This study presents a comprehensive investigation into the free vibration characteristics of an advanced composite sandwich plate featuring a novel viscoelastic auxetic core and three-phase functionally graded face layers. The research aims to characterize the synergistic damping effects arising from the combination of negative Poisson's ratio (NPR) geometry and viscoelastic behavior. The face layers consist of a three-phase functionally graded composite comprising graphene nanoplatelets (GPLs), graphite fibers, and polyimide matrix, with effective properties determined using the Halpin–Tsai micromechanical model. The auxetic core's structural properties are derived from Gibson's model, while its viscoelastic behavior is captured using the standard four-parameter Burger model. The governing equations are formulated based on Reddy's third-order shear deformation theory (TSDT) and solved using the Galerkin method. The parametric analysis shows that the viscoelastic auxetic (NPR) core significantly enhances damping performance, nearly doubling it compared to the conventional honeycomb configuration. The FG-VA distribution pattern yields the highest natural frequencies, while increased viscoelastic Burger model parameters substantially improve the plate’s loss factors. Additionally, an increase in the core-to-total thickness ratio and elastic foundation parameters also markedly increases the plate’s natural frequency. The combined use of auxetic geometry and the viscoelastic Burger model, which represents the novelty of this study, results in significantly enhanced vibration damping compared to conventional sandwich lattice structures. This work establishes a foundation for designing high-performance sandwich structures with tailored dynamic properties for engineering applications.

This study presents a mechanical analysis of sandwich panels composed of composite facesheets reinforced with graphene platelets (GPLs) and a functionally graded viscoelastic (FG-VE) core. The viscoelastic behavior of the core is characterized using Boltzmann's superposition principle and a Prony-series representation. The governing equations are derived based on three-dimensional elasticity theory and reformulated within a state-space framework through the corresponding stress-strain relations. To evaluate the time-dependent viscoelastic response, the Boltzmann integral is transformed into the Laplace domain and subsequently inverted to the time domain using Durbin's numerical inversion technique based on Fourier series. The structural response is examined under various boundary conditions, including simply supported, clamped, and free edges. Analytical solutions are obtained for simply supported configurations via Navier's method, while general boundary conditions are treated using the differential quadrature method (DQM), providing efficient and accurate computation of static responses. The proposed formulation is validated against available benchmark solutions. Parametric studies are conducted to investigate the influence of geometry, material gradation, GPL distribution patterns, boundary conditions, and length-to-radius ratio on the overall behavior of the sandwich structure. To the best of the authors' knowledge, the mechanical behavior of sandwich panels with a FG-VE core has not been previously reported in the literature. This study presents the first unified theoretical framework capable of capturing the coupled effects of core viscoelasticity, functional grading, and GPL reinforcement. Moreover, the combination of Laplace-domain transformation and state-space formulation for FG-VE sandwich panels offers a novel and computationally efficient approach for predicting time-dependent structural responses. The results provide useful insights for the design and optimization of advanced FG viscoelastic sandwich panels with improved mechanical performance.

This paper presents a comprehensive analysis of the free vibrations of a sandwich panel composed of a viscoelastic core and composite face sheets reinforced with graphene platelets. It considers various common patterns of graphene distribution throughout the panel's thickness. The viscoelastic core is modeled using the Boltzmann superposition integral and Prony series. The governing equations are derived from three-dimensional elasticity theory and reformulated into state-space equations. Unlike previous studies, which often utilize simplified models, this research employs exact elasticity theory, combined with rigorous modeling of the viscoelastic core, to achieve greater accuracy and broader applicability. To address the computational complexity associated with the viscoelastic formulation, the equations are transformed from the time domain to the Laplace domain. Radial (through-thickness) boundary conditions are implemented using the state-space technique, while in-plane (axial and circumferential) boundary conditions-such as clamped, simply supported, and free edges-are managed through both analytical solutions (Navier's method) and the differential quadrature method (DQM). This proposed hybrid approach enables efficient and precise analysis under various boundary conditions. Validation is conducted by comparing the numerical results with those available in existing literature.

