KSCE Journal of Civil Engineering

, Volume 23, Issue 5, pp 2303–2312

# Nonlinear Vibration of a Stiffened Plate Considering the Existence of Initial Stresses

• Tian-Qi Wang
• Rong-Hui Wang
• Niu-Jing Ma
Structural Engineering

## Abstract

This paper presents a study on the nonlinear dynamic behavior of a stiffened plate with the existence of initial stresses. A stiffened plate is assumed to be composed of a plate and some stiffeners, which are treated separately. The plate is analyzed based on Thin Plate Theory, while the stiffeners are considered as geometrically nonlinear Euler-Bernoulli beams. The equations of both kinetic energies and strain energies of the plate and stiffeners are established. After that, the dynamic equilibrium equations for the stiffened plate are derived according to Lagrange equation. The nonlinear frequency for single-mode result is obtained through Elliptic function, and the accuracy of the analytical solution is verified through comparison with Ansys finite element method. In addition, homotopy analysis method is used to solve 3:1 internal resonance of the stiffened plate. With parametric analysis being conducted, the investigation on how initial stresses influence the nonlinear dynamic properties is carried out. Some useful nonlinear dynamic properties and conclusions are obtained, and thees can provide references for engineering application.

## Keywords

stiffened plates initial stresses nonlinear vibration frequency internal resonance

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