Application of a Variational Method to Some Dissipative, Nonconservative Problems of Elastic Stability.
WATERVLIET ARSENAL N Y
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The report deals with the development of an adjoint variational principle that forms the basis of a method that is used to obtain approximate solutions for nonconservative problems 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 nonconservative 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 well as the magnitude of the external damping parameter. Author