On the symmetric modal interaction of the suspended cable: Three-to-one internal resonance

2006 ◽  
Vol 294 (4-5) ◽  
pp. 1073-1093 ◽  
Author(s):  
Yueyu Zhao ◽  
Lianhua Wang
Keyword(s):  
Internal Resonance ◽  
Modal Interaction ◽  
Suspended Cable

Nonlinear Dynamics of Functionally Graded Material Plates Under Dynamic Liquid Load and with Longitudinal Speed

2017 ◽  
Vol 09 (04) ◽  
pp. 1750054 ◽  
Author(s):  
Yan Qing Wang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Functionally Graded Material ◽  
Internal Resonance ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Modal Interaction ◽  
Liquid Load ◽  
Graded Material

This paper investigates the dynamics of functionally graded material (FGM) plates under dynamic liquid load and with longitudinal speed. The liquid is assumed to be ideal so that it is incompressible, inviscid and irrotational. Based on the D’Alembert’s principle, the mathematical model of the system is developed by taking into account geometrical and material nonlinearities as well as velocity potential and Bernoulli’s equation. The Galerkin method is employed to discretize the partial differential governing equation to a series of ordinary differential ones, which are then analyzed via the use of the method of harmonic balance. Analytical results are compared with numerical ones to validate the present method. The stability of the steady-state response is examined by means of the perturbation technique. Linear analysis of the system shows the possible appearance of internal resonance, and nonlinear frequency-response curves demonstrate strong hardening-spring property of the system. A modal interaction behavior through 1:1 internal resonance is detected; the behavior can happen in a wide domain of constituent volume fraction, which is a unique phenomenon in moving FGM plates compared with their metallic counterparts. Furthermore, results show the modal interaction can be easily evoked in the moving FGM plate under dynamic liquid load, even while the plate is subjected to minimal exciting force or large damping. In addition, influence of the plate location on nonlinear dynamics of the system is examined; results show the dynamic response of the plate will change considerably when the plate is near the container wall.

Comments on Energy Harvesting on a 2:1 Internal Resonance Portal Frame Support Structure, Using a Nonlinear-Energy Sink as a Passive Controller

2016 ◽  
Vol 10 (3) ◽  
pp. 147 ◽  
Author(s):  
Rodrigo Tumolin Rocha ◽  
Jose Manoel Balthazar ◽  
Angelo Marcelo Tusset ◽  
Vinicius Piccirillo ◽  
Jorge Luis Palacios Felix
Keyword(s):  
Energy Harvesting ◽  
Internal Resonance ◽  
Nonlinear Energy Sink ◽  
Support Structure ◽  
Portal Frame ◽  
Energy Sink ◽  
Nonlinear Energy

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

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