Efficient Analysis of Framed Structures for Vertical Vibration

The effect of the first mode vibration is predominant in seismic response of a framed structure while vertical vibration of a beam is significantly influenced by higher modes of vibration. Therefore, a beam can be modeled using only one element for seismic analysis of framed structures while several elements must be used to represent a vibrating hem As a result, analysis of a framed structure for vertical vibration requires increase number of elements leading to more complicated model with many degrees of freedom which requires large amount of computing resources for dynamic analysis. An efficient analysis method for vertical vibration of framed structures are proposed in this paper which is presented in three steps. The first step is to determine minimum nodes required to obtain dynamic response for vertical vibration. The second step is reduction of degrees of freedom through matrix condensation for efficient dynamic analysis of the structure. In this stage, the most effective selection of master degrees of freedom is pursued. The third step of this study employs the substructuring technique for local vertical vibration analysis. Efficiency and accuracy of the method proposed in this paper is verified comparing the analysis results to those of experiments performed using a three story framed structure.