scholarly journals Natural Frequencies and Stability of a Spinning Disk Under Follower Edge Tractions

1997 ◽  
Vol 119 (3) ◽  
pp. 404-409 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Analytical Methods ◽  
Natural Frequencies ◽  
Low Frequency ◽  
Circular Disk ◽  
Interaction Frequency ◽  
Modal Interaction ◽  
Frequency Range ◽  
Reflected Waves ◽  
Spinning Disk ◽  
The Difference

The vibration and stability of a spinning disk under follower edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, natural frequencies of most of the non-reflected waves decrease, except some of the zero-nodal-circle modes with small number of nodal diameters in the low frequency range. When the spinning disk is under nonuniform traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction (frequency loci veering or merging) occurs when the difference between the number of nodal diameters of these two modes is equal to ±k. Types of modal interaction vary as the radius ratio of the circular disk changes. Analytical methods for predicting how the eigenvalue changes and what type of modal interaction will occur are proposed and verified.

Vibration and Stability of a Spinning Disk Under Stationary Distributed Edge Loads

1996 ◽  
Vol 63 (2) ◽  
pp. 439-444 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Modal Interaction ◽  
Reflected Waves ◽  
Reflected Wave ◽  
Nonzero Integer ◽  
Spinning Disk ◽  
The Difference

The vibration and stability of a spinning disk under conservative distributed edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, it is found that no modal interaction occurs and the natural frequencies of all nonreflected waves decrease, while the natural frequencies of the reflected waves increase. When the spinning disk is under distributed traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction may or may not occur. It is observed that when the difference between the number of nodal diameters of these two modes is equal to ±k, frequency veering occurs when both modes are nonreflected, and merging occurs when one of these two modes is a reflected wave. In applying this rule, the number of nodal diameters of the forward and the reflected wave is considered as negative.

A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

scholarly journals A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

1996 ◽  
Author(s):  
Ming-Ta Yang ◽  
Jerry H. Griffin
Keyword(s):  
Monte Carlo ◽  
Eigenvalue Problem ◽  
Perturbation Analysis ◽  
Material Properties ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Modal Interaction ◽  
Eigenvalue Approach ◽  
The Difference

Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

Two ranges in blood pressure power spectrum with different 1/f characteristics

1994 ◽  
Vol 267 (2) ◽  
pp. H449-H454 ◽  
Author(s):  
C. D. Wagner ◽  
P. B. Persson
Keyword(s):  
Blood Pressure ◽  
Time Series ◽  
Power Spectrum ◽  
Low Frequency ◽  
Frequency Range ◽  
F Region ◽  
Autonomic Blockade ◽  
Beta Receptor Blockade ◽  
The Difference ◽  
Fast Fourier Analysis

Most time series of biological systems contain a considerable amount of 1/f noise. This form of noise is characterized by fluctuations in which power steadily increases at lower frequencies. To determine the origin of 1/f noise, blood pressure (BP) was measured over 4 h in conscious foxhounds. The power spectrum of BP was obtained by fast Fourier analysis. After log-log transformation, the power spectrum (log power vs. log frequency) characteristically revealed a linear regression. Surprisingly, there were two 1/f ranges. The first 1/f region was located within a low-frequency range (< 10(-1.7) Hz; slope -0.9; r = -0.9). The second 1/f range was identified at 10(-1.4) to 10(-1) Hz (slope -1.2; r = -0.7). After baroreceptor denervation (n = 7), the steepness of both slopes increased significantly (P < 0.05 for lower 1/f range, P < 0.001 for higher 1/f range), and the difference in slopes was clearly greater (slope in lower range -1.2; r = 0.96 vs. -3.1, r = -0.92 in the higher range; P < 0.001). Neither alpha-receptor (n = 6) nor beta-receptor blockade (n = 4) considerably changed the slopes after denervation. However, autonomic blockade (n = 5) restored the slope in the low-frequency range (-0.9; r = -0.9). In conclusion, there are two independently modulated 1/f frequency ranges in BP time series. Baroreceptors especially attenuate 1/f noise in the higher frequency range.

Experimental Observations of Nonlinear Nonplanar Oscillations of a Cantilever Beam

2007 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh ◽  
Bashar K. Hammad
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Harmonic Load ◽  
Bending Vibrations ◽  
Out Of Plane ◽  
Frequency Components ◽  
Plane Bending ◽  
The Difference

The dynamics of a thin cantilever beam undergoing combined torsion and bending vibrations are examined experimentally. The beam’s fundamental natural frequencies in the two orthogonal bending motions and in torsion are fv1 = 5.719 Hz, fw1 = 189.730 Hz, and fφ1 = 138.938 Hz, respectively. A base-excitation shaker imparts a harmonic load that acts parallel to the width of the beam. First, the response of the beam is examined when the excitation frequency is equal to the fundamental torsion natural frequency (i.e., f = 138.9 Hz). For low levels of excitation, the motion consists mainly of hardly noticeable twisting vibrations. For high levels of excitation, the energy of the first torsion mode excites the first out-of-plane bending mode. In this case, the beam responses exhibit modulated vibrations containing both high-frequency and low-frequency components. Second, the beam is excited at the frequency f = 132.0 Hz, which is in the neighborhood the difference of these two natural frequencies. For large excitation levels, the beam vibrates with large-amplitude out-of-plane bending motions that exhibit chaotically intermittent behaviors.

