GENERALIZATION OF THE UNIT DISPLACEMENT THEOREM WITH APPLICATIONS TO STRUCTURAL DYNAMICS.
Abstract
The Unit Displacement Theorem is generalized to include inertia, thermal and distributed loading on continuous and discrete element structures. The theorem is then applied to determine structural stiffnesses, thermal and inertia properties of structures, and equivalent concentrated forces due to 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, however, the 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 the modified characteristic equation in which higher order terms are present. A criterion for the condition when the higher order terms may be neglected is suggested. The use of the equivalent mass matrices and the modified characteristic equation greatly enhances the accuracy of the calculated frequencies and mode shapes. 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. A numerical example is included to illustrate the advantages of the equivalent mass matrices and the modified characteristic equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 10, 1967
- Accession Number
- AD0663924
Entities
People
- J. S. Przemieniecki
Organizations
- Air Force Institute of Technology