Optimal Isolation of a Single-Degree-of-Freedom System With Quadratic-Velocity Damping

1981 ◽  
Vol 48 (3) ◽  
pp. 676-678 ◽  
Author(s):  
T. L. Alley
Keyword(s):  
Closed Form ◽  
Simple Formula ◽  
Degree Of Freedom ◽  
Isolation System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Spring ◽  
Velocity Input

The response of a mass isolated by a linear spring and a quadratic-velocity damper subjected to a step-and-decay velocity input at the base is found in closed form. This solution leads immediately to the optimal isolation system for this input. The parameters of the optimal isolation system are given by a simple formula.

A Modular-Type Three-Axis Vibration Isolation System Using Negative Stiffness

2010 ◽  
Author(s):  
Md. Emdadul Hoque ◽  
Takeshi Mizuno ◽  
Yuji Ishino ◽  
Masaya Takasaki
Keyword(s):  
Vibration Isolation ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Negative Stiffness ◽  
Isolation System ◽  
Single Degree Of Freedom ◽  
Vibration Isolation System ◽  
Single Degree ◽  
In Series ◽  
Isolation Systems

A vibration isolation system is presented in this paper which is developed by the combination of multiple vibration isolation modules. Each module is fabricated by connecting a positive stiffness suspension in series with a negative stiffness suspension. Each vibration isolation module can be considered as a self-sufficient single-degree-of-freedom vibration isolation system. 3-DOF vibration isolation system can be developed by combining three modules. As the number of motions to be controlled and the number of actuators are equal, there is no redundancy in actuators in such vibration isolation systems. Experimental results are presented to verify the proposed concept of the development of MDOF vibration isolation system using vibration isolation modules.

Effect of Third Harmonic Vibratory Force on a Linear Spring-Mass System

1963 ◽  
Vol 67 (636) ◽  
pp. 799-803
Author(s):  
C. L. Kirk
Keyword(s):  
Resonant Frequency ◽  
Elastic System ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Third Harmonic ◽  
Single Degree ◽  
Linear Spring

SummaryThe response of an elastic system having a single degree of freedom, to a vibratory force whose waveform can be varied, is examined. The variable waveform is produced by a system of two pairs of unbalanced rotors in which one pair rotates at three times the speed of the other pair. The waveform depends on the frequency of excitation, the phasing of the rotors and the ratio of their amounts of unbalance. If the rotors are run at a speed at which the faster pair rotates above resonance while the slower pair rotates below resonance, a frequency is found at which the rate of change of amplitude with respect to frequency is zero. At this point, however, the waveform is quite sensitive to small changes in the frequency of excitation. If the rotor speeds cannot be maintained constant, and if stable vibration waveforms are required, it is necessary to run the slowest rotor well above the resonant frequency where both the amplitude and waveform will be virtually independent of frequency.

A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage

2000 ◽  
Vol 124 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Gordon R. Pennock ◽  
Atif Hasan
Keyword(s):  
Closed Form ◽  
Systematic Approach ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Special Point ◽  
Eighth Order ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Original Contribution ◽  
Curve Equation

This paper presents a closed-form polynomial equation for the path of a point fixed in the coupler links of the single degree-of-freedom eight-bar linkage commonly referred to as the double butterfly linkage. The revolute joint that connects the two coupler links of this planar linkage is a special point on the two links and is chosen to be the coupler point. A systematic approach is presented to obtain the coupler curve equation, which expresses the Cartesian coordinates of the coupler point as a function of the link dimensions only; i.e., the equation is independent of the angular joint displacements of the linkage. From this systematic approach, the polynomial equation describing the coupler curve is shown to be, at most, forty-eighth order. This equation is believed to be an original contribution to the literature on coupler curves of a planar eight-bar linkage. The authors hope that this work will result in the eight-bar linkage playing a more prominent role in modern machinery.

The Dynamics of Springboards

1994 ◽  
Vol 10 (4) ◽  
pp. 335-351 ◽  
Author(s):  
Bob W. Kooi ◽  
Max Kuipers
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Flight Phase ◽  
Single Degree ◽  
Linear Spring

The maneuvers of a competition diver on a springboard before takeoff may serve to maximize the height of the flight phase. To simplify analysis, it is often assumed that the diver performs motions at the top of a single degree-of-freedom (DOF) system, usually consisting of one mass and one linear spring. This system is expected to simulate the behavior of the board sufficiently. In this paper we propose a new single DOF system approximating the effects of a board with passable accuracy. This model is applied to three types of springboards to obtain numerical values for their virtual masses at the tip.

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