Application of a Variational Method to Dissipative, Nonconservative Problems of Elastic Stability.
Abstract
The nonconservative stability problems of Beck and Leipholz, consisting of an elastic cantilevered beam subjected to a concentrated follower force acting at the free end and to a tangential force uniformly distributed along the length of the beam, respectively, are formulated with velocity-dependent internal and external damping forces included. The respective adjoint boundary value problems are derived and are used in developing variational formulations of the original boundary value problems. Because of the difficulty of solving the original problems exactly, the variational principles are used as the foundations for solving the problems approximately, the procedure being closely related to the well-known Ritz method that is applicable to nondissipative, conservative problems of elastic stability. It is found that internal damping may be either of a stabilizing or destabilizing nature, depending upon the magnitude of the external damping parameter. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1971
- Accession Number
- AD0728819
Entities
People
- Gary L. Anderson
- Wayne W. Walter