Equation Solving Method for Nonlinear Vibration Analysis of Machinery

Abstract

The invention discloses a nonlinear dynamic equation solution method and system for mechanical nonlinear vibration analysis, comprising the following steps: according to the mechanical nonlinear vibration system to be analyzed, constructing and obtaining nonlinear finite element dynamics in the time domain of the system Equation; through the multi-harmonic balance method, obtain the nonlinear finite element dynamic equation in the frequency domain; use the automatic differentiation method to solve the Jacobian matrix of the nonlinear finite element dynamic equation in the frequency domain; use the arc length method to solve the non-linear finite element dynamic equation in the frequency domain Linear finite element dynamic equations, obtain the solution of the nonlinear finite element dynamic equations in the frequency domain; according to the solution of the nonlinear finite element dynamic equations in the frequency domain, through the generalized Fourier inverse transform, obtain the nonlinear finite element dynamic equations in the time domain The solution of the metadynamic equation is obtained, and then the frequency response curve is obtained, and the mechanical nonlinear vibration analysis is carried out.

Description

technical field [0001] The invention belongs to the technical field of mechanical vibration safety analysis and nonlinear dynamic equation solution, and in particular relates to a nonlinear dynamic equation solution method and system for mechanical nonlinear vibration analysis. Background technique [0002] A large number of strong nonlinear phenomena are involved in the vibration safety analysis of mechanical components, such as crack phenomena in rotor dynamics, dry friction damping of turbine blades, etc. It is difficult to solve dynamic equations involving strong nonlinear forces, and the harmonic balance method is usually used The original equation is transformed into a balanced equation of harmonic components, and then the nonlinear equation is solved by Newton iteration method. [0003] The core step of the Newton iterative method to solve the harmonic balance method is to derive the Jacobian matrix of the strong nonlinear force harmonic term to the displacement harmo...

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Problems solved by technology

The main problem to be solved by the present invention is that the existing solution technology is difficult to analyze the vibration safety of mechanical parts containing complex nonlinear forces, and there are shortcomings such as relying heavily on expert experience and consuming computing resources; the method of the present invention can quickly derive strong The Jacobian matrix of nonlinear force harmonic terms to displacement harmonic terms, thus speeding up the solution of mechanical nonlinear vibration analysis equations

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