On the Effects of Nonlinear Elastic Foundation on Free Vibration of Beams
Nonlinear free vibration of simply supported elastic beams with fixed distance between pin-ends was studied by Woinowsky-Krieger (1950) and Burgreen (1951). The nonlinearity was due to the nonlinear stretching of the elastic curve. The solution was represented as a product of a time function and the sinusoidal vibrational mode corresponding to linear motion. A Galerkin procedure yielded the nonlinear differential equation for the time function which was solved exactly in terms of elliptic functions. In this paper the authors consider the nonlinear free vibration of statically compressed hinged beams supported by a nonlinear cubic elastic foundation. Contrary to the previous works the ends are not necessarily restricted in the axial direction.
V. Birman, "On the Effects of Nonlinear Elastic Foundation on Free Vibration of Beams," Journal of Applied Mechanics, Transactions ASME, American Society of Mechanical Engineers (ASME), Jan 1986.
The definitive version is available at https://doi.org/10.1115/1.3171790
Mechanical and Aerospace Engineering
Article - Journal
© 1986 American Society of Mechanical Engineers (ASME), All rights reserved.