Vibration analysis method for uniform section beam structure

Abstract

The invention provides a vibration analysis method for a uniform section beam structure. The method comprises the steps that geometric size characteristics of the beam structure are extracted, a displacement field of the beam structure is separated to be in-section displacement and axial displacement; fitting is performed on the in-section displacement of the beam structure; extension is performedon the axial displacement of the beam structure; the in-section displacement and the axial displacement of the beam structure are combined to calculate integral displacement of the beam structure; strain vectors and stress vectors of an elastic plate structure are calculated; strain energy, a kinetic energy equation and boundary energy of the beam structure are calculated; a structural Lagrange energy function is established to obtain a core mass matrix and a stiffness matrix of the beam structure; an integral mass matrix, an integral stiffness matrix and an overall mass matrix are solved through iterative looping of the core matrix, and then a characteristic equation of the structure is obtained; and a characteristic equation matrix of the beam structure is solved, and inherent frequencyand a vibration mode are obtained through calculation. The method is suitable for the beam structure with multiple boundary conditions and multiple section shapes and is high in precision, fast in convergence, low in calculation cost and simple in calculation method.

Description

technical field [0001] The invention belongs to the field of structural dynamics, and in particular relates to a vibration analysis method of a uniform section beam structure. Background technique [0002] Slender structures are widely used in engineering equipment such as ships and ocean engineering, construction engineering, and aerospace, such as bridges, rod systems, shaft systems, and aircraft wings. 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. Beam theory is often used in engineering applications to deal with such slender structures in order to achieve both solution efficiency and calculation accuracy. [0003] The classical beam theory mainly includes two theories, Euler-Bernoulli and Timushenko. However, the Euler-Ber...

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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 beam structures by embedding the finite element method. Changing the shape of the beam section or increasing the number of elements often requires remodeling and analysis. In addition, the finite element method generally has Disadvantages such as large amount of calculation, low calculation accuracy, cumbersome application of boundary conditions, etc.

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