A NOTE ON VIBRATIONS OF A BEAM ON AN ELASTIC FOUNDATION,
Abstract
For cases in which the foundation modulus varies proportionately to the mass per unit length of the beam, the principal mode shapes of the free bending vibrations of a non-uniform beam will be exactly the same as without the elastic foundation, and a simple exact result for the effect of the foundation on the natural bending frequency in any mode is obtained. Extensions of the analysis and results for such cases are then made to obtain the exact effect of the elastic foundation on torsional vibrations and on bending vibrations with damping and axial end loads. A general solution for forced bending vibrations is shown. When the foundation modulus does not vary exactly proportionately to the mass per unit length of the beam, a simple approximate result for the effect of the elastic foundation on the natural bending frequency in any mode is obtained by the Rayleigh method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1965
- Accession Number
- AD0614072
Entities
People
- Morris Morduchow
Organizations
- New York University Tandon School of Engineering