NON-LINEAR MODAL INTERACTIONS IN SHALLOW SUSPENDED CABLES

1999 ◽  
Vol 227 (1) ◽  
pp. 1-28 ◽  
Author(s):  
V.N. PILIPCHUK ◽  
R.A. IBRAHIM
Keyword(s):  
Modal Interactions ◽  
Non Linear ◽  
Suspended Cables

Experimental Investigation of Isolated and Simultaneous Internal Resonances in Suspended Cables

1995 ◽  
Vol 117 (4) ◽  
pp. 385-391 ◽  
Author(s):  
C. L. Lee ◽  
N. C. Perkins
Keyword(s):  
Experimental Investigation ◽  
Large Amplitude ◽  
Resonant Response ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Theoretical Predictions ◽  
Suspended Cables ◽  
Elastic Cables

The near resonant response of suspended elastic cables driven by harmonic, planar excitation is investigated experimentally. Measurements of large amplitude cable motions confirm previous theoretical predictions of fundamental classes of internally-resonant responses. For particular magnitudes of equilibrium curvature, strong modal interactions arise through isolated (two-mode) or simultaneous (three-mode) internal resonances. Four qualitatively different periodic responses are observed: (1) pure planar response, (2) 2:1 internally resonant nonplanar response, (3) 1:1 internally resonant nonplanar response, and (4) simultaneous, 2:2:1 internally resonant nonplanar response. Quasiperiodic responses are also observed.

Non-Linear Modal Interactions in a Suspension Rope System with Time-Varying Length

2006 ◽  
Vol 5-6 ◽  
pp. 217-224 ◽  
Author(s):  
Rodanthi Salamaliki-Simpson ◽  
Stefan Kaczmarczyk ◽  
Phil Picton ◽  
Scott Turner
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Time Varying ◽  
Modal Interaction ◽  
Modal Interactions ◽  
Autoparametric Resonance ◽  
Non Linear ◽  
Varying Length ◽  
Host Structure ◽  
Rope System

This paper focuses on the investigation of the autoparametric coupling effects and modal interactions in a suspension rope system with a time varying length. Equations of motion of a multi-degree-of-freedom discrete, non-stationary and non-linear model are presented and are used to analyze the dynamic response of an elevator suspension rope system under resonance conditions. The equations of motion involve quadratic and cubic non-linear terms which are responsible for the modal interaction between the lateral and longitudinal oscillations of the rope and the car motions. The model takes into account the periodic excitations caused by motion of the host structure. The results confirm that adverse responses may arise and internal autoparametric resonance phenomena may occur.

Multimode Dynamics and Out-of-Plane Drift in Suspended Cable Using the Kinematically Condensed Model

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Lianhua Wang ◽  
Yueyu Zhao ◽  
Giuseppe Rega
Keyword(s):  
Primary Resonance ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Modulation Equations ◽  
Plane Vibration ◽  
Suspended Cable ◽  
Out Of Plane ◽  
Large Amplitude Vibration ◽  
Suspended Cables ◽  
Plane Mode

The large amplitude vibration and modal interactions of shallow suspended cable with three-to-three-to-one internal resonances are investigated. The quasistatic assumption and direct approach are used to obtain the condensed suspended cable model and the corresponding modulation equations for the case of primary resonance of the third symmetric in-plane or out-of-plane mode. The equilibrium, periodic, and chaotic solutions of the modulation equations are studied. Moreover, the nonplanar motion and symmetric character of out-of-plane vibration of the shallow suspended cables are investigated by means of numerical simulations. Finally, the role played by the quasistatic assumption, internal resonance, and static configuration in disrupting the symmetry of the out-of-plane vibration is discussed.

Experimental Investigation of Isolated and Simultaneous Internal Resonances in Suspended Cables

1993 ◽  
Author(s):  
Christopher L. Lee ◽  
Noel C. Perkins
Keyword(s):  
Experimental Investigation ◽  
Large Amplitude ◽  
Resonant Response ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Theoretical Predictions ◽  
Suspended Cables ◽  
Elastic Cables

Abstract The near resonant response of suspended elastic cables driven by harmonic, planar excitation is investigated experimentally. Measurements of large amplitude cable motions confirm previous theoretical predictions of fundamental classes of internally-resonant responses. For particular magnitudes of equilibrium curvature, strong modal interactions arise through isolated (two-mode) or simultaneous (three-mode) internal resonances. Four qualitatively different periodic responses are observed: 1) pure planar response, 2) 2:1 internally resonant non-planar response 3) 1:1 internally resonant non-planar response, and 4) simultaneous, 2:2:1 internally resonant non-planar response. Quasi-periodic responses are also observed.

Design of a Simple Controller to Control Suspension Bridge Non-linear Vibrations due to Moving Loads

2005 ◽  
Vol 11 (7) ◽  
pp. 867-885 ◽  
Author(s):  
M. Abdel-Rohman
Keyword(s):  
Bridge Deck ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Control Mechanisms ◽  
Control Force ◽  
Moving Loads ◽  
Non Linear ◽  
Linear Vibrations ◽  
Suspended Cables ◽  
Non Linear System

The flexibility and low damping of the long span suspended cables in suspension bridges make them prone to non-linear vibrations due to wind and moving loads. In this paper we consider the dynamic response of a suspension bridge due to a vertical load moving with a constant speed on the bridge deck. Control mechanisms are suggested to generate control forces to control the non-linear vibrations in the bridge deck and the suspended cables. A simple design is presented for the controller based on the feedback of the velocity measurements taken at the control force location. The design is made first on a linear model before applying it to the actual non-linear system. The method is applied on three different types of control mechanisms. Comparison between the controlled responses using the three controllers indicates that, in addition to the method of designing the control actions, the feasibility of the active control depends mainly on the type of the control mechanism.

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