Three-dimensional static behavior of cylindrical sandwich panels with a viscoelastic polymer core and functionally graded graphene platelets-reinforced composite (FG-GPLRC) face sheets, subjected to transverse uniform pressure and under various boundary conditions is investigated. For the case of simply supported boundary conditions, an analytical approach using Fourier series expansion in the circumferential and axial directions, combined with the state-space technique in the radial direction, is developed. For other types of boundary conditions, a semi-analytical solution employing the numerical differential quadrature method (DQM) in the circumferential and axial directions, along with the state-space method in the radial direction, is utilized. The governing equations are solved in the Laplace domain, and the obtained results are transformed back to the time domain using a numerical inverse Laplace transform method. Uniform and four types of functionally graded (FG) graphene distributions in the faces are considered. The mechanical properties of the composite face sheets are determined using the Halpin–Tsai model and the rule of mixtures. The time-dependent behavior of the viscoelastic core is modeled according to Boltzmann's superposition principle, and the relaxation modulus is defined using the Prony series based on the generalized Maxwell model. A numerical comparison is made with available published results to assess the validity of the present approach. Stress and displacement curves are plotted, and the effects of panel’s geometry, distribution patterns and weight fraction of graphene platelets (GPL) in the face sheets, boundary conditions, and elapsed time since the start of loading are discussed.

Functionally graded (FG) beams are critically important in advanced engineering applications due to their ability to tailor material properties for improved performance under extreme conditions. This study investigates the static and vibration behaviors of a sandwich beam with a functionally graded material (FGM) core and viscoelastic interfaces based on the two-dimensional theory of elasticity. Young's Module and material density of functionally graded material (FGM) core is assumed to vary exponentially in thickness direction and the Poisson's ratio is held constant. In bending analysis, the sandwich beam is subjected to uniform pressure at the top surface whereas the bottom surface is traction-free. State space differential equations are derived using differential equations of motion as well as stress-displacement relations. For simply supported boundary conditions, these equations are solved analytically by using Fourier series expansion along the longitudinal direction, and other boundary conditions are solved semi-analytically using one-dimensional differential quadrature method (DQM) along the axial direction and state space across the transverse direction. Imperfect interfaces are modeled by the Kelvin-Voigt viscoelastic law. Time-dependent behavior is specified by dissolving the first-order differential equation of sliding displacement at the viscoelastic interfaces. Moreover, the influence of solid/elastic/viscoelastic interfaces, different boundary conditions, length-to-thickness ratio, elastic spring coefficient, and time passing on the static and vibration behavior of the beam are investigated. Major insights include the significant impact of imperfect bonding on vibration and bending behavior, discontinuity in transverse displacement for elastic and viscoelastic models, and higher transverse stresses in solid interfaces compared to viscoelastic ones.

The present research explores the vibration characteristics of circular sandwich plates with electro-rheological (ER) core and carbon nanotubes (CNTs) reinforced face sheets. The material attributes of the ER core are considered according to the Yalcintas and Don models. Nanocomposite layers include a Polyvinylidene fluoride (PVDF) matrix, and their CNTs are functionally graded (FG) or distributed uniformly along the plate thickness. The extended mixture rule (EMR) approach is applied to acquire the material properties of nanocomposite face sheets. First-order shear deformation theory (FSDT) is exploited, and the extended Hamilton’s principle is adopted to extract the motion equations. The impacts of diverse parameters, including the core-to-face sheets thickness ratio, different CNT distributions in face sheets, external electric field intensity, and volume fractions of CNTs on vibration features of circular sandwich plates, are inspected. The differential quadrature method (DQM) approximates the modal loss factor (MLF) and vibration frequency of ER sandwich plates for diverse edge conditions. The presented findings are validated by comparing them with the published results in the technical literature. The findings illustrated that the ER sandwich plates exhibit a higher natural frequency as the volume fraction of CNTs in face sheets is enhanced. Additionally, the vibrational characteristics of ER sandwich plates can be controlled by fine-adjusting the external electric field intensity. The insights gained from this research can be effectively employed in designing and developing intelligent sandwich structures with enhanced control capabilities.

In this article the bending behavior of sandwich plates with a Functionally Graded (FG) core with Boltzmann-type viscoelastic behavior integrated with piezoelectric layers at the top and bottom surfaces, is reported under electrothermomechanical loading within the framework of three-dimensional elasticity theory. For various boundary conditions, differential quadrature method (DQM) is used to obtain a semi-analytical solution along the in-plane coordinate axes. The present formulation is validated by comparing numerical results on bending, and stress with those published in the literature. A complete parametric study is performed to reveal the effect of different parameters such as length to thickness ratio, temperature gradient, mechanical loading, piezo-to-core thickness ratio, relaxation time constant, and applied voltage on the bending behavior of sandwich rectangular plates. The results show that an increase in the relaxation time leads to a decrease in the deflection of the plate; Also due to the applied voltage, the deflection curve along-the-thickness is nonlinear for the FG viscoelastic core; but it was linear in both piezoelectric layers.