Seismic Interaction between a Lined Tunnel and a Hill under Plane SV Waves by IBEM

2019 ◽  
Vol 19 (02) ◽  
pp. 1950004 ◽  
Author(s):  
Zhongxian Liu ◽  
Hai Zhang ◽  
Alexander Cheng ◽  
Chengqing Wu ◽  
Guogang Yang
Keyword(s):  
Dynamic Response ◽  
Low Frequency ◽  
Radiation Condition ◽  
Dynamic Interaction ◽  
Frequency Range ◽  
Seismic Safety ◽  
Reflected Waves ◽  
Diffracted Waves ◽  
Plane Sv Waves ◽  
The Hill

This paper investigates the dynamic interaction between a lined tunnel and a hill under plane SV waves using the indirect boundary element method (IBEM), with the displacement and stress characteristics of the system presented in frequency domain. The IBEM has several unique advantages such as reducing calculation dimension, automatically satisfying the infinite radiation condition, etc. The numerical results indicated that the dynamic response of the tunnel–hill system is strongly dependent on incident wave characteristics, geometrical and material properties of the lined tunnel, as well as the topography of the hill. For a dimension ratio between the hill and tunnel of less than 10.0, the lined tunnel has large amplification or deamplification effect on the dynamic response of the hill. Correspondingly, the hill also greatly amplifies the displacement and stress concentration of the tunnel especially in the lower-frequency range, due to the complicated interference effect among the reflected waves and diffracted waves induced by the tunnel and hill. Also demonstrated is that the displacement and stress amplitude spectrums highly depend on the incident frequency and the space location, and there exist multiple peaks and troughs in the spectrum curve with the peaks usually appearing in the low-frequency range. Thus, for the seismic safety assessment of a hill slope or hill tunnel in practice, the dynamic interaction within the tunnel–hill system should be taken into consideration.

Modal Experiment Research on Fluid-Solid Coupling Vibration of Hydraulic Long-Straight Pipeline of Shield Machine

2011 ◽  
Vol 105-107 ◽  
pp. 286-293 ◽  
Author(s):  
Jing Hua Xie ◽  
Ke Tian ◽  
Li He ◽  
Tian Ren Yang ◽  
Xiang Heng Zhu
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Vertical Plane ◽  
Low Frequency ◽  
Pipeline System ◽  
Experiment Research ◽  
Coupling Vibration ◽  
The Difference ◽  
Shield Machine

The hydraulic long-straight pipeline system of the shield machine is to be studied in this paper. Modal parameters of the hydraulic long-straight pipeline whose length is 8m under three kinds of spans (single span, double spans and four spans) were measured and analyzed. Considering the inherent vibration characteristics of the shield machine, we limited the natural frequency of the multi-span long straight pipeline studied within the range of 0~ 200Hz.What the experiment shows is as follows: Firstly, the natural frequency of the hydraulic long-straight pipeline is densely distributed mainly in the low frequency; Secondly, the natural frequencies of vibration in the horizontal plane are slightly higher than those of corresponding orders in the vertical plane, although the difference is little; In addition, by increasing the number of supports, pipeline span can be reduced and the natural frequencies of pipeline can be significantly increased, but this will make the vibration mode change irregularly.

Evaluation of Special Hearing Aids for Deaf Children

1971 ◽  
Vol 36 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Norman P. Erber
Keyword(s):  
Hearing Aids ◽  
High Frequency ◽  
Hearing Aid ◽  
Low Frequency ◽  
Acoustic Stimulation ◽  
Deaf Children ◽  
Frequency Range ◽  
Frequency Limit ◽  
Unpublished Studies ◽  
Published Research

Two types of special hearing aid have been developed recently to improve the reception of speech by profoundly deaf children. In a different way, each special system provides greater low-frequency acoustic stimulation to deaf ears than does a conventional hearing aid. One of the devices extends the low-frequency limit of amplification; the other shifts high-frequency energy to a lower frequency range. In general, previous evaluations of these special hearing aids have obtained inconsistent or inconclusive results. This paper reviews most of the published research on the use of special hearing aids by deaf children, summarizes several unpublished studies, and suggests a set of guidelines for future evaluations of special and conventional amplification systems.

Dynamic Damping and Stiffness Characteristics of the Rolling Tire

2001 ◽  
Vol 29 (4) ◽  
pp. 258-268 ◽  
Author(s):  
G. Jianmin ◽  
R. Gall ◽  
W. Zuomin
Keyword(s):  
Dynamic Behavior ◽  
Variable Parameter ◽  
Low Frequency ◽  
Vertical Load ◽  
Frequency Range ◽  
Inflation Pressure ◽  
Vehicle Simulation ◽  
Dynamic Damping ◽  
Speed Range ◽  
Stiffness Characteristics

Abstract A variable parameter model to study dynamic tire responses is presented. A modified device to measure terrain roughness is used to measure dynamic damping and stiffness characteristics of rolling tires. The device was used to examine the dynamic behavior of a tire in the speed range from 0 to 10 km/h. The inflation pressure during the tests was adjusted to 160, 240, and 320 kPa. The vertical load was 5.2 kN. The results indicate that the damping and stiffness decrease with velocity. Regression formulas for the non-linear experimental damping and stiffness are obtained. These results can be used as input parameters for vehicle simulation to evaluate the vehicle's driving and comfort performance in the medium-low frequency range (0–100 Hz). This way it can be important for tire design and the forecasting of the dynamic behavior of tires.

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