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A piecewise linear suspension bridge model: Nonlinear dynamics and orbit continuation. (English) Zbl 0855.34041

The research of the paper under review refers to the effect of harmonic excitation on suspension bridges; these are the preliminary approaches for the understanding of the action of wind and certain kinds of earthquake. Their particular interest lies in the role of the one-sided stiffness of the hangers in the resultant transverse and torsional motions.

The study of the suspended bridge is based on a Lazer-Mckenna model, it consists of establishing the conditions for the existence of asymptotic periodic solutions and it is done using a two-part Poincaré map.

In order to classify stable and unstable solutions and to determine precisely the bifurcation points the authors develop a numerical solution of the ordinary differential equations which describe the evolution of the studied system.

Before the analysis of the conclusions which prove the compatibility of experimental results and theoretical assumptions, the last part of the paper illustrates the possibility of occuring both destructive and nondestructive solutions at the same point of parameter space.

Reviewer: I.Grosu (Iaşi)
MSC:
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C23Bifurcation (ODE)
37-99Dynamic systems and ergodic theory (MSC2000)
34C37Homoclinic and heteroclinic solutions of ODE