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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 study explores the free vibration characteristics of hybrid laminated nanocomposite truncated conical shells and panels incorporating functionally graded graphene platelet-reinforced (FG-GPLs) and functionally graded carbon nanotube-reinforced (FG-CNTs) materials, advancing understanding in hybrid material applications. The structures are assumed to be supported by a two-parameter elastic foundation, and the study also considers the influence of CNT agglomeration. The estimation of CNT agglomeration effect is performed using a two-parameter agglomeration model based on the Mori–Tanaka approach, considering the random orientation of carbon nanotubes. By employing a combination of various control parameters, it becomes possible to determine the optimal mode for setting the natural frequency of the system. To ensure accurate calculations for both thin and thick shells, a third-order shear deformation theory is employed. The governing equations and boundary conditions are formulated based on Hamilton's principle. Numerical solutions are obtained through the systematic differential quadrature method, wherein the Kronecker delta function is employed. By introducing subtle adjustments to the governing equations, this method effectively minimizes computational volume and complexity, proving particularly advantageous for addressing problems characterized by higher degrees of freedom. To estimate the effective mechanical properties of the CNT-reinforced nanocomposite layers, the rule of mixtures is employed. Meanwhile, the Halpin–Tsai micromechanical model is utilized for calculating the properties of the GPL-reinforced nanocomposite layers. The presented study establishes convergence and accuracy through evaluation, considering various parameters such as CNTs volume fraction, GPLs mass fraction, different distribution patterns, different geometries under various boundary conditions, vertex angle of the cone, agglomeration characteristics of CNTs, and different stiffness of the elastic foundation. [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]

The functionalization of graphene aims at altering its material properties to encourage its use in various new applications. In the present research, an investigation on a functionalized graphene oxide (FGO) reinforced nanocomposite (NC) plate is performed once the plate is subjected to thermal loading. The reinforcement of the plate is done with multiple functionally graded (FG) distributions through the thickness, specifically, uniform (U), X, V, and O. This action is for the purpose of finding the most effective distributional strategy for functionalized graphene oxide with ameliorated vibrational characteristics. Also, the Winkler–Pasternak elastic substrate serves as the support for the plate construction. To describe the mechanical properties of the FG nanocomposite plate, the Halpin–Tsai model is employed and a more advanced higher order shear deformation model is used to take the impact of shear deformation into account. Next, Hamilton's principle is utilized to derive the governing equations of the plate structure. These governing equations are then solved for a simply supported functionalized graphene oxide-reinforced nanocomposite plate. Ensuing, several parametric studies are presented to better delineate the impact of numerous variants including FGO's weight fraction, distribution patterns, temperature raise, elastic substrate coefficients, and geometrical properties on the nanocomposite plates' fundamental frequency. Results of our study indicate that raising the temperature and aspect ratio can decrease the natural frequency of FGO-reinforced NC plates, while increase in the FGO's weight fraction and elastic foundation does the opposite. [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 investigation, the influences of waviness and agglomeration factor of nanofillers on wave dispersion of embedded nanocomposite beams reinforced with multi-walled carbon nanotubes (MWCNTs) is investigated for the first time. These beams are supported on Winkler–Pasternak elastic foundation. The effective mechanical properties of nanocomposite beam are estimated by employing a blend of a new form of Halpin–Tsai micromechanical model and rule of mixture. The kinematic and kinetic relations of nanocomposite beam are computed based upon refined higher-order shear deformation theory. Moreover, the governing equations are derived by utilizing the Hamiltonian approach. Afterward, an analytical method is used in order to solve the obtained governing equations. Effects of the wide range of variants such as volume fraction of MWCNTs, slenderness ratio, waviness factor, random orientation factor, agglomeration factor and elastic foundation coefficient on the variation of wave frequency and phase velocity have been illustrated comparatively. Furthermore, the results are thoroughly discussed to obtain the highlights of each figure. [ABSTRACT FROM AUTHOR]

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

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]