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In this study, a thermomechanical rigid-flexible coupling vibration model of the rotating pre-twisted porous functionally graded (PP-FG) thick microplate in a thermal environment is established based on the third-order shear deformation theory (TSDT) and modified couple stress theory (MCST). Three thermal distributions are considered. The effects of temperature and porosity on the equivalent material parameters are accounted for in the modified Voigt rule of mixture. The governing equations of motion are derived using the Euler–Lagrange equation and numerically solved through the complex modal analysis method and the Chebyshev–Ritz method. After validating the convergence and accuracy of the proposed model, the effects of temperature, material length scale parameter (MLSP), rotational speed, porosity index, gradient index, presetting angle, and pre-twist angle on the vibration behavior of microplates were examined. The key findings of the study are as follows: (1) The effects of rotational speed on in-plane and out-of-plane frequencies are opposite. Temperature elevation weakens the size effect and centrifugal stiffening effect on the frequencies. (2) The effects of the porosity index on the frequencies are the opposite when the gradient index exceeds a specific critical value. (3) The effects of the presetting angle on the frequencies are periodic and symmetrical at about 0. The frequencies reach an extreme value when the pre-twist angle is approximately 2$\pi$/3 for the cantilever microplate. The proposed model is more sophisticated and comprehensive than others reported in the literature. It offers a more thorough analysis and insight into the behavior and performance of micro-electro-mechanical systems (MEMS) and micro air vehicles (MAVs), particularly when operating in challenging conditions.

This study primarily examines a badminton court that is modeled as a rectangular plate enabled by graphene-origami (G-Ori) metamaterials. The model’s dynamic performance is examined in a thermal environment to comprehend the effects of temperature variations. To enhance accuracy, a new quasi-three-dimensional shear and normal trigonometric hyperbolic theory is employed, elucidating the kinematic interactions of the structure. This new hypothesis accommodates transverse normal strain. Differential motion equations are derived from Hamilton’s principle and subsequently solved analytically using Fourier series functions. The primary objective of the study is to investigate the impact of different conditions on the natural frequencies of the model. The findings demonstrate that the incorporation of G-Ori enhances the rigidity of the structure and, as a result, its natural frequencies. Conversely, when the temperature increases, the frequencies diminish.

The free vibration of functionally graded (FG) beams with various boundary conditions resting on a two-parameter elastic foundation in the thermal environment is studied using the third-order shear deformation beam theory. The material properties are temperature-dependent and vary continuously through the thickness direction of the beam, based on a power-law distribution in terms of the volume fraction of the material constituents. In order to discretize the governing equations, the differential quadrature method (DQM) in conjunction with the Hamilton’s principle is adopted. The convergence of the method is demonstrated. In order to validate the results, comparisons are made with solutions available for the isotropic and FG beams. Through a comprehensive parametric study, the effect of various parameters involved on the FG beam was studied. It is concluded that the uniform temperature rise has more significant effect on the frequency parameters than the nonuniform case.

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the structural and acoustic analysis of the orthotropic plate under the thermal environment.

This paper concerns with a suspended cable in thermal environments under bi-frequency harmonic excitations, with a focus placed on the effect of temperature changes on one type of simultaneous resonance. First, the nonlinear equation of motion in thermal environments is obtained for the in-plane displacement of the cable. Then, the Galerkin method is employed to reduce the partial differential equation to an ordinary one. Second, based on the discretized form of the governing equation, the method of multiple scales is employed to obtain the second-order approximate solutions, with the stability characteristics determined. Third, numerical results are presented by using the perturbation method, together with numerical integration by the following means: frequency-response curves, time-displacement curves, phase-plane diagrams, and Poincare sections. The direct integration method is utilized to verify the results obtained by the perturbation method, while revealing more nonlinear dynamic behaviors induced by temperature changes. Both the softening and/or hardening behaviors, and the switching between them are observed for the cable in thermal environments. The response amplitude of the cable is very sensitive to temperature changes, but the number of circles in the phase diagrams and the number of cluster points in Poincaré sections is independent of the thermal effects in most cases. Finally, the vibration characteristics of the cable for different thermal expansion coefficients and temperature-dependent Young’s moduli are also investigated.

