Optimal Shock Isolation of a Two-Component Elastic Object

Abstract

We consider the problem of the optimal shock isolation of an object whose mechanical model is described by two masses with a linear elastic connection between them. The object is situated on a base whose movement is considered as a shock load. The base acceleration law (shock action) is given. For the sake of safety, the object is fastened to the base by a special device—an shock isolator. The isolator is characterized by the force of the action on the object. We pose the problem of constructing the force law of the isolator such that the stroke of the isolator (the maximum change in the distance between the fastening points of the isolator on the object and on the base) is minimal under the condition that the force of the elastic connection between the masses of the object does not exceed the given admissible value. We obtain approximate solutions of the problem, as well as exact solutions for various classes of shock actions. We provide examples. We show that the solutions include the summands that are the impulse functions. The results can be used to create highly effective devices to protect against shock of technical systems and humans in industry and in transport.