Solutions of Linear Vibration Mechanical Models Using Zhou Transform Method

Abstract

Vibration is a mechanical phenomenon that causes oscillations around an equilibrium point. Vibration is undesired in many areas, particularly engineered systems and inhabited spaces, and strategies to avoid vibration transfer to such systems have been proposed. Mechanical waves carry vibrations, and certain mechanical couplings transport vibrations more efficiently than others. By detecting equipment defects, vibration analysis (VA) in an industrial or maintenance setting seeks to save maintenance costs and downtime. Associated models from vibration settings can either be linear or nonlinear based on the modeling situation. This paper considers the Zhou Transform Method (ZTM) as a semi-analytical approach for obtaining the solutions of linear vibration mechanical models. Two illustrative examples are considered. The results obtained from the ZTM are compared with their exact forms for applicable case(s). The results show that the proposed method is very effective and reliable in obtaining approximate solutions based on the comparison.