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The main objective of this research work is focused on the vibration analysis of auxetic sandwich cylindrical shell structures resting on an elastic foundation. In the analysis, the sandwich shell structure is composed of three layers in which the middle layer consists of auxetic material with a negative Poisson's ratio, and the two skin layers are isotropic homogeneous materials. The motion equation is extracted according to the first-order shear deformation theory (FSDT) and the Hamilton principle. The governing equations of coupled partial differential equations are solved by the generalized differential quadrature (GDQ) method, and the natural frequencies are determined. By comparing the experimental results with the numerical results calculated by commercial finite element software, the validity of the proposed theoretical model is verified. Finally, the influences of geometrical parameters and elastic foundation on the vibration behavior of sandwich shell structures have been investigated. [ABSTRACT FROM AUTHOR]

The paper focuses on the nonlinear vibration of functionally graded graphene nanoplatelet reinforced composite doubly curved shallow shells resting on elastic foundations. The graphene nanoplatelet reinforced composites are assumed to be distributed uniformly and functionally graded through the thickness. The material properties are assumed to be temperature-dependent and are estimated through the Halpin–Tsai micromechanical model, while the Poisson's ratio, density mass, and thermal expansion are implemented by the rule of mixtures. The mathematical formulation is developed based on the classical shell theory and Von Karman-Donnell geometrical nonlinearity assumption. The dynamical responses of a simply supported functionally graded-graphene nanoplatelet reinforced composite doubly curved shallow shells are obtained by employing the Airy's stress function and the Galerkin's method. The responses of nonlinear vibration as time history, frequency-amplitude curve, phase plane graphs, and Poincare maps are carried out in this paper. In addition, the effects of the environment, graphene nanoplatelets weight fraction, graphene nanoplatelets distribution patterns, and thickness-to-length ratio are scrutinized. The obtained results are also compared and validated with those of other studies. [ABSTRACT FROM AUTHOR]

A new simple "four-variable shear deformation" plate model is proposed in this work to demonstrate the hygro-thermal environment effects on dynamic and buckling of functionally graded material "sandwich plates" supported by "Winkler–Pasternak" elastic foundations. Equations of motion are obtained from Hamilton's principle containing the hygro-thermal influences. This model uses only "four variables" and considers trigonometric variation of "transverse shear stress." In addition, these stresses become zero at the upper and lower surfaces of the "sandwich plate." The novelty of this formulation is the addition of the integral term in the field of displacement, which leads to a reduction of the number of unknowns and basic equations. Various kinds of functionally graded material "sandwich plates" are examined in this study. To verify the validity of the model, the calculated results are compared with the existing results. Comparison investigations reveal that the computed results of the proposed formulation are in excellent agreement with those of other "higher shear deformation theories." Parametric investigation is established to demonstrate the effects of temperature rise, moisture condition, elastic foundation coefficients, and power law index on the vibration and buckling of functionally graded material "sandwich plates." [ABSTRACT FROM AUTHOR]

This paper aims to present accurate solutions for flexural vibration of functionally graded sandwich plates resting on two-parameter elastic foundation with any combined boundary conditions. The governing equations of free vibration problem are derived from the first-order shear deformation theory that covers the important effects of shear deformation and rotary inertia. To solve the coupled differential equations governing vibration behavior of the plates with various boundary conditions, an effective tool, namely Chebyshev collocation method, is implemented to obtain the accurate solutions with several parametric studies. The influences of material volume fraction index, layer thickness ratio, side-to-height ratio, boundary conditions, etc., on natural frequencies of the plates are taken into investigation and discussed in details. Our numerical experiments reveal that the proposed method can offer the accurate frequency results of the plates as compared to those available in the literature. Additionally, the spring constants of elastic foundation have a significant impact on frequency changes of the plates. Increasing the values of spring constants leads to considerable increases of the frequencies. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

