Composite beam bending vibration inherent frequency analytical method

Abstract

The invention provides a composite beam bending vibration inherent frequency analytical method and belongs to beam vibration inherent frequency analytical methods. According to the geometric features of a composite beam, composite beam units ETE-B are established based on the classic Euler-Bernoulli (EB) beam theory and the Timoshenko beam (TB) theory; the EB beam units and the TB units in the ETE-Bs are continuously connected through boundary conditions, a dynamical model and a bending vibration equation of the composite beam are established, a parametric frequency equation of the composite beam on the boundary conditions is acquired, and finally the inherent frequency of the composite beam is determined through the one-dimensional searching method; according to the one-dimensional searching method, the feasible region of the inherent circular frequency is determined first, and then inherent frequency values are acquired in all the feasible regions through the bisection method. The method has the advantages that the physical significance involved in analysis of the dynamic characteristics of the composite beam is clear; acquisition of the inherent frequency is only related to the materials and dimensions of the beam, the established parametric frequency equation has universality, and a model test or finite element analysis under three-mode modeling is not needed.

Description

technical field [0001] The invention relates to a method for analyzing the natural frequency of beam vibration, in particular to a method for analyzing the natural frequency of composite beam bending vibration. Background technique [0002] When the span of the beam structure is large, under the action of its own weight, the deflection of the middle part of the beam is the largest. Generally, the stiffness of the beam is increased and the deformation is reduced by means of internal welding ribs. Because of the similarity between the stiffened plate and the beam structure, this kind of internally welded stiffened plate beam can be regarded as a composite beam. Composite beams are generally used for long-span load-bearing structures of heavy equipment (such as crane bridge arms), load-bearing structures of large buildings (such as house steel structures) and load-bearing structures of mineral processing equipment (such as large vibrating screen load-bearing beams), etc. Quant...

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Problems solved by technology

For composite beams, if the approach (1) is adopted, the dynamic model of the beam structure is established first, and the coupling effect of the one-dimensional beam structure and the two-dimensional plate structure must be considered when analyzing the bending vibration characteristics using the traditional structural dynamics theory. The analysis process of the differential equation is complicated and the numerical solution is difficult; if the method (2) is adopted, a structural test model of the beam structure that satisfies the similarity principle must be made first, and a suitable method

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