Accession Number : AD0715021

Title :   Maximum Frequency of Beams Including Shear Effects.

Descriptive Note : Technical rept.,

Corporate Author : NOTRE DAME UNIV IND DEPT OF AEROSPACE AND MECHANICAL ENGINEERING

Personal Author(s) : Brach,R. M. ; Walters,J. J.

Report Date : OCT 1970

Pagination or Media Count : 22

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)

Descriptors :   (*BEAMS(STRUCTURAL), VIBRATION), RESONANT FREQUENCY, STABILITY, DEFORMATION, CALCULUS OF VARIATIONS, NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION

Subject Categories : Structural Engineering and Building Technology
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE