Accession Number:

AD0631258

Title:

GENERALIZATION OF THE UNIT DISPLACEMENT THEOREM,

Descriptive Note:

Corporate Author:

AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO

Personal Author(s):

Report Date:

1966-01-01

Pagination or Media Count:

7.0

Abstract:

The Unit Displacement Theorem is generalized to include inertia, thermal and distributed loading on continuous and discrete element structures. The theorem can then be applied to determine not only structural stiffnesses but also thermal and inertia properties of structures and equivalent concentrated forces due to a distributed loading. Exact expressions are derived for the calculation of frequency dependent stiffness and equivalent mass matrices used in structural vibrations analysis. To facilitate practical calculations these exact expressions are expanded into a matrix series in ascending powers of the frequency. This in turn leads to the formulation of the modified equation of motion and modified characteristic equation in which higher order terms are present. The first two terms in the matrix series for the stiffness and equivalent mass matrices are derived for a uniform bar element. In addition, the first term for the equivalent mass matrix is derived for the following structural elements torsion bars, beams, triangular and rectangular plates, solid tetrahedra and solid parallelepipeds. The use of the equivalent mass matrices in structural dynamics is recommended in preference to the conventional lumped masses. Further studies are required to determine whether the additional complications associated with the use of the modified characteristic equation are justified in practice. Author

Subject Categories:

  • Numerical Mathematics
  • Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE