In this study, the nonlinear equation of motion of the beam on the elastic foundation is obtained via the Newton's second law of motion, and its free vibration nature is investigated. Considering the inextensional condition, the planar model of the beam accounting for the effects of the rotary inertia is derived. Then, the linear vibration and nonlinear vibration of the beam on the elastic foundation are examined. It is shown that the cut-off frequency can be observed in the frequency spectrum of the beam response. The effects of the rotary inertia on the natural frequencies are systematically investigated. Finally, the frequency differences, due to the different foundation models, and the possible modal interaction of the beam are discussed.
Refined Modeling and Free Vibration of Inextensional Beams on the Elastic Foundation
Manuscript received April 12, 2012; final manuscript received November 14, 2012; accepted manuscript posted November 19, 2012; published online May 23, 2013. Assoc. Editor: Alexander F. Vakakis.
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Wang, L., Ma, J., Zhao, Y., and Liu, Q. (May 23, 2013). "Refined Modeling and Free Vibration of Inextensional Beams on the Elastic Foundation." ASME. J. Appl. Mech. July 2013; 80(4): 041026. https://doi.org/10.1115/1.4023032
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