This study presents a comprehensive analysis of the static and free vibration behavior of a functionally graded carbon nanotube-reinforced FGM (functionally graded material) cylindrical panel embedded in piezoelectric layers and subjected to simply supported boundary conditions. While earlier studies have mainly addressed rectangular plates and complete cylindrical shells, the present investigation focuses on cylindrical panels (imperfect cylindrical). The formulation is based on the three-dimensional theory of elasticity. The elastic modulus and density vary continuously through the thickness according to an exponential distribution function. The FG configuration for CNT is further categorized into four distinct distribution types that oriented along the radial direction. Previous investigations on complete cylindrical shells composed of functionally graded carbon nanotube-reinforced FGM have primarily employed energy-based methods to obtain solutions. In the present study, however, the problem is addressed within the rigorous framework of three-dimensional elasticity theory. The coupled electromechanical governing equations are analytically solved by employing a Fourier series expansion in the axial and circumferential directions, alongside the state-space method through the thickness coordinate. A detailed numerical study is conducted to investigate the influence of the material gradient index, CNT volume fraction, piezoelectric layer thickness, and mid-radius-to-thickness ratio of the FGM panel.

In this study, free vibration and damping behavior of cylindrical sandwich panel with electro-rheological core and graphene platelets reinforced composite (GPLRC) facing sheets based on first-order shear deformation theory of thick cylindrical shells referred by Qatu (FSDTQ) is investigated. Effective material properties of graphene platelets reinforced composite are determined according to the Halpin–Tsai micromechanical model. The governing equations of motion with required boundary conditions are derived using Hamilton’s principle. Afterward, these equations are solved analytically using the Fourier series solution for simply-supported boundary conditions, and for the other edges boundary conditions, we used the generalized differential quadrature method. The exactness and correctness of the present formulation are validated by comparing the results with those of existing literature. Finally, the influences of various parameters such as the electric fields, geometrically parameters, boundary conditions, the volume fraction of GPL, and GPL distributions pattern on vibration behavior and modal loss factor is examined. According to the results, the influence of the GPL volume fraction and electric field on the frequencies and modal loss factor is significant. This achievement can help design intelligent controlling structures for various applications.

This research has been conducted to analyze the free vibration behavior of a five-layered composite plate with a viscoelastic auxetic core. The plate comprises a viscoelastic auxetic core layer, functionally graded carbon nanotube reinforced composite (FG-CNTRC) interior, and magneto-electro-elastic functionally graded porous (MEE-FGP) exterior skins, which is rested on Winkler-Pasternak foundation. According to the magnetic-electric boundary conditions and Maxwell equations, the electric and magnetic potentials of the plate are determined. The macro-mechanical properties of the auxetic core have been derived based on Gibson's model; the three-parameter Zener model has also been utilized to describe its viscoelastic behavior. Additionally, the equations of motion of the plate are obtained and solved by using Reddy's third-order shear deformation theory (TSDT) and the Galerkin method, respectively. Moreover, various aspects of the current research have been validated by comparing the numerical results with those reported in the literature section. Overall, in the numerical result section, the effects of different parameters and conditions such as geometrical parameters, position of the plate's interfaces of layers (thickness of the core and face layers), various distribution patterns and volume fractions of both CNT and porosity, external work parameters of the MEE skins, boundary conditions, Winkler-Pasternak stiffness coefficients, the relaxation time, and other parameters of the viscoelastic core on the natural frequency and loss factor of the composite plate are represented.

