Estimating the Roots of the Characteristic Determinant for Multicoupled Systems

1960 ◽  
Vol 82 (1) ◽  
pp. 87-95
Author(s):  
S. Lees ◽  
H. D. Felsenthal ◽  
E. M. Goldberg
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Residue Theorem ◽  
Characteristic Determinant ◽  
Underlying Theory ◽  
Undamped Natural Frequency ◽  
Inputs And Outputs

A procedure is developed, based on Couchy’s residue theorem, for bounding the undamped natural frequency, damping ratio, and real part of the roots of the characteristic determinant associated with a multicoupled system with several inputs and outputs. The method can lead to a locus of the roots as one or more parameters are varied. The underlying theory is developed and a numerical illustrative example is included.

Determination of frequency response from step response: application to fluid-filled catheters

1979 ◽  
Vol 236 (2) ◽  
pp. H376-H378 ◽  
Author(s):  
S. A. Glantz ◽  
J. V. Tyberg
Keyword(s):  
Decay Rate ◽  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Step Change ◽  
Step Response ◽  
Undamped Natural Frequency

The performance of a fluid-filled catheter can be described by reporting its undamped natural frequency and damping ratio. These parameters can be measured by subjecting the catheter to sinusoidally varying pressures at a wide variety of frequencies to obtain the frequency response. They can also be computed from the response to a step change in pressure, which is often easier to produce. This paper derives the required equations and includes a graph which permits one to look up the undamped natural frequency after measuring the period and decay rate of the oscillation following a step change in pressure.

scholarly journals Fluid-Induced Vibration Elimination of a Rotor/Seal System with the Dynamic Vibration Absorber

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Qi Xu ◽  
Junkai Niu ◽  
Hongliang Yao ◽  
Lichao Zhao ◽  
Bangchun Wen
Keyword(s):  
Natural Frequency ◽  
Nonlinear Differential Equations ◽  
Damping Ratio ◽  
Force Model ◽  
Vibration Absorbers ◽  
Dynamic Vibration Absorber ◽  
Major Purpose ◽  
Rotating Speed ◽  
Dynamic Vibration ◽  
Nonlinear Responses

The dynamic vibration absorbers have been applied to attenuate the rotor unbalance and torsional vibrations. The major purpose of this paper is to research the elimination of the fluid-induced vibration in the rotor/seal system using the absorber. The simplified rotor model with the absorber is established, and the Muszynska fluid force model is employed for the nonlinear seal force. The numerical method is used for the solutions of the nonlinear differential equations. The nonlinear responses of the rotor/seal system without and with the absorber are obtained, and then the rotating speed ranges by which the fluid-induced instability can be eliminated completely and partially are presented, respectively. The absorber parameters ranges by which the instability vibration can be eliminated completely and partially are obtained. The results show that the natural frequency vibration due to the fluid-induced instability in the rotor/seal system can be eliminated efficiently using the absorber. The appropriate natural frequency and damping ratio of the absorber can extend the complete elimination region of the instability vibration and postpone the occurrence of the instability vibration.

Enhancement of vibration characteristics in filament wound FRP composite shafts using nitinol wires

2018 ◽  
Vol 47 (5) ◽  
pp. 377-385 ◽  
Author(s):  
Kannan Murugesan ◽  
Kalaichelvan K. ◽  
M.P. Jenarthanan ◽  
Sornakumar T.
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Filament Winding ◽  
Fiber Reinforced ◽  
Content Type ◽  
Fiber Reinforced Plastic ◽  
Damping Characteristics ◽  
Filament Wound ◽  
Reinforced Plastic ◽  
Hollow Shafts

Purpose The purpose of this paper is to investigate the use of embedded Shape Memory Alloy (SMA) nitinol wire for the enhancement of vibration and damping characteristics of filament-wound fiber-reinforced plastic composite hollow shafts. Design/methodology/approach The plain Glass Fiber-Reinforced Plastic (GFRP) and plain Carbon Fiber-Reinforced Plastic (CFRP) hollow shafts were manufactured by filament winding technique. Experimental modal analysis was conducted for plain hollow shafts of C1045 steel, GFRP and CFRP by subjecting them to flexural vibrations as per ASTM standard C747, with both ends clamped (C-C) end condition to investigate their vibration and damping behavior in terms of first natural frequency, damping time and damping ratio. Nitinol wires pre-stressed at various pre-strains (2, 4 and 6 per cent) were embedded with CFRP hollow shafts following same manufacturing technique, and similar experimental modal analysis was carried out by activating nitinol wires. The first natural frequencies of all the shaft materials were also predicted theoretically and compared with experimental measurements. Findings Among the three materials C1045 steel, plain GFRP and plain CFRP, the vibration and damping behavior were found to be the best for plain CFRP. Hence, CFRP shafts were considered for further improvement by embedding nitinol wires at pre-stressed condition. For CFRP shafts embedded with nitinol wires, the damping time decreased; and damping ratio and first natural frequency increased with increase in percentage of pre-strain. In comparison with plain CFRP, 7 per cent increase in first natural frequency and 100 per cent increase in damping ratio were observed for nitinol embedded CFRP shafts with 6 per cent pre-strain. Theoretical predictions of the first natural frequencies agree well with the experimental results for all the shaft materials. Originality/value The effect of nitinol on vibration and damping characteristics of filament wound hollow CFRP composite shafts with different pre-strains has not been studied extensively by the previous researchers. This paper addresses the effect of embedded nitinol wires pre-stressed at three varied pre-strains, that is, 2, 4 and 6 per cent on the vibration and damping characteristics of composite hollow CFRP shafts manufactured by filament winding technique.

