Mathematical Modeling and Simulation of Frame under Earthquake Excitation

Abstract

Earthquake excitation causes lots of damage. Modern structural protective systems can be used to reduce the damaging effect of destructive Earthquake forces. History of Structural design can be divided into three eras. Classical era dealt only static loads. Modern era of Structural design added with specifications on dynamic response. The Post modern era anticipates specifications on the dynamic response. By Energy dissipating devices the earthquake performance of the Structure can be improved. Among various Energy dissipating Mechanisms Tuned mass dampers, Viscous, viscoelastic (VE) dampers and Base isolation techniques are popular. Viscoelastic are the simplest Energy dissipating device. It can easily fit into the the structure without causing any disruption in the functional use. Since certain regions in India is highly venerable to Earthquake. Need was felt to simulate the Earthquake forces on the structure using MATLAB. Single storey structure was analyzed by solving 2 order differential equation for El Centro Earthquake data. Results of the displacement of structure was plotted on a graph and compared with the response of structure without VE dampers. The effects of linear viscous dampers in controlling the response multistory frame have been investigated. Seismic response of the structure was computed. It has been demonstrated numerically that the response of a frame structure may be reduced to desired level by providing external dampers. Reduction in response depends on the energy dissipated through external dampers. Due to inherent uncertainties in the external VE dampers, it is recommended that external dampers be symmetrically placed wherever possible. Equation of motion of frame under Earthquake was modeled. Linear Elastic System was considered for the analysis having Single degree of freedom. By solving the differential equations seismic responses of structure are computed. MATLAB is easy to use interface and can solve high order differential equations. Response of the structure to the VE dampers was satisfactory