On the Dynamic Analysis of Regular Shear Structures

Abstract

This study presents a new solution for the classic problem of multistory shear buildings composed of equal masses and springs connected in series and fixed in position at the ground level. The governing equation of motion of this close-coupled system is derived in terms of the finite difference operators. Discrete sinusoidal functions are used to describe the time dependent excitations of such structures under arbitrarily applied joint loading. Typical mode shapes and eigenfrequencies are worked out to demonstrate the applications of the proposed formulae. It is argued that these solutions are exact within the bounds of the theoretical assumptions since they satisfy both the governing difference equation of motion as well as the prescribed boundary conditions. The concept of the “Affine” oscillator is also introduced to assess the base shear of the multidegree of freedom structure by means of a corresponding single degree of freedom system. The investigation of active control of an existing problem is reworked to demonstrate the accuracy and the simplicity of the proposed solution. The Affine oscillator is also used to study the total shear reduction of a base isolated shear type building. It is concluded that the proposed solutions provide simple yet powerful means of manual analysis for the class of structure considered in this paper.