Generalized Wave Equation in Finite Domains

by H. Don Fisher, Consulting Engr.; Mechanical Engineering Department, Combustion Engineering, Inc., Windsor, Conn. 06095,

Serial Information: Journal of the Engineering Mechanics Division, 1982, Vol. 108, Issue 1, Pg. 155-163

Document Type: Journal Paper


A generalized equation governing one dimensional wave propagation in finite domains is solved by employing the finite Sturm-Liouville transform. The formulation includes the effects of time dependent boundary conditions, non-zero initial conditions and the presence of body or surface forces or both. The modal solutions for the dynamic response are valid for the entire range of the temporal variable. The utility of the analysis is demonstrated by citing more than twenty references in which the derived time dependent response can readily be obtained from the generalized solutions presented here.

Subject Headings: Wave equations | Time dependence | Wave propagation | Boundary conditions | Surface waves | Dynamic response

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