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.

The Acceleration of a Single Degree of Freedom System Through its Resonant Frequency

1958 ◽  
Vol 62 (574) ◽  
pp. 752-757 ◽  
Author(s):  
S. Hother-Lushington ◽  
D. C. Johnson
Keyword(s):  
Resonant Frequency ◽  
Critical Speed ◽  
Bessel Functions ◽  
Degree Of Freedom ◽  
Series Solutions ◽  
Mechanical Vibrations ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Method Of Solution ◽  
Simple Integration

It is Sometimes required to find the maximum amplitudes of vibration attained and the speeds at which they occur when a machine is run through its critical speed with different accelerations. The solution of this problem for single degree of freedom systems has been obtained by Lewis and by Ellington and McCallion for mechanical vibrations and by Hok for the equivalent electrical case. These solutions require higher mathematics (contour integration, Fresnel's integrals or series solutions leading to Bessel functions). The purpose of this note is to show how, by using simple integration only, an alternative method of solution can be obtained for both zero and small values of damping.

scholarly journals The Spectrum Dip of Deck Mounted Systems

2010 ◽  
Vol 17 (1) ◽  
pp. 55-69
Author(s):  
R.J. Scavuzzo ◽  
G.D. Hill ◽  
P.W. Saxe
Keyword(s):  
Vertical Motion ◽  
Base Point ◽  
Degree Of Freedom ◽  
Mass System ◽  
Detailed Model ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Fixed Base ◽  
Grid Points ◽  
Modal Mass

In this paper, a detailed model of a ship deck and attached dynamic systems was developed and subjected to dynamic studies using two different shock inputs: a triangular shaped velocity pulse and the vertical motion of the innerbottom of the standard Floating Shock Platform (FSP). Two studies were conducted, one considering four single degree-of-freedom systems attached at various deck locations and another considering a three-mass system attached at one location. The two shock inputs were used only for the multi-mass system study. The triangular pulse was used for the four single degree-of-freedom systems study. For the single degree-of-freedom systems study, shock spectra were first calculated at the four mounting locations assuming the oscillators were not present. Then the oscillator systems were added to these grid points to determine the change in the shock spectra. First, the oscillators were added one at a time, and then all the oscillators were added to the deck. The multi-mass system was analyzed using both shock inputs. First, the fixed-base modal masses and frequencies were determined. Then, the system as a whole was attached to the deck and the spectrum values at the base point were determined and compared to those for the free deck case. In the last step each mode of the multi-mass system, represented by a single degree-of-freedom system with the modal mass and appropriate spring stiffness, was considered individually to determine the spectrum responses. Results of the free deck, the entire system and individual modal responses are compared.

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.

Extended Camus Theory and Higher Order Conjugated Curves

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Stationary Point ◽  
Higher Order ◽  
Degree Of Freedom ◽  
The Other ◽  
Body System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Pair Generation ◽  
Three Body ◽  
Two Bodies

According to Camus’ theorem, for a single degree-of-freedom (DOF) three-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold–Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e., slide along itself) on the line of the instant centers, a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotates about a stationary point, the stationary point embedded on a body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of Camus’ theorem. Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

Vibration Reduction and Isolation Using on-Off Control at Spring Support Joint: Application to Multi-Degrees-of-Freedom System

1999 ◽  
Author(s):  
Hideya Yamaguchi ◽  
Masahito Yashima ◽  
Takao Yoshikawa
Keyword(s):  
Degrees Of Freedom ◽  
Vibration Isolation ◽  
Degree Of Freedom ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Joint Application ◽  
Friction Joint ◽  
Modal Space ◽  
Spring Support

Abstract In order to achieve vibration isolation and reduction for a multi-degrees-of-freedom system, this paper develops the on-off control that has been proposed on the single-degree-of-freedom system by the authors. The method introduces an additional spring and mass system, and the additional mass is designed to control the clamping friction force by the friction joint switching mechanism. The non-linear control law for the single-degree-of-freedom system is applied to a multi-degrees-of-freedom system by incorporating the idea of the independent modal space control (IMSC) method. Numerical simulations and experiments demonstrate the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document