Approximate solutions to coupled shear walls on fixed and flexible foundations

Abstract

In this paper, closed form approximate solutions to the equations of motion for coupled shear walls are developed using Ritz-Galerkinmethod. Hamilton's principle is used to derive the equations of motion. These equations and solutions were developed for two different cases, one for the coupled shear wall on fixed foundation and the other for coupled shear wall on flexible foundation. Through literature review, it is identified that previous studies addressed only the free vibration of coupled shear wall system without considering external load. The main focus of this paper is to develop equations of motion with external load applied to coupled shear walls on both fixed and flexible base using variational approach. Then cast equations of motion and corresponding boundary conditions into non-dimensional form. The solution of equations of motion is developed through the use of the Ritz-Galerkin technique. Thus attempts were made to develop equations of motion considering a driving force, p(x,t) on the structure. By using selected shape functions for the longitudinal and lateral defelections, a matrix eigenvalue equation is derived for both cases yielding closed form approximate solution.