Numerical evaluation of the effect of Combined Pendulum Tuned Mass Damper on a basic vibrating system

Abstract

There are many engineering applications utilizing Tuned Mass Damper (TMD), Pendulum Tuned Mass Damper (PTMD) and Combined Pendulum Tuned Mass Damper (CPTMD) in order to alleviate the response of the buildings exposed to catastrophes, strong wind, and earthquake vibrations. The objective of this work is to study the effect of the added Combined Pendulum Tuned Mass Damper (CPTMD) on the vibrating system and to investigate if the added CPTMD will help in damping out the vibrations arises from any excitation source like wind force or from seismic earthquake force. The proposed basic system was modelled mathematically to get the governing Equations of Motion according to Lagrange’s equation where the whole system was described by three Degrees of Freedom two translation and one rotation. A parametric study was conducted with different values of constants for the springs and dampers and a simplified model has been derived after making linearization and order of magnitude analysis (OMA). The three Degree of Freedom (DOF) system was put in state-space format before being simulated using (MATLAB © ). Output graphs and curves have been obtained and discussed.