Maximum Frequency of Beams Including Shear Effects.
Abstract
The study considers the effect of shear deformation on the optimal design, with respect to the fundamental frequency of transverse vibration of a linear, elastic beam with a point mass attached. Since the system is conservative, Rayleigh's quotient furnishes an expression for the fundamental frequency. A constraint is placed on the total mass, and the calculus of variations is then used to determine the nonlinear differential equations and the natural boundary conditions, which constitute the necessary conditions for an extremum of the frequency. As the slope of the shear deformation can be discontinuous, an additional boundary condition is secured through the Weierstrass-Erdmann corner conditions. In an effort to solve these equations the method of quasilinearization is invoked. This method provides an itertive process whereby the solution to the nonlinear equations, is found as the limit of a convergent sequence of solutions of linear equations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1970
- Accession Number
- AD0715021
Entities
People
- J. J. Walters
- R. M. Brach
Organizations
- University of Notre Dame