Response of double-wall (sandwich) circular plates to random excitations - Analytical approach

Abstract

This article presents an analytical approach for the general response of double-wall circular plates subjected to random excitations. The excitations are either uniform random pressures or stationary random point loads. The double-wall construction is separated by a soft linear viscoelastic core. The equations of motion are developed for thin circular plates using Love's theory which has been modified to account for the coupling provided by the viscoelastic core. The analytical solution of forced response is obtained via modal decomposition and a Galerkin-type approach. Numerical results investigate the effect of coupling and structural parameters for response minimization. is soft, bending and shearing stresses in the core can be ne- glected, and consequently, its behavior can be described by a uniaxial constitutive law. Furthermore, the inertia effects of the core follow a linearly apportioned mass distribution law. The boundary conditions for the system are taken to be simply supported, which from a physical viewpoint represent either circular knife-edge supports or hinges. Henceforth, the boundary value problem is mathematically defined. The general solution of forced response is obtained via modal decomposition and a Galerkin-like approach.4'9'11 Ini- tially, the deflection response is written as a series expansion in terms of time-varying generalized coordinates, and the nor- mal modal eigenfunctions. The modal eigenfunctions are writ- ten in terms of Bessel functions, modified Bessel functions, and transcendental functions26 that are chosen to satisfy the appropriate boundary conditions. The arguments of the Bes- sel functions constitute solutions to the characteristic fre- quency equation obtained from the boundary conditions. Us- ing the orthogonality principle of the modal functions, the problem is reduced to a set of coupled differential equations for determining the generalized coordinates. Taking the Four- ier transformation of these equations and maximizing the so- lutions for generalized coordinates, the coupled natural fre- quencies for the system are obtained. The series solution for the complex response, in the frequency domain, is then given in terms of generalized coordinates and modal eigenfunctions. The spectral density of the response can be estimated by taking the mathematical expectation of the solution series.27 The finite element model employs the NASTRAN finite element code.28 It consists of 1026 nodes (6156 dof) and 1529