The main objective of this study is to investigate the vibration and static analysis of a sandwich composite plate in the hygrothermal environment. The plate consists of three layers such as an Aluminum auxetic core and Graphene platelet-reinforced composite (GPLRC) facing sheets. Based on the Halpin-Tsai theory and Gibson's model, the macro mechanical properties of facing sheets and auxetic core are derived. Via Reddy's third-order shear deformation theory (TSDT), the equations of motion of the sandwich plate are obtained and solved by both Navier and the generalized differential quadrature method (GDQM). The current formulation is validated by comparing the numerical results with those that are reported in the literature. Finally, the influence of different parameters such as the inclined angle of auxetic cells, thickness to the length, and core to total thickness on the natural frequencies, deflection and stresses of the sandwich plate, is examined. Even though some studies have been conducted to investigate the bending or vibration behavior of sandwich structures with negative Poisson's ratio (NPR) cores, the bending and vibration behavior of such structures in the hygrothermal environment is remained unexplored. Additionally, the analysis of stress component variations along the thickness of the plate was a novel feature that has not been addressed in prior studies on the similar structure.

The present research aims to examine the free vibrational behavior of a sandwich plate comprising a viscoelastic auxetic core and functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) face layers, which are rested on a Winkler–Pasternak foundation. The macro-mechanical characteristics of the plate’s skins have been determined utilizing the Halpin–Tsai theory. Additionally, for the core layer, besides the features characterized using Gibson’s model, the Zener model is employed to describe its viscoelastic behavior. The equations of motion for the sandwich plate were derived based on Reddy’s third-order shear deformation theory (TSDT), and they were solved using the Galerkin method. To validate the numerical results of the current study, they have been compared with findings documented in prior ones. Overall, the effects of several parameters such as geometrical parameters, various GPL distribution patterns, boundary conditions, Winkler–Pasternak coefficients, and the volume fractions of GPL have been investigated on the natural frequency and loss factor of the sandwich plate.

This research numerically and analytically examines the dynamics of underwater movable porous functional gradient (FG) microsize beams integrated with a piezoelectric layer. Also, the efficiency and accuracy of support vector machine (SVM) techniques in the vibration prediction of the microbeam are assessed. The dynamical simulation is conducted by considering the assumptions of Rayleigh beam theory, different porosity distribution models, nonlinear and linear stress-temperature relationships, and modified couple stress theory (MCST). The eigenvalues of the system, critical temperature increment, and critical speed of the microbeam are computed. Comparative studies are carried out, frequency analyses are performed, and stability diagrams are drawn. The impacts of microbeam geometry, fluid mass ratio, piezoelectric voltage, and axial force on stability behavior in variable complex environmental conditions are parametrically inspected. The outcomes revealed that the smaller the contribution of voids on the outer surface of the microbeam, the better the microbeam stability. It is understood that among the utilized regression-based SVMs, the quadratic polynomial and medium Gaussian kernel models have the highest performance and speed, respectively. These research outcomes will be advantageous for designing the next generation of targeted drug delivery devices.

This paper deals with the nonlinear vibration behavior of sandwich panels composed of Graphene platelet reinforced composite (GPLRC) skins and auxetic core embedded with piezoelectric layers subjected to the thermo-magneto-electric loading. The nonlinear equations are obtained by applying Hamilton’s principles in the framework of higher-order shear deformation theory (HSDT) and von Karman’s nonlinear theory. Linear and nonlinear equations of motion are solved by applying the differential quadrature method (DQM) and homotopy perturbation technique, respectively. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of auxetic core, applied voltage, magnetic potential, GPL volume fraction, different boundary conditions, and temperature rise on the nonlinear frequency response of sandwich panel are studied. From numerical results, it was concluded that the sandwich panel incorporating auxetic core and piezoelectric layers could increase the magneto-electrical power output.

In this paper, thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) are investigated within the framework of third-order shear deformation theory (TSDT). CNT distribution along the thickness direction of the plate is uniformly or functionally graded. The equivalent properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations of motion are derived using the Hamilton principle. Obtained governing differential equations are analyzed by utilizing Fourier series expansion along the longitudinal and latitudinal direction for simply supported edges boundary conditions whereas for other edges boundary conditions we used the differential quadrature method (DQM) to solve numerically. Validation of the present formulation is assessed by comparing the results with those reported in the open literature. The effect of CNT volume fraction, the different patterns of CNT distribution, temperature difference, aspect ratio, and thickness-to-length ratio on buckling and vibration behavior of carbon nanotube-reinforced composite (CNTRC) plate is studied. The numerical illustration reveals that in the FG-X pattern of CNT distribution natural frequency and thermal buckling load is more significant compared with the other patterns of CNT distribution.

