Vibration analysis method of elastic plate structure

Abstract

The invention discloses a vibration analysis method of an elastic plate structure. The method includes the steps that the Carrera high-order interception technology is utilized for conducting fittingon the thickness-direction displacement of the elastic plate structure; the two-dimensional improved Fourier series is adopted for conducting full-solution-domain expansion on the plane displacement of the elastic plate structure; the overall displacement of the elastic plate structure is obtained through calculation based on the cross-section plane displacement and axial displacement of the elastic plate structure; the strain vector and stress vector of the elastic plate structure are calculated; a strain energy and kinetic energy equation of the elastic plate structure is calculated, and a virtual spring boundary is set to obtain boundary energy; a structural Lagrangian energy functional is established, and a kernel mass matrix and a stiffness matrix of the elastic plate structure are obtained through calculation; the overall mass matrix and stiffness matrix and the characteristic equation of the structure are obtained through an iterative loop kernel matrix; the inherent frequency of the elastic plate structure is calculated, and the vibration mode of the structure is output according to the feature vector. The method is suitable for elastic plate structures with multiple shapesand multiple boundary conditions, high in precision, fast in convergence and low in calculation cost.

Description

technical field [0001] The invention belongs to the field of structural dynamics, and in particular relates to a vibration analysis method of an elastic plate structure. Background technique [0002] Elastic plate structures are widely used in engineering equipment such as ships and ocean engineering, construction engineering, and aerospace, such as submarines, automobiles, and aircraft fuselages. In-depth study of the vibration characteristics of this type of structure and its parameter influence rules has important theoretical and practical guiding significance for the prediction of vibration and noise levels in the early design stage of equipment and the realization of low-noise design. [0003] The traditional elastic plate theory mainly includes thin plate bending theory and shear deformation theory, but the thin plate bending theory ignores the influence of strain, shear deformation and moment of inertia in the thickness direction of the structure, and is only suitable...

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Problems solved by technology

[0004] However, most of the existing Carnot high-order intercept fitting techniques solve the dynamic problems of elastic plate structures by embedding the finite element method (the typical literature is Carrera E. Theories and finite elements formultilayered, anisotropic, composite plates and shells[J ].Archives ofComputational Methods in Engineering,2002,9(2):87-140.Cinefra M,Valvano S.Avariable kinematic doubly-curved MITC9shell element for the analysis oflaminated composites[J].Mechanics of Advanced Materials&Structures,2016,23( 11): págs.1312-1325.), changing the shape or boundary conditions of the elastic plate often requires increasing the number of elements or even remodeling analysis. In addition, the finite element method generally has a large amount of calculation, low calculation accuracy, and the application of boundary conditions is more cumbersome and other shortcomings

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