Solving method used for dynamic response when elastic boundary shallow arch generates internal resonance

Abstract

The invention discloses a solving method used for dynamic response when an elastic boundary shallow arch generates internal resonance. The method is carried out on the basis of a dimensionless kinetic equation, corresponding rigidity parameters are used for representing the magnitudes of vertical elastic constraint and rotating-direction elastic constraint on the shallow arch, the modality of the elastic boundary shallow arch is supposed through a general solution and a particular solution to a differentiation equation, the natural vibration frequency is obtained due to the fact that a determinant corresponding to a modality coefficient matrix is equal to zero, an average equation in the polar form under the three internal resonance conditions of 1:2, 1:1 and 1:3 is derived through Galerkin discretization of the kinetic equation of the shallow arch and multiscale perturbation analysis, and therefore dynamic response used when the internal resonance is generated can be obtained. Due to the thought that constraint rigidity is considered in the modality and the natural vibration frequency, existing technical problems generated in a dynamic response solving process when the elastic boundary shallow arch generates the internal resonance are solved. Safety and reasonability of the built shallow arch are guaranteed, and the service life of the shallow arch can be prolonged.

Description

technical field [0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a method for solving the dynamic response of a shallow arch with an elastic boundary when internal resonance occurs. Background technique [0002] Shallow arch is a kind of mechanical member whose mechanical performance is between arch and beam. Its dynamic characteristics under external load are of great significance for grasping the mechanical performance of shallow arch structures. Shallow arches are prone to large-scale vibrations under the design conditions of light weight, low resistance and full load, while internal resonance excited by external excitation is a typical destructive dynamic behavior, which must be avoided in consideration of design parameters. [0003] The existing research on the internal resonance of shallow arches is mainly aimed at the ideal hinged, consolidated, and other boundaries. Under these ideal boundary conditions, the mode...

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Problems solved by technology

[0004] The purpose of the present invention is to provide a method for solving the dynamic response of shallow arches with elastic boundaries when internal resonance occurs, which solves the problem in the prior art that the natural vibration frequency and mode of shallow arches with elastic boundaries can be analyzed and considered. Influence of determined elastic restraint stiffness, displacement and deformation problems in the construction of shallow arches

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