Free Vibration Analysis of Prestressed Timoshenko Beams Using the Modal Analysis Method

Abstract

Natural frequency and mode shape are important features in the dynamic analysis of beam structures. They are used in the analysis, design, and verification of beam structures. In dynamic problems, these characteristics influence the dynamic response of the beam. This study presents the equations for the free vibration analysis of prestressed Timoshenko beams and derives the characteristic equations to determine the natural frequencies and general mode functions using the modal analysis method. For each different boundary condition of the beam, the corresponding characteristic equations and eigenforms are then obtained. Using numerical methods, the change in natural frequencies is investigated and compared with the natural frequencies of ordinary Timoshenko beams and Euler-Bernoulli beams. As the beams undergo pre-compression, the gap in natural frequencies between the prestressed Timoshenko beam and the unstressed beam widens with increasing prestress. The natural frequency of the pre-tensioned beam is higher than that of the beam without pre-tension. This difference is most noticeable at the first order of the frequency, where it is most significant, but it decreases quickly as the frequency order rises.

Keywords

• natural frequency
• mode shape
• timoshenko beam
• prestressed beam
• modal function