Finite-element approach to determining the natural frequencies and modes of vibration of prestressed bodies

Abstract

In determining the frequency and mode of vibration and the stress--strain state of different objects in vibration engineering, it is often necessary to consider the presence of preliminary reinforcement. Such reinforcement is used in structures to improve their service characteristics. The linear theory of elasticity [I] cannot be used to solve problems concerning vibration with allowance for the effect of the initial stress state, since it assumes that the extensions and shears are negligible compared to unity and that the squares of the angles of rotation of the cross section are negligibly small compared to the extensions and shears.