Experimental Observation of Amplitude- and Phase-Modulated Responses of Two Internally Coupled Oscillators to a Harmonic Excitation

1988 ◽  
Vol 55 (3) ◽  
pp. 706-710 ◽  
Author(s):  
A. H. Nayfeh ◽  
L. D. Zavodney
Keyword(s):  
Perturbation Theory ◽  
Qualitative Agreement ◽  
Coupled Oscillators ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Lower Mode ◽  
Quadratic Nonlinearities ◽  
Two Degree Of Freedom ◽  
Second Order Perturbation Theory

An experiment is performed on a two degree-of-freedom mechanical system having quadratic nonlinearities and linear natural frequencies ω1 and ω2 approximately in the ratio of two-to-one (i.e., ω2 ≈ 2ω1). When the lower mode is excited by a harmonic excitation whose frequency Ω is nearly equal to ω1, amplitude- and phase-modulated responses of the system have been observed for a range of the excitation frequency Ω, in qualitative agreement with the results of a second-order perturbation theory.

Vibration Control of Two-Degree-of-Freedom Structures Utilizing Sloshing in Nearly Square Tanks

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Shota Ninomiya
Keyword(s):  
Vibration Control ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Response Curves ◽  
Chaotic Motions ◽  
Installation Angle ◽  
Two Degree Of Freedom ◽  
Theoretical Results

This paper investigates the vibration control of a towerlike structure with degrees of freedom utilizing a square or nearly square tuned liquid damper (TLD) when the structure is subjected to horizontal, harmonic excitation. In the theoretical analysis, when the two natural frequencies of the two-degree-of-freedom (2DOF) structure nearly equal those of the two predominant sloshing modes, the tuning condition, 1:1:1:1, is nearly satisfied. Galerkin's method is used to derive the modal equations of motion for sloshing. The nonlinearity of the hydrodynamic force due to sloshing is considered in the equations of motion for the 2DOF structure. Linear viscous damping terms are incorporated into the modal equations to consider the damping effect of sloshing. Van der Pol's method is employed to determine the expressions for the frequency response curves. The influences of the excitation frequency, the tank installation angle, and the aspect ratio of the tank cross section on the response curves are examined. The theoretical results show that whirling motions and amplitude-modulated motions (AMMs), including chaotic motions, may occur in the structure because swirl motions and Hopf bifurcations, followed by AMMs, appear in the tank. It is also found that a square TLD works more effectively than a conventional rectangular TLD, and its performance is further improved when the tank width is slightly increased and the installation angle is equal to zero. Experiments were conducted in order to confirm the validity of the theoretical results.

scholarly journals Snapping of a Shallow Arch With Harmonic Excitation at One End

2007 ◽  
Vol 129 (4) ◽  
pp. 514-519 ◽  
Author(s):  
Jen-San Chen ◽  
Der-Wei Chang
Keyword(s):  
Natural Frequencies ◽  
Stable Equilibrium ◽  
Excitation Frequency ◽  
Longitudinal Direction ◽  
Harmonic Excitation ◽  
Small Distance ◽  
The Other ◽  
Base Line ◽  
Shallow Arch ◽  
Mechanical Shaker

In this paper we demonstrate both numerically and experimentally that it is possible to make a pinned-pinned shallow arch snap to and remain vibrating on the other side by harmonic excitation in the longitudinal direction at the end. One end of the arch is fixed in space, while the other end is attached to a mechanical shaker via a spring. The shaker-mount is first moved a small distance toward the arch to ensure that the arch assembly possesses two stable equilibrium positions, one on each side of the base line. The spring connecting the arch end and the mechanical shaker is carefully chosen such that a small shaker stroke can induce a large vibration amplitude in the arch. The natural frequencies of the two (initial and snapped, respectively) positions are measured first. By adjusting the excitation frequency of the mechanical shaker to the first natural frequency of either position of the arch, we demonstrate that the arch can be snapped to and remain vibrating on the other side when the magnitude of the electric current flowing through the shaker is properly chosen. The vibrant snapping action of the arch recorded in the experiment is confirmed by numerical simulation.

Nonlinear Vibrations of Elastic Structures Carrying Two Rectangular Liquid-Filled Tanks Under Horizontal Excitation

2005 ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Natural Frequencies ◽  
Hydrodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Response Curves ◽  
System Parameters ◽  
Chaotic Vibrations ◽  
Multi Mode

Nonlinear vibrations of an elastic structure carrying two liquid-filled tanks under horizontal harmonic excitation are investigated. When a 1:1:1 ratio of internal resonance is satisfied among the natural frequencies of the structure and sloshing in the two liquid tanks, modal equations are derived by using Galerkin’s method, taking into account the nonlinearity of the hydrodynamic force. Then, frequency response curves are calculated by using Andronov and Witt’s method. Peculiar vibrations, referred to as ‘multi-mode vibrations’, sometimes may appear depending on the values of the system parameters. They never occur in a structure carrying only one liquid-filled tank. In other words, even if the dimensions of the two tanks are identical, the sloshing which occurs in each tank differs depending on the excitation frequency. The multi-mode vibrations include constant amplitude vibrations and amplitude modulated motion as well as chaotic vibrations.

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

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