Application of a variational method to dissipative, non-conservative problems of elastic stability

✍ Scribed by G.L. Anderson

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 893 KB
• Volume: 27
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(73)80346-3

✦ Synopsis

This study deals with the development of an adjoint variational principle that forms the basis ofa method that isused to obtain approximate solutions for non-conservativeproblems of elastic stability in which dissipative forces are present. For a general fifth-order partial differential equation in time and one space variable, the associated adjoint boundary value problem is derived. A variational principle embodying both the original and the adjoint problems is developed. Three specific non-conservative stability problems are studied by this method and the numerical convergence of the approximate solutions is studied by enlarging suitably the number of modes retained in the assumed expansions of the deflection functions. It is found that internal damping may be either of a stabilizing or destabilizing nature, depending upon its magnitude as wellas the magnitude of the external damping parameter.