This paper is concerned with the nonlinear vibration and dynamic response of carbon nanotube (CNT) reinforced composite truncated conical shells resting on elastic foundations in a thermal environment. The material properties of shells are assumed to be temperature-dependent and graded in the thickness direction according to various linear functions. The nonlinear equations of motion are expressed in the form of two-component deflection function and solved by the analytical method. Detailed studies for the influences of various types of distribution and volume fractions of CNTs, geometrical parameters, Winkler and Pasternak elastic foundations on the dynamic response and nonlinear vibration of CNT polymer composite truncated conical shells are examined and the comparison study is carried out to verify the accuracy and efficiency of the proposed method.

This work presents the nonlinear post-buckling behavior of carbon nanotubes (CNTs) reinforced sandwich composite annular spherical (AS) shells supported by elastic foundations in the thermal environment. This paper takes advantage of the sandwich-structured configuration with three layers: two nanocomposite face sheets and an isotropic core to analyze the static problem. Due to the precious properties, CNTs are applied to reinforce nanocomposite face sheets of AS shells. The governing equations of the nonlinear mechanical response of CNTs reinforced sandwich-structured composite (SSC) AS shells are achieved by using the classical shell theory (CST) and taking von Kármán’s geometrical nonlinearity into account. Applying Airy’s stress function and an approximate solution, we propose a form of stress function for CNTs reinforced SSC AS shells. The detailed effects of different types of CNTs’ reinforcement and volume fractions, geometrical parameters, core to face sheet thickness ratio, Winkler and Pasternak elastic foundations on the nonlinear mechanical post-buckling analysis are examined.

In this study, the vibration suppression effect of a fiber reinforced polymer (FRP) spherical–cylindrical shell coated with the porous graphene platelet (PGP) in a thermal environment is investigated. The dynamic equilibrium equation is derived by combining the first-order shear deformation theory and the Rayleigh–Ritz approach, together with the virtual spring technology and the multi-segment partition technique. After the free and forced vibration responses of this FRP combined shell with PGP coating are solved. The model is validated by the convergence analysis and comparison of the present results and literature or finite element results for different shell structures with and without coating under various boundary conditions. Using the present model, the parametric study is conducted to explore the effects of porosity distribution type, dispersion pattern of volume fraction porosity, nanofiller weight fraction, and thickness ratio of PGP coating on the transient response. This study provides a useful model and some suggestions for better improving the vibration suppression capability of coated shell structures in a thermal environment.

The thermal vibration characteristics of fiber-reinforced composite (FRC) cylindrical thin shells (FRCCTSs) coated with functionally graded porous graphene platelet (FGPGP) are investigated in this work, which is based on a theoretical model constructed by a mixed analytical and finite element method. Firstly, the porosity distributions of the FGPGP coating are assumed to be uniform or nonuniform along thickness direction with four porous forms of coating being taken into account. Next, the displacement field functions along with the axial, circumferential, and transverse directions are assumed on the basis of Love’s first-order approximation theory. Furthermore, this coated thin shell is discretized by the four-node shell element method to calculate the mass and stiffness matrices, with the artificial spring technology being adopted to simulate arbitrary boundary conditions. After the frequency parameters and dynamic responses are successfully solved, the proposed model with and without coating material is roughly validated by comparing with literature results at different boundary conditions without considering the temperature effect. Meanwhile, by utilizing the natural frequencies and vibration responses measured via a thermal vibration experiment bench, the comprehensive verification is performed within a temperature range of 20–200^∘C. Finally, parametric studies are undertaken to study the influences of boundary condition, porosity distribution of coating, fiber layup pattern, the predefined thickness ratio, and elastic modulus ratio on the corresponding thermal vibration properties.

In this paper, the isogeometric method is developed to study mechanical buckling behavior of nanocomposite plates reinforced by graphene sheets with temperature-dependent (TD) material properties in thermal environment. The plate is separately subjected to in-plane uniaxial, biaxial and shear loadings. It is assumed that the plate has different number of layers. By considering different volume fraction for each layer of graphene sheets, different functionally graded (FG) patterns of graphene sheets may be achieved. Furthermore, in some cases, it is considered that more than one FG patterns exist along the plate thickness. The energy statement of the plate is obtained using a logarithmic higher-order shear deformation theory (HSDT). Then, the isogeometric method is used to establish the desired eigenvalue problem. The comparison and convergence studies are presented for a wide range of numerical examples in all considered cases to show the correctness and ability of the solution. Afterwards, by presenting a set of numerical examples, the effects of plate significant parameters on the critical buckling load of the plate are examined. It is shown that the highest critical buckling loads occur when the plate has the minimum number of layers.

