Search

This research employs a multiple scales perturbation approach to evaluate the nonlinear wave propagation behaviors of a doubly curved sandwich composite piezoelectric shell with a flexible core in a hygrothermal environment. Stress and strain calculations for the flexible core and face sheets are carried out using Reddy's third-order shear deformation theory (TSDT) and third-order polynomial theory, respectively. The study explores the synergistic effects of a multilayered shell, flexible core, and magneto-rheological layer (MR) in revealing the nonlinearity of both in-plane and vertical moment within the core. The Halpin–Tsai model is employed to derive the properties of polymer/carbon nanotube/fiber (PCF) and polymer/graphene platelet/fiber (PGF) three-phase composite shells. The governing equations for the multiscale shell are derived using Hamilton's formulation. The research investigates temperature variations, diverse distribution patterns, curvature ratios, and magnetic fields through numerical analysis, presenting the results graphically and prior research has demonstrated the accuracy of these methods. Notably, these factors exert significant influence on the frequency-amplitude curves of the smart structure. [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 objective of this investigation is to propose a thermoelasticity model for analyzing the propagation of thermoelastic waves in a composite hollow circular cylinder with an LEMV/CFRP interface layer. The model incorporates a modified nonlocal couple stress theory and addresses the challenges associated with higher order time derivatives. The derivation results in three partial differential equations for the modified nonlocal couple stress of the cylinder in axisymmetric mode. Applying linear elasticity theory, the equations are solved to obtain frequency equations for the external surface of the cylinder under traction-free conditions, while ensuring continuity at the boundaries. The study explores the influence of variations in wave number and thickness on the frequency, temperature, and displacements within the field. To assess the impact of different thermoelasticity theories and nonlocal coupled stress parameters, the research utilizes tables and graphs for comparison and estimation. From the numerical evaluation, it is revealed that the impact of modified nonlocal couple stress parameter shows substantial effects on the physical quantities. [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]

This work is an attempt to examine the wave propagation of thermally loaded graphene platelets (GPL)s reinforced nanocomposite plates. Particularly, an analytical approach is made to determine the extent of wave dispersion in functionally graded nanocomposite plates reinforced with graphene platelets (GPL)s when thermal loading is added to the structure. Along with thermal loading, the plate structure is rested on an elastic foundation to derive a more realistic outcome. Variety of thermal loads with different temperature rises have been studies in the present research; these loads include: uniform temperature rise (UTR), sinusoidal temperature rise (STR), and linear temperature rise (LTR). Moreover, the nanocomposite (NC) plate is rested on a Winkler–Pasternak elastic foundation. GPL particles are dispersed in the polymer base along the thickness of the plate in four differing distribution patterns. Furthermore, Hamilton's principle along with refined higher-order plate theory is utilized to derive the governing equations of the problem. Afterwards, these differential equations are solved in an analytical format to attain the wave frequency, as well as, the phase velocity of GPL-reinforced NC plate. Before, assessing the impact of numerous parameters on the wave propagation characteristics of GPL-reinforced NC plate, our analytical model had been validated with previous studies. Results of this study indicates that the wave dispersion of NC plates reinforced with GPLs is heavily depended on parameters such as GPL distribution pattern, thermal loading type, GPL weight fraction and so on. [ABSTRACT FROM AUTHOR]

Our study employs the Timoshenko beam theory to thoroughly investigate the propagation of waves in auxetic metamaterial beams enabled by functionally graded graphene origami. This exploration is conducted while the Winkler–Pasternak foundation supports the beams. In addition, many distinct graphene origami (GOri) distribution patterns have been explored, and the results have been shown to be uniform and functionally graded across the thickness direction. The kinetic equations of auxetic metamaterial beams may be captured with the help of Hamilton's principle, which is applied here. The analytical solution of the governing equations for the auxetic metamaterial beam is determined based on the received information. Comparisons have been made between the effects that a wide variety of parameters have on the wave frequency and phase velocity of the auxetic metamaterial beam. These parameters include graphene distribution pattern and content, GOri folding degree, temperature, wave number, and elastic foundation coefficients. The crucial aspects of each figure have been identified through in-depth analysis and comparison of the results. [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]