The nonlinear torsional buckling and post-buckling of ceramic functionally graded material (C-FGM-M) stiffened cylindrical shell surrounded by Pasternak elastic foundation in thermal environment are investigated in this paper. The C-FGM-M cylindrical shell is reinforced by ring and stringer stiffeners system in which the material properties of shell are assumed to be continuously graded in the thickness direction. Based on the classical shell theory, theoretical formulations are derived with the geometrical nonlinearity in von Karman sense and the smeared stiffeners technique. The three-term approximate solution of deflection is chosen more correctly and the explicit expression for finding critical load and post-buckling torsional load–deflection curves are given. The effects of geometrical parameters, temperature, stiffeners and elastic foundation are investigated. [ABSTRACT FROM AUTHOR]

In this study, the behavior of vibration of sandwich cylindrical shells covered by functionally graded coatings and resting on the Pasternak elastic foundation considering combined influences of shear stresses and rotary inertia are examined. It is assumed that the effective material properties of functionally graded coatings changes exponentially in thickness direction. The modified Donnell type equations of motion of functionally graded and homogeneous sandwich cylindrical shells on the Pasternak elastic foundation are deduced using the first-order shear deformation theory. Basic equations are reduced to an algebraic equation of the sixth order and numerically solving this algebraic equation gives the dimensionless fundamental frequency. The expressions for the dimensionless fundamental frequencies of functionally graded and ceramic coated sandwich cylindrical shells with and without taking into account the effects of Pasternak elastic foundation and shear stresses obtained in a special case. Calculations, the influences of an elastic foundation, compositional profiles of coatings, shear stresses, rotary inertia, and sandwich shell geometry parameters on the nondimensional fundamental frequency are described. The results are verified by comparing the obtained values with those in the existing literature. [ABSTRACT FROM AUTHOR]

Based on the three-dimensional elasticity theory, this paper focuses on the free vibration characteristics of functionally graded sandwich rectangular plates resting on Pasternak foundations. The two-constituent functionally graded plate consists of ceramic and metal. These constituents are graded through the thickness according to a three-parameter power-law distribution. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. In this research work, a detailed parametric study is carried out to highlight the influences of different profiles of fiber volume fraction, three parameters of power-law distribution and two-parameter elastic foundation modulus on the vibration characteristics of the functionally graded sandwich plates. [ABSTRACT FROM PUBLISHER]

This article focuses on dynamic stability of smart sandwich beams resting on Winkler elastic foundation subjected to harmonic axial loads. To increase the dynamic buckling load and the stability region of the beam, an electro-rheological layer is adhered as a core. The finite element method is employed to derive a three layer smart sandwich beam element. By inspecting dynamic response of the beam in different load amplitudes, critical dynamic loads are calculated. Parametric study is done to investigate effects of various parameters such as beam geometry, foundation stiffness, static load, applied voltage and properties of core layer on critical dynamic loads and stability regions of the beam. This study indicates that by applying electric field to the electro-rheological core, dynamic critical load and consequently, dynamic stability of the beam increase efficiently. Furthermore, the elastic foundation reduces the unstable region and increases the critical dynamic load of the smart beam. Proper use of these parameters makes the beam less sensitive to axial harmonic loading by relocating the instability region. [ABSTRACT FROM AUTHOR]

Panelized construction of residential buildings is gaining popularity due to the architectural and energy efficiency benefits that can be achieved. An important challenge to the design of panel structures for buildings is the balance between long-term structural performance and the thermal insulating requirement. In this study, foam core and web core panels are designed for residential roofs. Both panels are comprised of two face sheets and an insulating foam core. In the web core panel, thin metal webs that connect the face sheets are added to improve panel shear stiffness and enable longer spans. A design procedure is developed that considers R-value, panel deflection, core shear failure, bearing failure, and buckling of the face sheets and webs. The buckling model includes the ability of the foam core stiffness to restrain the buckling deformation. Panel designs are presented that provide R-5.3 m2 K/W for roof loads of 1500, 2000, and 3000 N/m2, corresponding to climate zones in the US. It is demonstrated that the web core panel can be designed for these structural and thermal requirements with unsupported span lengths as long as 7 m, while span lengths for foam core panels are limited to 4 m. Web shear buckling and R-value are the two performance criteria that limit panel span length and depth. [ABSTRACT FROM AUTHOR]