Hamilton's law and the stability of nonconservative continuous systems
Abstract
The application of Hamilton's law of varying action to a nonconservative continuous system (a beam column) was demonstrated without the use of variational principles, D'Alembert's principle, differential equations, or work functions. Eigenvalues from the direct analytical solution are compared to eigenvalues from the exact solution for a wide range of the load parameter. Curves of eigenvalues vs load magnitude for the lowest four modes of the Beck problem are presented. First and second normalized modes for a tension load, no load, and the critical compressive load are plotted.
- Publication:
-
AIAA Journal
- Pub Date:
- March 1980
- DOI:
- 10.2514/3.7662
- Bibcode:
- 1980AIAAJ..18..347B
- Keywords:
-
- Beams (Supports);
- Continuum Mechanics;
- Hamiltonian Functions;
- Structural Stability;
- Structural Vibration;
- Systems Stability;
- Displacement;
- Eigenvalues;
- Equations Of Motion;
- Nonconservative Forces;
- Tensile Stress;
- Physics (General)