Abstract
In this paper, modes of vibrations and frequency responses of a rectangular frame are analyzed from a wave vibration standpoint based on two- and three-dimensional structural models, respectively. All possible vibration motions, namely the in- and out-of-plane bending, axial, and torsional vibration, are considered, with bending vibrations analyzed based on the Euler-Bernoulli bending theory and the Timoshenko bending theory, respectively. Comparisons are made among the analyses based on two- and three-dimensional structural models. The theoretical analysis results are validated through experiments. What is novel in this study is the application of a three-dimensional free body diagram in analyzing vibrations in a planar structure. Such an idea allows all possible vibration modes in a planar structure being analyzed through a one-step process accurately and efficiently.
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