Exact Evaluation of Natural Frequency and Damping Ratio from a Frequency Response Curve

2000 ◽  
Vol 123 (3) ◽  
pp. 403-405 ◽  
Author(s):  
M. V. Drexel ◽  
J. H. Ginsberg
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Fundamental Property ◽  
Response Curves ◽  
Single Degree Of Freedom ◽  
Analysis Techniques ◽  
Modal Damping ◽  
Exact Evaluation ◽  
Simple Characteristic

Several experimental modal analysis techniques fit resonance peaks to the response curves of a single degree of freedom system in order to identify the natural frequencies and modal damping ratios. The present study identifies a fundamental property of frequency response curves that allows the natural frequency to be identified from a simple characteristic of the curve, independently of the damping ratio. After the natural frequency has been determined, the damping ratio can be computed directly. The fundamental property holds for all values of damping, which eliminates the need to approximate either the natural frequency or damping ratio.

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.

Dynamic Analysis and Parameter Identification of a Single Mass Elastomeric Isolation System Using a Maxwell-Voigt Model

2006 ◽  
Vol 128 (6) ◽  
pp. 713-721 ◽  
Author(s):  
Jie Zhang ◽  
Christopher M. Richards
Keyword(s):  
Parameter Identification ◽  
Dynamic Analysis ◽  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Response Spectra ◽  
Isolation System ◽  
Single Mass ◽  
Voigt Model ◽  
Stiffness And Damping

Dynamic analysis and parameter identification of a single mass elastomeric isolation system represented by a Maxwell-Voigt model is examined. Influences that the stiffness and damping values of the Maxwell element have on natural frequency, damping ratio, and frequency response are uncovered and three unique categories of Maxwell-type elements are defined. It is also shown that Voigt and Maxwell-Voigt models with equivalent natural frequencies and damping ratios can have considerably different frequency response spectra. Lastly, a parameter identification method is developed for identifying Maxwell-Voigt models from frequency response spectra. The method is based on constant natural frequency and damping ratio curves generated from modal analysis of potential Maxwell-Voigt models.

Damping Ratio Estimation Techniques for Rotordynamic Stability Measurements

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
C. Hunter Cloud ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett
Keyword(s):  
Complex Systems ◽  
Damping Ratio ◽  
Ratio Estimation ◽  
Single Degree Of Freedom ◽  
Estimation Techniques ◽  
Single Degree ◽  
Modal Damping ◽  
Alternative Approach ◽  
Measurement Setting ◽  
Stability Measurements

Rotor stability is most commonly estimated using methods derived from a simple single degree of freedom system. When the modes of more complex systems, such as rotors, are closely spaced, we demonstrate that such methods can yield very poor estimates of the modal stability (damping ratio). Multiple output backward autoregression (MOBAR) is proposed as an alternative approach and is demonstrated to yield reasonably accurate estimates of modal damping even when modes are closely spaced. The performance of the MOBAR approach is then examined on an experimental rotor in tilt-pad bearings, demonstrating good performance in a realistic measurement setting.

Mitigation of Vortex-Induced Vibrations of a Pivoted Circular Cylinder Using an Adaptive Pendulum Tuned-Mass Damper

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Sina Kheirkhah ◽  
Richard Lourenco ◽  
Serhiy Yarusevych ◽  
Sriram Narasimhan
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Damping Ratio ◽  
Tuned Mass Damper ◽  
Single Frequency ◽  
Fundamental Frequencies ◽  
Transverse Vibrations ◽  
Synchronization Region ◽  
Vortex Induced Vibrations ◽  
Mass Damper

