Nonlinear dynamic analysis of porous eccentrically stiffened double curved shallow auxetic shells in thermal environments

Abstract

Abstract In this paper, an analytical approach is proposed to investigate the nonlinear dynamic analysis of porous eccentrically stiffened (PES) double curved shallow auxetic shells with negative Poisson’s ratio (NPR) subjected to blast, mechanical and thermal loads resting on Visco-Pasternak foundation model. The three-layer double curved shallow shell consists of auxetic honeycombs core layer with NPR integrated, isotropic homogeneous materials at the top and bottom of surfaces. Besides, the outer surfaces of the system reinforced by PES are made of functionally graded materials (FGM) and auxetic shells are placed in thermal environments. Combining with the first-order shear deformation theory and Von-Karman strains, governing equations for nonlinear dynamic response of PES double curved shallow auxetic shells in thermal environments are derived. Then, the stress function and Galerkin methods are proposed to obtain the result equations: fundamental frequency, dynamic response, and frequency–amplitude relation. Compared with the published literature, the feasibility and accuracy of the proposed analysis approach are validated. Finally, the effects of stiffeners, Poisson’s ratio, cell inclined angle, mechanical, thermal and blast loads, elastic foundations, boundary conditions, geometrical parameters of auxetic honeycombs core and shell on the nonlinear dynamic response of PES double curved shallow auxetic shells in thermal environments are also carried out in the paper.