Abstract
The influence of the complex pre-stress on the circular plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain–stress equation, the motion differential equations of the circular thin plate with complex pre-stress distribution are derived. Based on the Rayleigh–Ritz theory of energy method, the complex pre-stress distribution function and vibration-displacement function are expanded into the cosine trigonometric series, and the approximate analytical solutions of structural free vibration for circular plate are proposed. A circular plate with simply supported boundary condition, for example, the effectiveness of the proposed method is confirmed through numerical calculations and the finite element method verification. The influence of different type’s distribution of welding residual stress on the natural frequency and mode shape for circular plate structure are compared. The proposed approach in present article can be used in arbitrary pre-stress distribution problem.
Highlights
The circular thin plate structure is widely used in marine, aerospace, and automotive engineering
The energy method based on Hamiltonian dual equations or Rayleigh–Ritz method becomes a hot issue in dynamic response analysis of the circular plate structure.[9,10,11]
The Rayleigh–Ritz method has extensively gained the attention of researchers because the assumed deflection functions are required to satisfy the geometrical boundary conditions only.[12,13]
Summary
The circular thin plate structure is widely used in marine, aerospace, and automotive engineering. The energy method based on Hamiltonian dual equations or Rayleigh–Ritz method becomes a hot issue in dynamic response analysis of the circular plate structure.[9,10,11] The Rayleigh–Ritz method has extensively gained the attention of researchers because the assumed deflection functions are required to satisfy the geometrical boundary conditions only.[12,13]. Pre-stress includes welding residual stress, assembly stresses, and hydrostatic pressure, and so on. These types of pre-stress are defined as complex pre-stress. The existence of pre-stress provides a considerable influence on the local and global stiffness matrices and on natural frequencies, mode shapes, dynamic response, and so on.[15,16] Nowadays, much of studies focused on models of uniformly distributed pre-stress, such as hydrostatic pressure or water pressure.[17,18] most of the existing studies are limited to a uniform or specific pre-stress distributions problem; nonuniform pre-stress distributions are often encountered, while the former methods cannot be used to solve this
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