Prestressed Modal Analysis Using Finite Element Package ANSYS

Abstract

It is customary to perform modal analysis on mechanical systems without due regards to their stress state. This approach is of course well accepted in general but can prove inadequate when dealing with cases like spinning blade turbines or stretched strings, to name but these two examples.

It is believed that the stress stiffening can change the response frequencies of a system which impacts both modal and transient dynamic responses of the system. This is explained by the fact that the stress state would influence the values of the stiffness matrix.

Some other examples can be inspired directly from our daily life, i.e., nay guitar player or pianist would explain that tuning of his playing instrument is intimately related to the amount of tension put on its cords. It is also expected that the same bridge would have different dynamic responses at night and day in places where daily temperature fluctuations are severe.

These issues are unfortunately no sufficiently well addressed in vibration textbooks when not totally ignored.

In this contribution, it is intended to investigate the effect of pre-stress on the vibration behavior of simple structures using finite element package ANSYS. This is achieved by first performing a structural analysis on a loaded structure then make us of the resulting stress field to proceed on a modal analysis.