Error Caused by Damping Formulating in Multiple Support Excitation Problems

Abstract

The effect of multiple support excitation is an important issue in studying large-span structures. Researchers have shown that the damping related terms in the equation of motion can induce errors in the analysis. Wrongly modelling the damping matrix can induce false damping forces between the structure and the reference coordinates. In multiple support excitation problems, this error is increased when absolute coordinates are used. In this paper, this part of the error is defined as virtual damping error. The error caused by using Rayleigh damping instead of Modal damping is called damping truncation error. This study focuses on the virtual damping error and the damping truncation error that exist in the modeling methods widely used in multiple support excitation problems, namely, large mass method (LMM), relative motion method (RMM), and absolute displacement method (ADM). A new Rayleigh damping formula is proposed for LMM to prevent virtual damping error. A form of equation of motion derived from the converged LMM was proposed in the authors’ previous work. This equation of motion is proved in this paper to be equivalent to RMM when modal damping and the new Rayleigh damping formula are used. RMM is proved free from the virtual damping error. The influence of multiple support excitation effect on the damping formulating errors is studied by spectral analysis. One simplified spring-mass model and two bridge models are used for numerical simulation. The results from the numerical simulation testify to the conclusions from the spectral analysis.