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• The free vibration and nonlinear dynamic response of sandwich plates with an auxetic honeycomb core and piezoelectric face sheets are freshly addressed. • An analytical solution based on the first-order deformation plate theory and von Karman-type nonlinear strain-displacement relationship is established for movable simply supported and immovable simply supported plates. • The Galerkin and Runge–Kutta fourth-order methods are used to solve the system of nonlinear differential equations and capture the displacement-time and acceleration-displacement curves. • New parametric studies regarding the influence of the material, geometrical parameters, and elastic foundation coefficients, the geometrical parameters of the auxetic honeycomb core layer, as well as the electric boundary condition on the free vibration and nonlinear dynamic response of piezoelectric-auxetic sandwich plates are examined. This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation. [ABSTRACT FROM AUTHOR]

A review of the literature reveals a dearth of works on functionally graded material sandwich shells having an auxetic core layer. This study contributes an analytical approach for the free vibration analysis of doubly curved stiffened sandwich shells with the face sheets of functionally graded materials and the core layer of the auxetic honeycomb material. The theoretical formulation is established based on first-order shear deformation theory associated with the smeared stiffener method. The free vibration solution of simply supported shallow shells with the rectangular platform is derived using Navier's form. The proposed methodology is general and can be applied to examine the natural frequencies of various shell types, including flat, cylindrical, spherical, and hyperbolic paraboloidal panels. Numerical results indicate that the fundamental frequency is largely influenced by the relative proportion of the constituent materials of the face layers, the geometrical parameters of the auxetic honeycomb core layer, as well as the stiffeners. Additionally, a simple optimization technique based on Rao algorithms is introduced to obtain the maximum fundamental frequency of the shell. It is shown that the shell parameters, particularly the thickness of the auxetic core and the number of stiffeners, can be tailored to maximize the natural frequency. Moreover, the optimal solutions are fully dependent on the material proportion of the functionally graded material, the geometry of the shell, and the geometrical parameters of the auxetic honeycomb core. • Free vibration of doubly curved stiffened sandwich shells with FGM faces and auxetic core is freshly addressed • Simple optimization technique based on Rao algorithms is introduced to obtain the maximum fundamental frequency of the shell • New parametric studies on the frequencies of doubly curved stiffened auxetic sandwich FGM shells are examined [ABSTRACT FROM AUTHOR]