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.

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.

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.

Vibration control of a servomotor-driven coupled elastic shaft-elastic beam system

2004 ◽  
Vol 218 (10) ◽  
pp. 1115-1124
Author(s):  
H Diken ◽  
A Ankarali
Keyword(s):  
Control System ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Step Response ◽  
Elastic Shaft ◽  
Disc Rotation ◽  
Frequency Ratios ◽  
System Frequency

In this study an elastodynamic control system consisting of servomotor, elastic shaft, disc and elastic beam, which is attached to the disc, is considered. Non-dimensional parametric equations of motions are obtained. The control system damping ratio, the frequency ratio of the torsional natural frequency to the beam natural frequency and also the frequency ratio of the beam natural frequency to the control system frequency are used as parameters. Simulation results are obtained for the step response of the disc rotation and for the beam tip vibration for different frequency ratios. Results show that even for highly flexible systems the effect of flexibility on the control system behaviour can be substantially reduced by proper selection of the control system frequency.

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.

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.

scholarly journals Dynamic Analysis and Experiment of 6-DOF Compliant Platform Based on Bridge-Type Amplifier

Micromachines ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 1024
Author(s):  
Chao Lin ◽  
Shan Zheng ◽  
Mingdong Jiang
Keyword(s):  
Dynamic Model ◽  
Natural Frequency ◽  
Theoretical Calculations ◽  
Lagrange Equation ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Analytical Models ◽  
Step Response ◽  
Element Analysis ◽  
Bridge Type

In this paper, we establish a dynamic model of a six-degrees-of-freedom (6-DOF) compliant positioning platform based on bridge-type amplifiers. Based on the elastic beam theory and energy relationship, we derived the bridge-type amplifier’s dynamic model using the Lagrange equation. Then, we established a dynamic model of the compliant platform based on the equivalent mass and equivalent stiffness of the bridge-type amplifier, and the analysis formula of the natural frequency was derived. Finally, the analytical models of natural frequencies of the bridge-type amplifier and the compliant platforms were verified using the finite element analysis (FEA) method. Through modal experiments, the damping ratio and natural frequency were identified. Step response experiments in the X/Y direction and Z direction were performed. The phenomenon that the experimental results appeared to match the theoretical calculations indicates that the dynamic model was accurate.

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.

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Linear Theory ◽  
Lateral Force ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Rotating Disks ◽  
Critical Speeds ◽  
Applied Forces ◽  
Thin Disks

Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.

Sign in / Sign up

Export Citation Format

Share Document