A frequency-domain pseudo-force method for dynamic structural analysis nonlinear systems and nonproportional damping

Abstract

A frequency-domain method for nonlinear analysis of structural systems with viscous, hysteretic, nonproportional and frequency-dependent damping is presented. The nonlinear effects and nonproportional damping are considered through pseudo-force terms. The modal coordinates uncoupled equations are iteratively solved. The treatment of initial conditions in the frequency domain which is necessary for the treatment of the uncoupled equations is initially adressed

Frequency and time domain dynamic structural analysis: convergence and causality

“…The computational efficiency depends very much upon the problem and the preference of the analyst. Numerical solutions in the FD through the ImFT concept are competitive with TD ones with regard to accuracy and computational efficiency, as indicated by the examples in [8,9]. In conclusion, FD methods are theoretically consistent and mandatory for rigorous analysis of systems with hysteretic damping and frequency-dependent properties [8,9].…”

“…This conclusion proves finally the causality of the response of the TD and FD dynamic analysis expressed, respectively, by Eqs. (9) and (1).…”

“…On the other hand systems with frequency-dependent properties, like interaction systems (soil-structure, fluid-structure) and with hysteretic damping can be rigorously analyzed only by FD methods. This is an important asset of these methods which is not present in TD methods [8,9].…”

On the use of pseudo-forces to consider initial conditions in 3D time- and frequency-domain acoustic analysis

“…In all cases analyzed, a quite good agreement with the analytical solutions was attained (see Figs. [2][3][4][5][8][9][10][11]. As observed in Fig.…”

“…The proposed method, which is based on the concepts of pseudo-forces, see Refs. [9,18], and generalized functions [6], will be applied to the solution of three-and two-dimensional scalar problems, in the time-and frequency-domain, modeled with finite elements. Initially, the time-dependent and frequency-dependent partial differential equations governing wave propagation problems are presented.…”