Natural Frequencies of Composite Lattice Structure Surrounded by Winkler--Pasternak Ambient using Galerkin Method

Abstract

. The present work contains an analytical expression and solution for free vibration problem of a composite lattice cylindrical shell surrounded by Winkler– Pasternak elastic foundation with clamped edges. The foundation is simulated using a large number of linear, homogenous shear and radial springs with variable stiffness. An integrated formula for calculation of the natural frequency of lattice structure and its foundation is derived from the equations of motion of the shell implemented by Winkler–Pasternak terms based on Fourier decomposition and Galerkin method. The fundamental frequency formula concerning the foundation elements and lattice parameters is an effective means of estimation frequency in earlier design phase and also a tool to assess the vibration analysis of composite lattice cylindrical shell surrounded by an elastic foundation in design analysis and numerical solutions. The results are verified and confirmed using finite element analysis which show a very good agreement.