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.