Ground motion isolation using a newly designed vibration absorber

A new vibration absorber setup for vibration attenuation in single degree of freedom systems subjected to harmonic base motion is proposed. The absorber is placed so as to separate between the vibrating ground and the main undamped system. It consists of a mas spring damper directly connected to the vibrating ground. The main system is modelled as a mass spring attached to the absorber's mass. The optimal absorber parameters are determined with the aim of reducing the steady-state amplitude of the main mass. It is shown that the amplitude of the main mass passes through three fixed points, two of which are used in the determination of the optimal shape of the transfer function. One of the fixed points is independent of the damping ratio and the second is independent of both the damping and tuning ratios. For this setup, the solution is not unique since the ultimate design is reached by a complete isolation of the main mass from the moving ground and is attained by removing the absorber's damper and stiffness. Since this solution is not physically achievable, for a given mass ratio of the system, the smallest tuning ratio which ensures structural integrity of the system is selected. The optimal damping ratio which yields the optimal shape of the objective function is determined analytically in terms of the mass and tuning ratios. A design flowchart is presented to be used for the design of such absorbers.