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Nonlinear kinetic equation solving method and system for mechanical nonlinear vibration analysis

A nonlinear dynamics and nonlinear vibration technology, which is used in mechanical vibration safety analysis and nonlinear dynamic equation solving, nonlinear dynamic equation solving field, and can solve the problem of consuming computing resources, difficult vibration safety analysis of mechanical parts, Issues such as relying on expert experience

Active Publication Date: 2020-07-17
XI AN JIAOTONG UNIV
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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

Method used

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  • Nonlinear kinetic equation solving method and system for mechanical nonlinear vibration analysis
  • Nonlinear kinetic equation solving method and system for mechanical nonlinear vibration analysis
  • Nonlinear kinetic equation solving method and system for mechanical nonlinear vibration analysis

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Embodiment Construction

[0098] In order to make the purpose, technical effects and technical solutions of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention; obviously, the described embodiments It is a part of the embodiment of the present invention. Based on the disclosed embodiments of the present invention, other embodiments obtained by persons of ordinary skill in the art without making creative efforts shall all fall within the protection scope of the present invention.

[0099] see figure 1 , a method for solving nonlinear dynamic equations for mechanical nonlinear vibration analysis according to an embodiment of the present invention is a method for solving nonlinear dynamic equations based on automatic differentiation-pseudo-arc length extension, comprising the following steps:

[0100] Step...

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Abstract

The invention discloses a nonlinear kinetic equation solving method and system for mechanical nonlinear vibration analysis. The method comprises the following steps: constructing and obtaining a nonlinear finite element kinetic equation in a system time domain according to a to-be-analyzed mechanical nonlinear vibration system; obtaining a nonlinear finite element kinetic equation in a frequency domain through a multi-harmonic balance method; solving a Jacobian matrix of a nonlinear finite element kinetic equation in a frequency domain by utilizing an automatic differential method; solving thenonlinear finite element kinetic equation in the frequency domain by adopting an arc length method to obtain a solution of the nonlinear finite element kinetic equation in the frequency domain; according to the solution of the nonlinear finite element kinetic equation in the frequency domain, the solution of the nonlinear finite element kinetic equation in the time domain is obtained through generalized inverse Fourier transform, then a frequency response curve is obtained, and 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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Application Information

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IPC IPC(8): G06F30/23G06F17/14G06F17/16G06F119/14G06F111/04
CPCG06F17/141G06F17/16Y02T90/00
Inventor 谢永慧孙磊刘天源张荻
Owner XI AN JIAOTONG UNIV
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