In this research, the stability, and vibrational characteristics of functionally graded single-walled carbon nanotube-reinforced composite (FG-SWCNTRC) plates resting on a Visco-Hetenyi medium are perused based on a 12 unknown higher-order shear deformation theory (HSDT). The system is subjected to hygro-thermal environments and both compressive and tensile in-plane loads in both x- and y-direction. In addition to both linear and nonlinear thermal conditions, a two-dimensional (2D) magnetic field's effects on the stability of the system are studied. The governing equations of motion are solved numerically by means of the generalized differential quadrature method (GDQM) due to its capability to consider the various geometric boundary conditions (BCs). In order to validate the current work, a comparative study is accomplished between the present outcomes and reported ones in the open literature. The impact of the carbon nanotube (CNT) volume fraction, patterns of CNT distribution, environmental attacks, magnetic field strength and direction, structure aspect ratios, BCs, and foundation types on the vibrational behavior of the considered structure are scrutinized. Obtained results represent that considering the impacts of in-plane tensile forces and the magnetic field in modeling improves the system's vibrational behavior. While imposing the hygro-thermal effects similar to the axial compressive loads have destabilizing influences on the system and make the structure more vulnerable to static instability. Moreover, uncertain conditions are assessed for sensitive parameters which have effects on the performance of the system. Finally, using a supervised neural network (NN) learning approach, the accuracy of the model is proved.

The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated.

In this study, the free vibration behavior of an embedded sandwich beam consisting of an aluminum auxetic core and two polymer nanocomposite face sheets reinforced with carbon nanotubes (CNTs) was investigated. The CNTs were dispersed along the thickness of the face sheets through various functionally graded (FG) and uniformly distributed (UD) patterns (i.e., FG-X, FG-V, FG-O, and UD). In addition, the structure was embedded on a Winkler-Pasternak elastic substrate in order to make the problem more realistic. The effective material properties of the face sheets and the core were estimated using the extended rule of mixtures and the relations of the auxetic materials, respectively. Next, the governing differential equations were derived based on the incorporation of the first-order shear deformation theory and Hamilton's principle. To obtain the natural frequencies of the structure, the differential equations were solved by implementing the generalized differential quadrature method, which is a well-known numerical strategy. In addition, the results were validated by comparing them with the results obtained in a reputed literature study, in which perfect agreement was achieved. Finally, the influences of various parameters such as the length-to-thickness ratio, cell inclined angle, substrate parameters, CNT volume fractions, various boundary conditions, and core-to-face sheet ratio on the first natural frequency of the sandwich beam were investigated.

In this study, nonlinear aeroelastic instability of a composite sandwich panel subjected to a supersonic airflow and thermal loading is investigated. The sandwich panel is composed of three-phase composites with polymer/Graphene platelet/fiber skins at the top and bottom surfaces and an auxetic honeycombs core layer with a negative Poisson’s ratio. The motion equations of the panel within the framework of higher-order shear deformation theory (HSDT) and von Kármán nonlinearity are driven. In addition to Krumhaar’s modified supersonic piston, unsteady aerodynamic pressure in the supersonic flow regime is considered. The governing equations of the sandwich panel are derived by implementing Hamilton’s principle and solved by the generalized differential quadrature method (GDQM). Validation of the present formulation is assessed by comparing the numerical results with those available in the open literature. Then, the effects of several parameters such as geometric parameters, volume fraction, Mach number, different boundary conditions, yaw angle, and different inclined angles on the nonlinear aeroelastic stability of sandwich panels are examined. Finally, it was found that the ratio of core thickness, inclined angle, and Mach number have significant effects on aerodynamic pressure.

This study deal with the nonlinear vibration of sandwich panel, composed of functionally graded material (FGM) skins and double U auxetic core subjected to heat conduction. The nonlinear equations are obtained by applying Hamilton's principles in framework higher order shear deformation theory (HSDT) and von Karman's nonlinear theory. Linear and nonlinear equations of motion are solved by applying the differential quadrature method (DQM) and homotopy perturbation technique, respectively. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of auxetic core, power-law exponent, different boundary conditions, and temperature gradient on the nonlinear frequencies of sandwich panel are studied. Finally, the important findings of this research indicate that the ratio of core thickness, inclined angle, and thickness to inclined length have significant effects on nonlinear frequency response. Based on the results of this article designers can development of different parts of aircraft.