A novel adaptive pendulum tuned-mass damper (TMD) was integrated with a two degree-of-freedom (DOF) cylindrical structure in order to control vortex-induced vibrations of the structure. The natural frequency of the TMD was adjusted autonomously in order to control the vortex-induced vibrations. The experiments were performed at a constant Reynolds number of 2100 and for four reduced velocities, 4.18, 5.44, 6.00, and 6.48. Two TMD damping ratios, 0 and 0.24, were investigated for a constant TMD mass ratio of 0.087. The results demonstrate that tuning the natural frequency of the TMD to the natural frequency of the structure decreases the amplitudes of transverse and streamwise vibrations of the structure significantly. Specifically, the transverse amplitudes of vibrations are decreased by a factor of ten and streamwise amplitudes of vibrations are decreased by a factor of three. Depending on the value of the TMD damping ratio, the frequency of transverse vibrations is either characterized by the natural frequency of the structure or by two other fundamental frequencies, one higher and the other lower than the natural frequency of the structure. The results demonstrate that, independent of the TMD damping and tuning frequency ratios, the frequency of streamwise vibrations matches that of the transverse vibrations in the synchronization region, and the cylinder traces elliptic trajectories. A mathematical model is proposed to gain insight into the frequency response of the structure and fluid-structure interactions. The model shows that, for low TMD damping ratios, the frequency response of the structure equipped with the TMD is characterized by two fundamental frequencies; whereas, for relatively high TMD damping ratios, the frequency response of the structure is characterized by a single frequency, i.e., the natural frequency. In both cases, the fluid forcing within the synchronization region is linked to the fundamental frequency/frequencies of the structure. Thus, the classical definition of synchronization applies to multiple DOF structures undergoing vortex-induced vibrations.

Operational Modal Analysis of Broaching Machine

2012 ◽  
Vol 159 ◽  
pp. 170-175
Author(s):  
Lv Gao Lin ◽  
Shen Shun Ying ◽  
Shu Qiong Chen ◽  
Xiao Tian Lv
Keyword(s):  
Cutting Force ◽  
Natural Frequency ◽  
Fundamental Frequency ◽  
Dynamic Properties ◽  
Damping Ratio ◽  
Modal Parameters ◽  
Modal Shape ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Cutting Velocity

Modal parameters for LG51SH broaching machine from operational responses are studied to examine the dynamic properties of mechanical structure. The operational modal is analyzed using PolyMAX method with responsive data of key point in broaching machine, which is excited in practical broaching operation and tested by LMS SCADAIII-105 system. The identified steady state modal, representative modal shape, modal damping ratio and natural frequency in broaching are presented. The test and analysis result shows that there are natural frequency of 38Hz and 192Hz, which are close to multiple of the fundamental frequency of cutting force in broaching, 6Hz, therefore, reasonable cutting velocity should be adopted to void producing fundamental frequency of cutting force in broaching.

Numerical Study of a New Variable Friction TMD

2011 ◽  
Vol 243-249 ◽  
pp. 5450-5457 ◽  
Author(s):  
Li Qin ◽  
Wei Ming Yan ◽  
Sheng Bo Guo
Keyword(s):  
Frequency Response ◽  
Numerical Study ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Structural Response ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Equivalent Damping ◽  
Response Characteristics ◽  
Variable Friction

The paper proposes a new variable friction system, of which the friction force can increase linearly with the displacement of system. This new system can be used in TMD to avoid the disadvantage of Coulomb friction TMD. Using first order harmonic balance method, the equivalent damping ratio and frequency of SDOF variable friction system is deduced and analyzed. The frequency response characteristics of SDOF variable friction system is discussed. The control effectiveness of variable friction TMD under harmonic excitation is analyzed theoretically. The results demonstrate that the frequency response curves of variable friction TMD and classically damped TMD are similar and both can effectively reduce structural response under harmonic excitation.

Damping Ratio Estimation Techniques for Rotordynamic Stability Measurements

2008 ◽  
Author(s):  
C. Hunter Cloud ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett
Keyword(s):  
Complex Systems ◽  
Damping Ratio ◽  
Ratio Estimation ◽  
Single Degree Of Freedom ◽  
Estimation Techniques ◽  
Single Degree ◽  
Modal Damping ◽  
Alternative Approach ◽  
Measurement Setting ◽  
Stability Measurements

Rotor stability is most commonly estimated using methods derived from a simple, single degree of freedom (SDOF) system. When the modes of more complex systems, such as rotors, are closely spaced, we demonstrate that such methods can yield very poor estimates of the modal stability (damping ratio). Multiple output backward autoregression (MOBAR) is proposed as an alternative approach and is demonstrated to yield reasonably accurate estimates of modal damping even when modes are closely spaced. The performance of the MOBAR approach is then examined on an experimental rotor in tilt-pad bearings, demonstrating good performance in a realistic measurement setting.

