Dynamical modeling and multi-pulse chaotic dynamics of cantilevered pipe conveying pulsating fluid in parametric resonance

Multiple internal resonances and modal interaction processes of a cable-stayed bridge physical model subjected to an invariant single-excitation

The internal resonance of a two degree-of-freedom mechanical system with all typical (quadratic and cubic) geometric nonlinearities is studied, limiting to the case of free dynamics. The Multiple Time Scale method is used to provide an analytical, closed form, approximation of the backbone curves. The cornucopia of different possible behaviours that can been obtained by varying the nonlinear stiffnesses is discussed in depth, illustrating them with some examples and verifying with numerical simulations. Some partially unexpected or relevant behaviours are highlighted, and some hints on how to exploit the proposed results to design nonlinearly tailored systems are given.

1:1 internal resonance in a two d.o.f. complete system: a comprehensive analysis and its possible exploitation for design

Planar multimodal 1:2:2 internal resonance analysis of cable-stayed bridge

Based on a double cable-stayed shallow arch model of the cable-stayed bridge, the novel dynamic theory and analysis of nonlinear dynamic behavior of the system when cables' upper ends are subjected to harmonic excitation introduced by motion of tower are established and carried out. A set of partial differential equations governing the motion of present system are derived firstly according to the classic dynamic theories of cables and the shallow arch. Then, they are used to obtain the ordinary differential equations of the system by Galerkin's integral method. The corresponding modulation equations are derived by implementing the standard process of perturbation method of multiple scales when the 1:1:1 internal resonance among the lowest modes of cables and the shallow arch and external resonance of the system occur simultaneously. Frequency- and force-response curves are plotted to explore the rich dynamic behaviors of the system. The research shows the asymmetric harmonic excitations can cause the different jump phenomenon of cables, even the reverse jump is observed when the subharmonic resonance occurs.

Planar nonlinear dynamic behavior of a cable-stayed bridge under excitation of tower motion

A novel nonlinear dynamic double-cable-stayed shallow-arch model of cable-stayed bridge is established and the in-plane 1:1:1 internal resonance between three first modes of shallow arch and two cables under both external primary and subharmonic resonance is investigated, respectively. The Galerkin discretization and the method of multiple scales are applied to obtain the modulation equations of the dynamic system. The stable equilibrium solutions of the modulation equations are examined by Newton-Raphson method. Numerical simulations are carried out to investigate the dynamic behavior of the new dynamic system and Runge-kutta method is also used to solve the ordinary differential equations to verify the results. The results show the rich nonlinear phenomena and some new conclusions are also drawn.

/pdf/dynamic-modeling-and-in-plane-1-1-1-internal-resonance-4f33gwbkp1.pdf

Lian Hua Wang

Papers

Dynamic modeling and in-plane 1:1:1 internal resonance analysis of cable-stayed bridge