Nonlinear oscillations in systems with large static deflection of elastic elements

Abstract

In mechanical systems the static deflection of the elastic elements is usual not appeared in the equations of motion. The reason is that either a linear model of the elastic elements or their too small static deflection assumption was accepted.

In the present paper both nonlinear model of elastic elements and their large static deflection are considered, so that the nonlinear terms in the equation of motion appear with different degrees of smallness. In this case the nonlinearity of the system depends not only on the nonlinear characteristic of the elastic element but on its static deflection. The distinguishing feature of the system under consideration is that if the elastic element has soft characteristic, the nonlinear system also belongs to the soft one. If the elastic element has hard characteristic, the system may be either soft or hard or neutral type, depending on the relation between the parameters of the elastic element and its static deflection.