An Introduction to Modal Design and Analysis of Structures: Part I

Abstract

Structures in civil engineering may be analyzed using the displacement method, which is based on a stiffness approach, or the flexibility method, which is based on the flexibility approach. In the displacement method of analysis, the stiffness matrix for a structure is determined based on material and geometrical properties of the members and the connections. The flexibility matrix for a structure is the inverse of the stiffness matrix. This paper examines the fundamental characteristics of the stiffness and flexibility matrices of civil structures based on modal properties, specifically, mode shapes and natural frequencies. Typically, in modal testing of civil structures, only the lowest modes are measured. The modal properties of a damped free structure are examined herein. The stiffness and flexibility matrices of a structure based on limited mode shapes and natural frequencies are examined and compared with the exact analytical matrices. Based on the results of a simple structure, the stiffness matrix is shown to be strongly influenced by the highest “practical” modes, while the flexibility matrix is strongly influenced by the lowest modes. But is this true of more complicated structures? And, what role does this have in terms of Modal Design and Analysis (MDA) of structures? By understanding the modes of vibration, civil engineers can better design structures. The findings are of value to the practicing structural engineering community.