Natural frequencies and mode shapes are important features in the static analysis of beam structures. They are used in analysis, design as well as verification of beam structures. They also play an important role in influencing the dynamic response of beams. For example, just changing the natural frequency by a certain amount will cause the forced vibration of the structure from the near-resonance region to out of the near-resonant region. Therefore, in this study, the modal analysis method is used to establish the characteristic equations to determine the natural frequencies and the vibration modal functions for prestressed beams with different boundary conditions. By numerical method, this work analyzed and compared these natural frequencies with the natural frequencies of ordinary Timoshenko beams and Euler – Bernoulli beams.
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