Normalized quasi-static mass — A new definition for multi-support motion problems

Abstract

An efficient algorithm called the modal reaction method for calculating the modal participation factors in support motion problems has been proposed by Chen et al. [1]. In this paper, we extend this method to determine the number of modes needed to satisfy 90% of the sum of the base-shear modal mass as UBC(uniform building code) suggests. The sum of all the modes for each support in multi-support motions is found to be equal to the normalized quasi-static mass which is defined in this paper. The normalized quasi-static mass is equivalent to the total structure mass in the case of single supported structure. By extracting the reaction from the SPC force in data recovery using SOL 3 (linear modal analysis) or SOL 106 (nonlinear modal analysis) in MSC/NASTRAN, the modal participation factor and the base-shear modal mass ratio can be directly determined free from calculation of the influence vector, or the so-called quasi-static solution. To demonstrate this new concept of the normalized quasi-static mass, several examples including rod, beam, tower structures are given to check the validity of the proposed method using MSC/NASTRAN program. Finally, the minimum number of modes needed to reach 90% of the normalized quasi-static mass for each support is proposed as a reference for analysis and design engineers.