Currently, few studies are focused on the stationary random vibration for composite laminated shell structures of revolution (CLSSR), including composite laminated cylindrical shell (CLCY), composite laminated conical shells (CLCO), and composite laminated annular plates (CLAP). To fill this void corresponding to the above research in the literatures, a combination of the spectro-geometric method (SGM) and pseudo-excitation method (PEM) was developed to construct the theoretical model within the first-order shear deformation theory (FSDT). The different boundary restraints and coupling conditions were achieved by taking the appropriate stiffness values of artificial springs, and the thermal effect induced by thermal load was considered. Moreover, the Rayleigh–Ritz method was employed to deduce the governing differential equation. Further, the solution accuracy of the established model was assessed by comparing the obtained results with those from the literatures and the finite element method (FEM). Finally, the effect of specific parameters (i.e. fiber angle, temperature value and ply number) on the stationary random response of CLSSR was explored. According to the results, the proposed method proved effective for predicting the stationary random response characteristics of CLCY, CLCO, and CLAP in a thermal environment.

The excellent properties of graphene reinforced composites (GRC) enable them to be promising material candidates for developing high-performance and multifunctional devices and structures. When subjected to thermal environment, temperature can significantly affect the structural behaviors of these components. It is necessary to consider the effects of temperature while conducting structural analysis. This work first attempts to investigate the nonlinear vibration of functionally graded (FG) graphene nanoplatelet (GNP) reinforced composite (FG-GNPRC) dielectric beams with comprehensively considering the effects of FG distribution of the reinforcements, temperature, electrical field and damping. The established governing equations for the FG-GNPRC dielectric beam are discretized and solved by differential quadrature (DQ) and direct iterative methods. The numerical results demonstrate that the application of pre-strain can attenuate the effect of electric fields and temperature on the frequency ratio, resulting in a more stable structure. Among the FG distribution patterns as involved, the FG-GNPRC beam with profile $X$ exhibits lower frequency ratio and higher stability. This work is envisaged to provide guidelines for the design of FG-GNPRC structures with optimized performances in thermal environment.

The nonlinear buckling and postbuckling of functionally graded carbon nanotube reinforcement composite (FG-CNTRC) plates resting on the nonlinear effect of elastic foundation under combined load including external pressure and axial compression loads with uniformly distributed temperature rises are fully investigated in this paper. The FG-CNTRC plates are reinforced by FG-CNTRC stiffeners and the plate-foundation interaction is modeled using a nonlinear model. The higher-order shear deformation plate theory with the geometrical nonlinearities of von Kármán is applied to establish the basic formulations. Additionally, by using the anisotropic higher-order shear deformation beam theory, a new smeared stiffener technique is successfully developed for FG-CNTRC stiffeners. Galerkin’s method is used to achieve the equilibrium equation system in the nonlinear algebraic forms, and the critical load and postbuckling load–deflection curve expression are explicitly determined. The numerical investigations discuss the influences of FG-CNTRC stiffeners, hardening/softening nonlinear elastic foundation, uniformly distributed temperature rises, geometrical and material features on nonlinear stability of stiffened FG-CNTRC plates.

A meshless model is proposed to carry out the free and stationary stochastic vibration analysis of the functionally graded combined rectangular and cylindrical shells (FG-CRCS) structure under the aerodynamic and thermal environment. The FG-CRCS structure contains three combined structure types including rectangular–cylindrical shell (RC-type), cylindrical–rectangular–cylindrical shell (CRC-type), and closed rectangular–semicylindrical shell (CRS-type). The effects of aerodynamic and thermal loads on the dynamic behaviors of the FG-CRCS structure with temperature-dependency of material properties are investigated by introducing the supersonic piston theory and thermo-elastic theory. Furthermore, the pseudo-excitation method (PEM) is adopted to simulate the random loads applied to the FG-CRCS structure. The dynamic equations of the FG-CRCS structure are established in the theoretical frame of the first-order shear deformation theory (FSDT), whose general boundary conditions and coupling relationship are regulated by the artificial springs. Then, the reasonableness of this meshless model to predict free and random vibrations in aerodynamic and thermal environments is verified by comparing it with published literature and FEM results. On this basis, the contribution of essential parameters (including the aerodynamic load, thermal load, and boundary condition) on the free and random vibration behaviors of the FG-CRCS structure is presented, which may serve as guidance for the design of the plate–shell coupled structures in aerospace.

