Effect of Winkler foundation, inhomogeneity and orthotropy on the frequency of plates

Abstract

This study investigates the frequencies of inhomogeneous orthotropic plates on elastic foundation. The inhomogeneity of orthotropic materials varies linearly with the coordinates of length and thickness. The basic equation is derived applying the Donnell-Mushtari theory and solved using the Galerkin method. The effects of inhomogeneity, Winkler elastic foundation and orthotropy on the frequencies are investigated in detail.

Analysis free oscillations of a non-homogeneous pipe along's thickness and length, taking into account the resistance of the external environment

“…It is considered that, modulus of elasticity E of the pipe material and density ρ -thickness and length vary continuously [6]:…”

“…In arbitrary approximation ω 2 (13) the algebraic line is determined from the system equation. Since the system consists of a system of homogeneous equations, the main determinant must be zero in the absence of its trivial solution [6,10]:…”