Bifurcation Modes of Periodic Solution in a Duffing System Under Constant Force as Well as Harmonic Excitation

2019 ◽  
Vol 29 (13) ◽  
pp. 1950173 ◽  
Author(s):  
Lei Hou ◽  
Xiaochao Su ◽  
Yushu Chen
Keyword(s):  
Frequency Response ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Nonlinearity Parameter ◽  
Constant Force ◽  
Response Curves ◽  
Duffing System ◽  
Singularity Method

This paper focuses on the classification of the bifurcation modes of a Duffing system under the combined excitations of constant force and harmonic excitation. The Harmonic Balance method combined with the arc-length continuation is used to obtain the periodic solutions of the system, and the Floquet theory is employed to analyze the stability of the corresponding solutions. Accordingly, the frequency-response curves affected respectively by the constant force and the magnitude of the harmonic excitation are analyzed to show the basic dynamical properties of the system. Afterwards, the bifurcation investigations are carried out with the aid of the two-state variable singularity method. It is derived that there are a total of six different types of bifurcation modes due to the effects of the constant force and the magnitude of the harmonic excitation. At last, the effects of the nonlinearity parameter and the damping ratio on the bifurcation modes of the system are also discussed. The results obtained in this paper extend the findings in reference that the system can have markedly three types of frequency-response curves: with only one solution, or with maximum three or five solutions for a certain excitation frequency, and contribute to a better understanding of the significant influence of the constant force.

An Analysis of Higher Order Effects in the Half Power Method for Calculating Damping

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
Ivan Wang
Keyword(s):  
Frequency Response ◽  
Classical Method ◽  
Damping Ratio ◽  
Higher Order ◽  
Order Effects ◽  
Power Method ◽  
Response Curves ◽  
Third Order ◽  
Truncation Errors ◽  
Half Power

The half power method is a technique commonly used for calculating the system damping using frequency response curves. Past derivations typically assume a small damping ratio but do not keep track of the order of magnitude when simplifying results and focus mainly on displacement frequency response curves. This paper provides two separate and rigorous derivations of the half power bandwidth for displacement and acceleration frequency response functions. The exact expressions are simplified systematically using binomial expansions to include third order effects. The third order and classical approximations are compared with the exact expressions, and the truncation errors are presented for both displacement and acceleration cases. The high order effects are more apparent and the truncation errors are greater for the acceleration case. The classical method is sufficiently accurate for many practical cases where the damping ratio is less than 0.1 but higher order corrections may be used to reduce truncation error for systems where the damping ratio is higher.

Frequency response of human soleus muscle

1976 ◽  
Vol 39 (4) ◽  
pp. 788-793 ◽  
Author(s):  
P. Bawa ◽  
R. B. Stein
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Soleus Muscle ◽  
Damping Ratio ◽  
Low Frequency ◽  
Second Order ◽  
Order System ◽  
Pass Filter ◽  
Stimulus Pulse ◽  
Low Pass Filter

1. The properties of human soleus muscle were studied by systems analysis. Single stimulus pulses and random stimulus pulse trains were applied to a branch of the nerve to soleus muscle and the resultant tension fluctuations were recorded. 2. The frequency-response function between stimulus pulses and tension conforms to that of a second-order, low-pass filter. The parameters of the second-order system, low frequency gain, natural frequency, and damping ratio, varied systematically with the angle of the ankle. As the ankle was flexed (the length of the muscle was increased), the low frequency gain increased, the natural frequency decreased, and the damping ratio was unaffected or increased slightly. 3. These results are discussed in relation to the twitch responses of human soleus muscles and the responses previously observed in cat muscles.

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