Fast frequency response analysis of large‐scale structures with non‐proportional damping

Abstract

SUMMARYModal frequency response analysis is an economical approach for large and complex structural systems since there is an enormous reduction in dimension from the finite element frequency response problem. However, when non-proportional damping exists, the modal frequency response problem is expensive to solve at many frequencies because modal damping matrices are fully populated. This paper presents a new algorithm to solve the modal frequency response problem for large and complex structural systems with structural and viscous damping. The newly developed algorithm, fast frequency response analysis (FFRA) algorithm, solves the damped modal frequency response problem with O(m 2 ) operations at each frequency. Then the FFRA algorithm is extended for solving a system of equations in optimization application with the modal correction approach, in which the mass, stiffness and damping matrices of a modified configuration differ from the original configuration. Numerical results show that the FFRA algorithm dramatically improves the performance of the modal frequency response analysis compared to conventional methods in industry while obtaining the same accuracy.

On a component mode synthesis on multi-level and its application to dynamics analysis of vehicle system supported with spring-stiffness damper system

“…Damping should be applied to slow down the spring action. In particular, the nonproportional damping [19] is essential to describe the suspension system. Damping generally uses oil or air, for which viscous damping should be applied.…”

“…(19) Then, with the mode superposition method [18], the Eq. (19) is projected onto the modal space by substituting X(ω)= Once the modal solution Z(ω) is obtained over the desired excitation frequency range, the modal solutions is back transformed to get the frequency response in the FE dimension as:…”

Successive mth approximation method for the nonlinear eigenvalue problem

“…The NEP arises in a number of various applications, such as eigenvalue problems of nonlinear ordinary differential equations (Sun and Liu 2001), dynamic analysis of the damping structure systems (Kim and Bennighof 2007), the stability analysis of fluid mechanics (Bramely and Dannis 1982) and the stability analysis of linear time-delay systems (Hu et al 1998), and so on. However, due to the nonlinearity of T (λ), the Schur factorization of T (λ) does not exist, there will be many difficulties in essence and serious challenges to design numerical algorithms for solving the NEP.…”

An efficient numerical solution for frequency response function of micromechanical resonator arrays

“…Automatic multilevel substructuring [3], substructuring reduction for the iterated improved reduced system [4], fast frequency response analysis [5,6], and algebraic substructuring [7] are included in this category. A variant of algebraic substructuring among them has recently been developed to solve only the modes of the interior eigenvalues [8], which contribute more to the frequency responses near a specific mode of a higher range than the extreme eigenvalues do.…”