An inverse method for structural modification without changing the specified resonance frequency and its modal vector

Abstract

NV (Noise and Vibration) performance is determined by the influence of all components constituting a whole structure. It is difficult to design NV performance efficiently because the structural modification of a certain component affects the performance of the whole structure. As one of the effective ways to design the performance, this paper presents an inverse method for structural modification that keeps the specified eigenfrequency and its modal vector of the whole structure the same. Firstly, the matrices for structural modification are calculated as dynamic stiffness matrix variation from the zero-divisors of a specified modal vector. Furthermore, it is possible to represent the calculated matrices redundantly by using an arbitrary non-zero weighting matrix. This makes it possible to obtain various solutions for structural modification. However, the matrices are generally calculated as fully populated and non-symmetric matrices. Therefore, with these matrices, it is difficult to feasibly find a symmetrical and sparse mass or stiffness matrix to use for structural modifications in applications that focus on designing specified regions of the whole structure. Secondly, we propose how to transform the matrices as the zero-divisors into the sparse matrix of reduced row echelon form in advance. This transformation simplifies building symmetric and sparse matrices for realizable structural modification. The sparse matrix, redundantly represented by a weighting matrix, allows a value analysis to select among alternative structural changes to lighten the product or simplify its complexity. Finally, the proposed method was applied to a numerical case study.

Keywords

• structural modification
• modal analysis
• resonance
• modular design
• null space
• zero divisor