Transient Response of Nonlinear Systems

by P. F. Cuniff,


Serial Information: Journal of the Engineering Mechanics Division, 1963, Vol. 89, Issue 2, Pg. 19-46


Document Type: Journal Paper

Abstract: The transient response of nonlinear, nonconservative structures, idealized as lumped parameter chains, is treated by a combination graphical-numerical method. The step-by-step solution of the set of ordinary second-order nonlinear differential equations is in the form of trajectory curves in multiple phase-plane space. Examples of one and two-degree-of-freedom systems with cubic hardening springs are treated in which the forcing function is a prescribed foundation velocity. Relative displacement response curves obtained from an analog computer show good agreement with the graphical-numerical results. A scaling law is derived for nonlinear multi-degree-of-freedom systems. Prescribed restrictions are imposed on the parameters and input of the model system and the prototype system. Application of the scaling law is made for a system consisting of a finite number of masses connected by cubic hardening springs and linear dashpots.

Subject Headings: Nonlinear response | Transient response | Parameters (statistics) | Graphic methods | Curvature | Degrees of freedom | Fouling | Nonlinear analysis

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