A vibration solution method for plates with arbitrary elliptical openings based on elliptical energy elements

By constructing an elliptical energy element and Gauss-Legendre integral method in a dimensionless coordinate system, the computational complexity problem of the vibration response of an elliptical plate with a hole is solved, and high-precision vibration solution and numerical integration are achieved. It is suitable for elliptical plates with arbitrary shapes and hole positions.

CN120579345BActive Publication Date: 2025-09-30NORTHWESTERN POLYTECHNICAL UNIV
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Patent Information

Application Number
CN202511056225.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-07-30
Publication Date
2025-09-30
Estimated Expiration
2045-07-30

AI Technical Summary

Technical Problem

When solving the vibration response of an elliptical hole plate, the existing technology requires conversion between the rectangular coordinate system and the polar coordinate system, which makes the calculation complex and non-standardized, making it difficult to solve the vibration problem of an elliptical hole plate of any shape with high precision.

Method used

Using a method based on elliptic energy elements, an elliptic equation is constructed in a dimensionless coordinate system. Combined with Legendre polynomials and boundary condition functions, high-precision numerical integration is achieved through geometric Boolean operations and Gauss-Legendre integral method, and energy functional and matrix integration formulas are established to solve the vibration problem.

Benefits of technology

High-precision numerical integration and vibration solution of elliptical hole plates of arbitrary shapes in a dimensionless coordinate system are achieved. The calculation process is standardized and applicable to elliptical holes of arbitrary number and position.

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Abstract

The present application discloses a vibration solution method for an elliptical perforated plate of arbitrary shape based on an elliptical energy element, which belongs to the field of thin-walled structure technology and includes: overall mapping of the elliptical perforated plate of arbitrary shape, establishing the elliptical equation in a dimensionless coordinate system, and implementing Boolean operation modeling on the geometry; constructing a boundary condition function to simulate the constraint; simulating the plate deformation according to the first-order shear deformation theory, and constructing a global test function in combination with Legendre polynomials and boundary condition functions; establishing a total energy functional based on the minimum potential energy principle and the Ritz method, solving the stationary value of the total energy functional, and obtaining the calculation formula of each element in the stiffness matrix and the mass matrix; constructing an elliptical energy element based on local mapping, and numerically integrating each element of the matrix based on the elliptical energy element and completing the solution to the vibration problem. In this method, the energy functional and the numerical integration formula are both constructed on the square solution domain in the overall mapping stage, so that the calculation and solution process for the elliptical perforated plate of arbitrary shape is completely standard.
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