Free Vibration of Elastically Supported Beams on Nonlinear Elastic Foundation


The problem of free nonlinear vibrations of beams on nonlinear elastic foundation is considered. The boundary conditions include elastic support at both ends, elastic support at one end and simple support at the other end and simple support at both ends. Nonlinear elastic foundation is assumed to be cubic; additional nonlinearity is contributed by the stretching of the beam axis resulting from the axial elastic restraint. The solution is sought as a product of a time function and the eigenfunction of the corresponding linear problem. This eigenfunction can be found only numerically or graphically if one or two ends of the beam are elastically supported. However, the direct method is discussed that provides the stiffness of elastic supports as a function of beam natural frequencies. This simplifies the solution of linear problem. When the eigen function is found, Galerkin procedure results in a homogeneous second order differential equation with cubic nonlinearity. The period of motion described by this equation can be easily calculated.

Meeting Name

American Society of Mechanical Engineers (Paper) (1986, Montvillargenne, Fr)


Mechanical and Aerospace Engineering

Document Type

Article - Conference proceedings

Document Version


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© 1986 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Jan 1986

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