surface elasticity, temperature rise, plate thickness, and various boundary conditions on the vibration frequencies of thermally affected flexoelectric nanoplate. [ABSTRACT FROM AUTHOR]

In the present research, free vibration study of functionally graded (FG) nanobeams with graded nonlocality in thermal environments is performed according to the third-order shear deformation beam theory. The present nanobeam is subjected to uniform and nonlinear temperature distributions. Thermo-elastic coefficients and nonlocal parameter of the FG nanobeam are graded in the thickness direction according to power-law form. The scale coefficient is taken into consideration implementing nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of nonlocal Euler–Bernoulli and Timoshenko beam models, and it is revealed that the proposed modeling can accurately predict the vibration frequencies of the FG nanobeams. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio, and thermal loading in detail. The present study is associated to aerospace, mechanical, and nuclear engineering structures that are under thermal loads. [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]

In the present article, a nonlinear, eccentric, low-velocity impact response of a polymer-carbon nanotubefiber multiscale nanocomposite plate on elastic foundations in hygrothermal conditions using the finite element method is performed. In this regard, the governing equations are derived based on higher-order shear deformation plate theory and von Kármán geometrical nonlinearity. Three types of distributions of the temperature field and moisture concentrations, namely, uniformly, linearly, or nonlinearly through the thickness direction of the plates are considered. The effective material properties of the multiphase nanocomposite are calculated using fiber micromechanics and Halpin-Tsai equations in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the matrix. The contact force between the impactor and the plate is obtained with the aid of the modified nonlinear Hertzian contact law models. After examining the validity of the present work, the effects of the weight percentage of CNT, moisture concentration, temperature variations, distribution of temperature and moisture concentration, elastic foundation, and the eccentricity on the contact force, indentation, and central deflection of polymer-CNT-fiber multiscale nanocomposite plate are studied in details. [ABSTRACT FROM AUTHOR]

In this article, free vibration of functionally graded (FG) viscoelastic nanobeams resting on viscoelastic foundation subjected to hygrothermal loading is investigated employing a higher order refined beam theory which captures shear deformation influences needless of any shear correction factor. The three-parameter viscoelastic medium consists of parallel springs and dashpots as well as a shear layer. Temperaturedependent material properties of FGM beam are graded across the thickness via the power-law model. Employing non-local elasticity theory of Eringen and Hamilton's principle, non-local governing equations of a size-dependent viscoelastic nanobeam are obtained and solved analytically for various boundary conditions. To verify the reliability of the developed model, the results of the current work are compared with those available in literature. The effects of viscoelastic foundation parameters, internal damping coefficient, hygrothermal loading, non-local parameter, gradient index, mode number, and slenderness ratio on the vibrational characteristics of nanoscale viscoelastic FG beams are explored. [ABSTRACT FROM AUTHOR]

In this article, nonlocal free vibration analysis of curved functionally graded piezoelectric (FGP) nanobeams is conducted using a Navier-type solution method. The model contains a nonlocal stress field parameter and also a nonlocal strain-electric field gradient parameter to capture the size effects. Inclusion of these nonlocal parameters introduces both stiffness-softening and stiffness-hardening effects in the analysis of curved nanobeams. Nonlocal governing equations of curved FGP nanobeam are obtained from Hamilton's principle based on the Euler–Bernoulli beam model. The results are validated with those of curved FG nanobeams available in the literature. Finally, the influences of electric voltage, length scale parameter, nonlocal parameter, opening angle, material composition, and slenderness ratio on vibrational characteristics of nanosize curved FG piezoelectric beams are explored. These results may be useful in accurate analysis and design of smart nanostructures constructed from piezoelectric materials. [ABSTRACT FROM AUTHOR]