Research On The Eigenvector Optimization For Structural Vibration Systems

Topology optimization has a wide range of applications in fields such as aerospace,intelligent manufacturing,biomimetic design,and metamaterials.Most current work focuses on frequency of optimizing for structural vibrating systems.structural mode shapes can characterize the global and local vibration properties of a structure more detailed.Therefore,the optimization of structural vibration modes(i.e.eigenvectors),is more challenging and necessary.The main content of this thesis is as follows:(1)Sensitivity analysis accounts for the majority of the computational cost in topology optimization of structures.The rank of the coefficient matrices of the governing equations is lower than those of the simple eigenvalues.The calculation of the derivatives of eigenvectors with repeated eigenvalues is more difficult.This thesis proposes a new algebraic method.a new governing equation is obtained and proved to be nonsingular by constructing a preconditioned operator with regularization conditions.During the solution process,the iterative method is used for solving modal sensitivity of non-definite symmetric systems.The new method does not require reordering or expansion of matrix.Besides,compared with the traditional Nelson method,it has faster calculation speed.(2)This thesis proposes objective functions for optimizing the eigenvectors of vibration systems for both local node control and global modal control.For local node control,a Boolean matrix is used to identify the controlled nodes,and the bi-directional evolutionary structural optimization(BESO)method is applied for optimization.Modal jumping is frequently encountered in optimization processing.We use the modal assurance criterion to track modal information,which is also employed to characterize the objective function of global modal control.When solving modal sensitivity,the rapid calculation method of objective function sensitivity greatly accelerates the calculation speed.Finally,the effectiveness of the proposed method is showed by numerical examples.