Mathematical Modeling of a Transient Vibration Control Strategy Using a Switchable Mass Stiffness Compound System

A theoretical control strategy for residual vibration control resulting from a shock pulse is studied. The semiactive control strategy is applied in a piecewise linear compound model and involves an on-off logic to connect and disconnect a secondary mass stiffness system from the primary isolation device, with the aim of providing high energy dissipation for lightly damped systems. The compound model is characterized by an energy dissipation mechanism due to the inelastic collision between the two masses and then viscous damping is introduced and its effects are analyzed. The objective of the simulations is to evaluate the transient vibration response in comparison to the results for a passive viscously damped single degree-of-freedom system considered as the benchmark or reference case. Similarly the decay in the compound system is associated with an equivalent decay rate or logarithmic decrement for direct comparison. It is found how the compound system provides improved isolation compared to the passive system, and the damping mechanisms are explained. 1. Introduction Mechanical shock is a common problem characterized by a suddenly applied excitation in a short period of time. Usually it involves very large forces and displacements which could lead to damage to sensitive equipment, human discomfort, and other effects [1]. Thus the effective isolation of shock generated vibration is a very important matter in engineering. Shock isolation is normally achieved through energy storage by elastic foundations but optimum isolation is compromised due to the high energy levels requiring large deformations of the isolator where normally space is a constraint. Additionally the isolation system must be able to dissipate the stored energy quickly once the shock has finished in order to minimize residual vibrations. The classical approach to shock isolation is based on a single degree-of-freedom system with linear stiffness and viscous damping elements. Many shock scenarios can be analyzed considering this method to select proper isolators. Most of the literature related to shock isolation dates from 1950 to 1960 when authors like Ayre [2], Snowdon [3], and Eshleman and Rao [4] studied this phenomenon and settled the fundamental theory of shock analysis and isolation. However, linear passive elements are limited. For instance, there is the compromise aforementioned between isolation performance and space limitations. In order to improve shock isolation, the use of variable or switchable rate elements has been considered. Optimal shock isolation has been considered