Abstract
The influence of complex pre-stress on the circular thin plate is investigated in this study to solve the non-uniform stress distribution problem. The differential equation of the circular plate with complex pre-stress distribution is derived based on the strain-displacement equation. The analytical method of free vibration for the circular plate with complex pre-stress distribution is proposed, in which the complex pre-stress and displacement function of the circular plate are expanded into the cosine trigonometric series. The influence of the different types of welding residual stress distribution on the natural frequency and the mode shape of the circular plate structure is compared. Finally, the effectiveness of the proposed model is verified through finite element method.
Highlights
The circular thin plate structure is widely used in marine, aerospace, and automotive engineering
The forces and moments that act on the element body consist of two parts when the circular plate structure is vibrating, that is, the force and moment caused by the vibration displacement and the coupling force caused by the vibration displacement and pre-stress
The analytical solution can be applied to the circular plate structure with arbitrarily distributed stress and has a wide range of applications than previous analytical methods
Summary
The circular thin plate structure is widely used in marine, aerospace, and automotive engineering. Few works have stated the solution for the vibration problem of a circular plate with welding residual stress distribution despite its frequent existence in structure. The present study aims to provide an efficient analytical method for a circular plate structure with non-uniform pre-stress distributions. This remainder of this paper is organized as follows.
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