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]

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]

Due to rapid development of process manufacturing, composite materials with porosity have attracted commercial attention in promoting engineering applications. For this regard, in this research wave propagation-thermal characteristics of a size-dependent graphene nanoplatelet-reinforced composite (GNPRC) porous cylindrical nanoshell in thermal environment are investigated. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the laminated composite cylindrical nanoshell in thermal environment have been evolved using Hamilton's principle and solved with the assistance of the analytical method. For the first time, wave propagation-thermal behavior of a GNPRC porous cylindrical nanoshell in thermal environment based on NSGT is examined. The results show that by increasing the thickness, the effect of porosity on the phase velocity decreases. Another important result is that by increasing the value of the radius, the difference between the minimum and maximum values of the phase velocity increases. Finally, influence of temperature change, wave number, angular velocity and different types of porosity distribution on phase velocity are investigated using the mentioned continuum mechanics theory. As a useful suggestion, for designing of a GPLRC nanostructure should be attention to the GNP weight function and radius, simultaneously. [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]

This article deals with the wave propagation problem of nanosize double-layered plates while subjected to a longitudinal magnetic field. To achieve more reliable answers, nonlocal strain gradient theory (NSGT) is utilized which takes into account both decreasing and increasing influences of small scale. Moreover, Kirchhoff plate theory is reviewed and incorporated with the Hamilton’s principle to obtain the equations of motion for each nanoplate. Afterwards, the equations of motion are mixed with those of NSGT in order to derive the nonlocal governing equations of nanoplates. Then, the achieved equations are solved analytically to reach the wave frequency and phase velocity values of propagated waves. Accuracy of the introduced model is verified by setting a comparison between this research and former published attempts. Finally, influence of each parameter on the wave dispersion answers of double nanoplate systems is shown in some diagrams. [ABSTRACT FROM AUTHOR]

In this article, wave dispersion responses of a temperature-dependent functionally graded (FG) nanobeam undergoing rotation and exposed to thermal load are presented based on nonlocal strain gradient theory. Mori-Tanaka model has been considered to express the gradual variation of material properties across thickness. Governing equations are derived as a function of axial force due to centrifugal stiffening and displacements by applying Hamilton’s principle in context of Euler-Bernoulli theory. Dispersion relations of rotating FG nanobeam are analytically derived by solving an eigenvalue problem. Obviously, numerical results indicate that different parameters such as angular velocity, gradient index, temperature change, wave number, and nonlocality parameter have significant influences on wave characteristics of rotating FG nanobeams. Hence, results of this research can provide useful information for the next generation studies and accurate deigns of nanomachines including nanoscale molecular bearings and nanogears. [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]

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 paper investigates wave propagation of size-dependent functionally graded (FG) nanobeams resting on elastic foundation subjected to axial magnetic field based on the nonlocal strain gradient theory and Euler-Bernoulli beam model by using an analytical approach. The nonlocal beam model has a length scale parameter and captures the size influences. Material properties are spatially graded according to sigmoid distribution. A derivation of the governing equations for the wave propagation analysis of nanoscale S-FGM beams is conducted. Then, the dispersion relations between wave frequency and phase velocity with the wave number is investigated. It is found that wave propagation characteristics of nonlocal S-FGM beams are influenced by various parameters including length scale parameter, material graduation, elastic foundation parameters and magnetic field intensity. [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]

In this article, an analytical model for the wave propagation analysis of inhomogeneous functionally graded (FG) nanobeam in thermal environment is developed based on nonlocal strain gradient theory, in which the stress accounts for not only the nonlocal elastic stress field but also the strain gradients stress field. The nanobeam is modeled through a higher order shear deformable refined beam theory which has a trigonometric shear stress function. The temperature field supposed to have a nonlinear distribution across the nanobeam thickness. Temperature-dependent material properties of nanobeams are spatially graded based on Mori–Tanaka model. The governing equations of the temperature-dependent functionally graded (FG) nanobeam are derived using the Hamilton’s principle. Numerical examples show that the characteristics of the wave propagation of FG nanobeam are influenced by various parameters such as nonlocality parameter, length scale parameter, gradient index, and temperature changes. [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]