Abstract
The free vibration behavior of a statically deflected Timoshenko microbeam under uniformly distributed static load is studied based on modified couple stress theory. In the first step of the analysis, the beam configuration under large static deflection is obtained through a nonlinear static analysis in which the governing equations are derived employing minimum potential energy principle and incorporating von Karman geometric nonlinearity. In the subsequent step, the free vibration behavior of the statically deflected microbeam is investigated employing Hamilton’s principle and incorporating the tangent stiffness of the statically deflected beam configuration. The solutions of the governing equations for both the steps are obtained by approximating the displacement fields following Ritz method. The model is validated using the available results in the literature for some reduced problems. The results for the first two vibration modes are presented in nondimensional frequency–amplitude plane for clamped, simply supported, and clamped–simply supported beams.
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Bhattacharya, S., Das, D. (2020). A Study on Free Vibration Behavior of Microbeam Under Large Static Deflection Using Modified Couple Stress Theory. In: Maity, D., Siddheshwar, P., Saha, S. (eds) Advances in Fluid Mechanics and Solid Mechanics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0772-4_14
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DOI: https://doi.org/10.1007/978-981-15-0772-4_14
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