Dynamic Vibration Absorber for a Ropeway Carrier

1997 ◽  
Author(s):  
Hiroshi Matsuhisa ◽  
Osamu Nishihara
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Moving Mass ◽  
Dynamic Vibration Absorber ◽  
Damping Effect ◽  
The World ◽  
Dynamic Absorber ◽  
First Time ◽  
Suspended Bridge

Abstract Ropeways such as gondola lifts have attracted increasing interest as a means of transportation in cities. However, swing of ropeway carriers is easily caused by wind, and usually a ropeway cannot operate if the wind velocity exceeds about 15m/s. The study of how to reduce the wind-induced swing of ropeway carriers has attracted many researchers. It had been said that it was impossible to reduce the vibration of pendulum type structures such as ropeway carriers by a dynamic absorber. But in 1993, Matsuhisa showed that the swing of carrier can be reduced by a dynamic absorber if it is located far above or below from the center of oscillation. Based on this finding, a dynamic absorber composed of a moving mass on an arc-shaped track was designed for practical use, and it was installed in chairlift-type carriers and gondola type carriers in snow skiing sites in Japan in 1995 for the first time in the world. It has been shown that a dynamic absorber with the weight of one tenth of the carrier can reduce the swing to half. The liquid dynamic absorber was also investigated. It has the same damping effect as the conventional solid absorber. It is easy to adjust the natural frequency and the damping ratio, and the structure is simple. Therefore, it will be applied for not only ropeway carriers but also ships and rope suspended bridge and others.

The Optimization of Thermocouple Galvanometer System Dynamics When Measuring Temperature Transients

1973 ◽  
Vol 6 (9) ◽  
pp. 384-388
Author(s):  
W. H. McKenzie ◽  
A. H. Richards
Keyword(s):  
System Dynamics ◽  
Natural Frequency ◽  
Time Constant ◽  
Exponential Type ◽  
Natural Frequencies ◽  
Low Voltage ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Ultra Violet ◽  
Dimensional Parameter

When using thermocouples directly connected to ultra-violet galvanometers for recording temperature transients, the low-voltage outputs necessitate the use of galvanometers with low natural frequencies. This puts a limitation on the overall dynamic performance. In a particular application, the user has to select the damping resistor for the galvanometer and the work describes how this is done so that the system is optimised for minimum integrated errors during a transient. The transient considered was of an exponential type which occurs frequently in practice and it is shown that the correct damping ratio and hence damping resistor for the galvanometer depends upon the non-dimensional parameter defined by the product of the natural frequency of the galvanometer and the time constant of the exponential. The results show that the usual value of damping ratio of 0·64 based on minimum sinusoidal distortion has to be modified for best dynamic performance. However, if the non-dimensional parameter is sufficiently large, higher values of damping can be used, which produce a large trace with acceptably small errors.

Effects of Additional Mass on Modal Experimental Analysis of 3-Dimension and 5-Direction Braided Composites

2010 ◽  
Vol 34-35 ◽  
pp. 1467-1470
Author(s):  
Yan Gao ◽  
Jia Lu Li
Keyword(s):  
Natural Frequency ◽  
Influence Factor ◽  
Damping Ratio ◽  
Force Response ◽  
Braided Composites ◽  
Additional Mass ◽  
Response Curves ◽  
Ratio Increase ◽  
Modal Test ◽  
Relative Errors

The work of vibration test has significant meanings for the researches and applications of 3-dimension and 5-direction braided composites. This article discusses the effects of added mass with different weight on the modal test of 3-dimension and 5-direction braided composites. The comparison of the modal parameters of 3-dimension and 5-direction braided composites tested by different weight of mass reveals that the additional mass is a mostly influence factor for vibration property of 3-dimension and 5-direction braided composites. The results of frequency response and force response curves show that smaller mass accelerometer is more effective for a wider range of frequencies around the resonance frequency, a higher natural frequency and a larger peak in these points. Force-response curves show that force response amplitude increases with the increase of additional mass weight, and the larger additional mass, the shorter time taken for reaching stationary state. The errors of natural frequency and damping ratio increase when the weight of additional mass increases. With the increase of modal orders, relative errors of modal characteristics have slighter decreasing degrees. The results derived from this article will provide a useful reference for precise modal analysis of 3-dimension and 5-direction braided composites.

Development and Design of the Dynamic Vibration Absorber Using Magneto-Rheological Elastomer for the Weight and Power Consumption Saving

2019 ◽  
Author(s):  
Osamu Terashima ◽  
Mika Nakata ◽  
Toshihiko Komatsuzaki
Keyword(s):  
Magnetic Field ◽  
Power Consumption ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Wide Band ◽  
Test Results ◽  
Dynamic Vibration Absorber ◽  
Small Power ◽  
Dynamic Absorber ◽  
Magneto Rheological

Abstract In this study, a broadband frequency tunable dynamic absorber was designed and fabricated based on the primary design principle of a mass damper. A magneto-rheological elastomer that can change the relative stiffness when an external magnetic field is applied was used to control the natural frequency of the movable mass of the absorber. A coil to generate the magnetic field was also used as a movable mass to decrease the total weight and to create a constant closed loop of the magnetic force. The hammer impact test results show that the present absorber could change its natural frequency with minimal electric power and had a constant damping ratio. Experimental results of vibration absorbing of an acrylic flat plate show that the proposed absorber could change the natural frequency of the movable mass and reduce the vibration over a wide band by constantly applying the optimum current to the coil in the device with a small power consumption (less than 10 W). Therefore, the proposed absorber works effectively. Further, a technique to determine the electric current applied to the coil automatically based on the phase difference of the vibrational acceleration of the movable mass and the vibrating objective was also presented.

Sign in / Sign up

Export Citation Format

Share Document