Journal ArticleDOI
Transient Response of Nonlinear Systems
TLDR
In this article, the transient response of nonlinear, nonconservative structures, idealized as lumped parameter chains, is treated by a combination graphical-numerical method, and a scaling law is derived for nonlinear multi-degree-of-freedom systems.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.read more
Citations
More filters
Journal ArticleDOI
A survey on non-linear oscillations
Derek P. Atherton,H. T. Dorrah +1 more
TL;DR: A comprehensive review of work in the field of non-linear oscillations can be found in this paper, where a brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems.
Journal ArticleDOI
Some improvements in the phase-plane delta method
TL;DR: In this paper, the phase-plane δ-dot-based method was used to obtain the entire phase-portrait of a non-linear system, and error analysis showed that the δ dot -method is more accurate than the existing δ method.
Journal ArticleDOI
Transient dynamic response of some nonlinear structural systems
Robert S. Ayre,John R. Mays +1 more
TL;DR: In this article, the transient dynamic response of various single-degree of freedom and many-degree-of-freedom simplified nonlinear structural systems are shown through a presentation of general equations of motion, nonlinear damping and restoring force functions, and the use of nonlinear-system response spectra.
Related Papers (5)
Dynamics of High-Speed Cam-Driven Mechanisms—Part 2: Nonlinear System Models
Fan Y. Chen,N. Polvanich +1 more