The utilization of functionally graded graphene platelet-reinforced composites (FG-GPLRC) and honeycomb sandwich constructions is prevalent in the field of engineering. Therefore, it is crucial to investigate the buckling and vibration properties of these materials under heat circumstances. This paper specifically focuses on the vibration and thermal buckling characteristics of a novel multi-arc concave honeycomb sandwich plate (MACHSP) equipped with an adjustable positive-negative Poisson’s ratio. The governing equations of motion for the system are derived based on the first-order shear deformation theory in conjunction with Hamilton’s principle. The formulation of the system’s characteristic equation involves the establishment of displacement functions that satisfy distinct boundary conditions. Using computational programming, natural frequencies, mode shapes, and critical buckling temperatures of MACHSP with three different FG-GPLRC distributions under thermal influences are determined. Subsequently, these results are compared with outcomes from finite element simulations and findings from previously published literature. Additionally, the amplitude-frequency response characteristics of the structure under harmonic excitation are analyzed, followed by a discussion of the impact of structural parameters on its buckling and vibration characteristics. The results indicate that the established theoretical model for predicting the buckling and vibration characteristics of MACHSP with FG-GPLRC distribution aligns well with simulation models and prior research. In contrast to solid plates, MACHSP not only achieves a substantial reduction in weight but also demonstrates a significant increase in natural frequency. Furthermore, graphene platelets have the potential to enhance the structure’s natural frequency values and critical buckling temperatures. Lastly, various structural parameters exert a notable influence on the structure’s performance.

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners.

Boundary slip effect caused by low gas density has an important influence on the thermal environment of the vehicles. Numerical studies on the boundary slip effect and accommodation for moment and energy have been carried out in this paper. The simulations considering slip boundary and surface catalysis are validated with Arc-jet test data. Mechanism and rules of impact on surface heat flux by different boundary slip level (Knudsen number from 0.0028 to 0.05) has been investigated in typical hypersonic flow conditions. The results show that mechanisms of boundary slip effect on mass diffusion heat flux and convective heat flux are different; slip boundary diminishes the convective heat, whereas enhances the mass diffusion heat flux. Smaller moment and energy accommodation coefficient is equivalent to more rarefaction. As Knudsen number goes up, the influences of accommodation on heatflux are enhanced, it mainly affects the convective heat flux.

This paper adopts the Moving Kriging (MK) interpolation meshless method to analyze the static and dynamic behaviors of stiffened functionally graded material (FGM) plate in thermal environment based on the physical neutral surface. The ribbed FGM plate is regarded as a composite structure of a FGM plate and ribs. The displacement transformation relationship between stiffeners and FGM plates is obtained through the displacement compatible conditions and MK interpolation. The meshfree model for ribbed FGM plate is obtained by superimposing the total energy of the FGM plate and the stiffeners based on the first-order shear deformation theory (FSDT) and physical neutral surface. The nonlinear temperature field along thickness direction is introduced into the meshless model of stiffened FGM plate. The equations governing the bending and free vibration of the ribbed FGM plate in thermal environment are obtained according to the principle of Minimum Potential Energy and Hamilton’s Principle. Thereafter, several ribbed FGM plate examples in different temperatures and with different locations of ribs are calculated. The results are compared with those given by the ABAQUS and literature. The results show that the effectiveness and accuracy of the proposed method in analyzing the ribbed FGM plate in thermal environment.

The free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates rested on two-parameter elastic foundation and in thermal environment is presented. The formulation is based on the first-order shear deformation theory (FSDT). The material properties are assumed to be temperature-dependent and graded in the thickness direction. The solution procedure is composed of transforming the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. After studying the convergence of the method, its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for isotropic rectangular and FG rectangular and skew plates. Then, the effects of thickness-to-length ratio, elastic foundation parameters, volume fraction index, geometrical shape and the boundary conditions on the frequency parameters of the FG plates are studied.

A study on vibration and acoustic radiation characters of an isotropic rectangular thin plate under thermal environments is presented in this paper. It is assumed that thermal loads caused by thermal environments just change the structure stress state. Thermal stresses induced by uniform temperature rise of the plate are determined with the thermo-elastic theory. Then the stress state is used in the following dynamic analysis as a pre-stressed factor. It is observed that thermal loads influence the natural frequencies evidently, especially the fundamental natural frequency. The order of mode shapes stays the same. Dynamic response peaks float to lower frequency range with the increment of structure temperature. Acoustic radiation efficiency of the plate subjected to thermal loads decreases in the mid-frequency band. For validation, numerical simulations are also carried out. It can be found that the combined approach of finite element method (FEM) and boundary element method (BEM) is more appropriate for radiation problems.