Abstract
First-order models are used in the analysis of the tension–compression and transverse bending modes of beam vibration. The equation of motion for each mode and the expressions for boundary conditions are obtained using the generalized variational principle. Systems of partial differential equations for the longitudinal and bending modes of vibrating beams are reduced to a single fourth-order equation, and frequency equations are obtained. The problem of free and forced vibrations of beams that are simply supported at both ends is presented. An analysis and comparison with well-known theories is performed using computer algebra system Mathematica.
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