Research On Dynamic Response Optimization Based On Isogeometric Analysis

In the field of power machinery engineering,dynamic response optimization has always been an important research direction.The dynamic response analysis of power machinery structure can truly reflect the motion state of power machinery.Due to the complex structure of the power machinery system,there are problems in the accuracy and efficiency of the system dynamics equations.In order to solve this problem,this paper proposes the dynamic response analysis and optimization of the power machinery system based on isogeometric analysis.The isogeometric analysis method is a very novel numerical calculation method.Its core idea is to use NURBS basis functions to interpolate the system response.Although the isogeometric analysis method has been applied in many fields,the development of dynamic response analysis and optimization of power mechanical systems is not very mature.This article mainly solves how to use isogeometric analysis method to analyze and optimize the dynamic response of power machinery system.First,the dynamic response analysis of the dynamic mechanical system is carried out by combining the isogeometric analysis with the modal superposition method.The modal superposition method is used to decouple the dynamic equations,and the independent single degree of freedom dynamic response is analyzed based on the isogeometric analysis method.The degree of dynamic response is superimposed,and finally the dynamic response of the power mechanical system is obtained.Secondly,the isogeometric analysis method is used to directly analyze the dynamic equations of the power machinery system,and combined with the key point method,the GLL point method and the equidistance method to separately deal with the constraint conditions,and the dynamic response of the power machinery system is optimized by introducing artificial design variables.Aiming at the dynamic response of the dynamic mechanical system,it is proposed to convert the general structural dynamics control equations from physical coordinates to modal coordinates,so that each equation contained in the structural dynamics equations becomes independent equations;from the Bubnov-Galerkin principle Start,discretize the solution space of dynamics governing equations into linear combinations of NURBS basis functions and express them as line equations;use a unified form to express Dirichlet condition,Neumann condition and Luoping condition,and use total stiffness matrix and The characteristic of the total load vector is that the unknown differential value in the boundary value is expressed with a known initial condition and absorbed into the total stiffness matrix and the total load vector.As a theoretical basis research,the feasibility of the method is verified by calculation and analysis of single-degree-of-freedom mass spring damping system,multi-degree-of-freedom spring damping system,cantilever vibration and free vibration analysis of diesel engine power transmission system.The first-order differential equations involved in dynamic response analysis are transformed from general structural dynamics control equations,including the conversion of initial conditions;the first-order differential equations are transformed into parameter domains and converted into NURBS basis functions The parameter domain of is [0,1];Combining the Bubnov-Galerkin principle and the idea of isogeometric analysis,transform the first-order differential equations into integral form,and integrate them by parts,and then use the GaussLobatto quadrature formula Express the first-order differential equations in matrix form;In the dynamic response optimization,artificial design variables are introduced to improve the performance of the optimization model and stabilize the optimization iteration process;use key point set method and GLL(Gauss-Lobatto-Legendre)method to deal with And the dynamic response constraints of the equidistant point method.Use examples of different degrees of freedom,such as the optimal design of linear single-degree-of-freedom shock absorber,and the optimal design of linear two-degree-of-freedom shock absorber to realize dynamic response optimization design.