High- to Low-Frequency Modal Interactions in a Cantilever Composite Plate

1998 ◽  
Vol 120 (2) ◽  
pp. 579-587 ◽  
Author(s):  
K. Oh ◽  
A. H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Power Spectra ◽  
Low Frequency ◽  
Time History ◽  
Laser Vibrometer ◽  
Modal Interactions ◽  
Flexible Beams ◽  
Torsional Mode ◽  
Bending Mode ◽  
Simultaneous Activation

We have shown through experiment a complicated dynamic behavior of a cantilever (90/30/–30/–30/30/90)s graphite-epoxy plate. The plate was base excited using a 2000-lb table shaker near its seventh (third torsional) mode. We monitored the input excitation condition using a base mounted accelerometer and the plate response using a laser vibrometer. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by amplitude and phase modulations of the seventh mode. The energy transfer from the high- to low-frequency modes observed in the plate configuration is similar to those observed in flexible beams by Anderson, Balachandran, and Nayfeh (1994) and Nayfeh and Nayfeh (1994) and in frames by Popovic, Nayfeh, Oh, and Nayfeh (1995). Therefore, we conclude that this type of modal interactions is possible for all ranges of structural stiffnesses and configurations whenever there exist modes whose natural frequencies are much lower than the natural frequencies of the directly excited modes. In addition, we also observed simultaneous activation of a two-to-one internal resonance along with the high- to low-frequency modal interactions for some excitation amplitudes and frequencies. We used time-history and power-spectra plots to characterize the experimental data and force-response plots to characterize the dynamics of the plate.

Nonlinear Combination Resonances in Cantilever Composite Plates

1995 ◽  
Author(s):  
Kyoyul Oh ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Low Frequency ◽  
Composite Plates ◽  
High Amplitude ◽  
Mode Shapes ◽  
Laser Vibrometer ◽  
Combination Resonance ◽  
Response Curves

Abstract We experimentally investigated nonlinear combination resonances in a graphite-epoxy cantilever plate having the configuration (–75/75/75/ – 75/75/ – 75)s. As a first step, we compared the natural frequencies and mode shapes obtained from the finite-element and experimental modal analyses. The largest difference in the obtained frequencies was 2.6%. Then, we transversely excited the plate and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance Ω≈12(ω2+ω5) and the internal combination resonance Ω≈ω8≈12(ω2+ω13), where the ωi are the natural frequencies of the plate and Ω is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.

Transfer of Energy From High- to Low-Frequency Modes in the Bending-Torsion Oscillation of Cantilever Beams

1999 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Virtual Work ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Nonlinear Bending ◽  
Torsional Mode ◽  
Bending Mode ◽  
Plane Bending

Abstract We investigate the nonlinear bending-torsion response of a cantilever beam to a transverse harmonic excitation, where the forcing frequency is near the natural frequency of the first torsional mode. We analyze the case where the first in-plane bending mode is activated by a nonresonant mechanism. We use the method of time-averaged Lagrangian and virtual work to determine the equations governing the modulations of the phases and amplitudes of the interacting modes. These equations are then used to investigate the nonlinear behavior of limit-cycle oscillations of the beam as the excitation amplitude is slowly varied. As an example, we consider the response of an aluminum beam for which the natural frequency of the first in-plane bending mode is fv1 ≈ 5.7 Hz and the natural frequency of the first torsional mode is fϕ1 ≈ 138.9 Hz.

Modal Interactions in Resonant Microscanners

2006 ◽  
Author(s):  
Mohammed F. Daqaq ◽  
Elihab M. Abdel-Rahman ◽  
Ali H. Nayfeh
Keyword(s):  
Multiple Scales ◽  
Fast Response ◽  
Modal Interactions ◽  
Lumped Mass ◽  
Mass Model ◽  
Torsional Mode ◽  
Large Rotation ◽  
Wavelength Sensitivity ◽  
Bending Mode ◽  
Lumped Mass Model

The fast response of micromirrors and their ability to achieve large scanning angles and low wavelength sensitivity, has made them an appealing substitute for traditional scanning and display technologies. To achieve large rotation angles, while minimizing the voltage requirements, the microscanner is excited at its resonance frequency and then used to steer a light beam along a surface. In this work, we develop a comprehensive model of a torsional microscanner. Based on the eigenvalue problem, we reduce the model to a 2-DOF lumped-mass model that captures the significant dynamics of the microscanner. We use the method of multiple scales to derive an approximate analytical solution of the microscanner response to combined DC and resonant AC voltage excitation. We examined the characteristics of the solution and found that, for a range of DC voltage, a two-to-one internal resonance occurs between the first two modes. Therefore, the energy fed to the first (torsional) mode may be channeled to the second (bending) mode causing an undesirable steady-state response. This phenomenon results in significant degradation in the microscanner performance, therefore, the designer needs to identify it, design around it, or control it.

Stress and Modal Analysis Assessment of Race Cars Chassis Structure

2014 ◽  
Vol 663 ◽  
pp. 103-107
Author(s):  
S. Fazidah ◽  
N.A. Nor Azrin ◽  
A.L. Zulkarnain
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Material Selection ◽  
Frame Structure ◽  
Maximum Displacement ◽  
Torsional Mode ◽  
Race Car ◽  
Bending Mode ◽  
Bending Loads ◽  
Race Cars

A simulation investigation was conducted to compare and validate results for using bended and non-bended chassis structure for race cars. In this study, the basic engineering design criteria which are material selection, type of material used and production processes were presented. Modal analysis was used to validate the effect of chassis stiffness between the two different frames which is bended and non-bended frame using torsional and bending loads. The results reveals that the maximum displacement and Von Misses stress of the frame occur at the non-bended frame, instead of the bended frame with the value of 539.93 mm and 4.67 x 1010 Nm2 respectively. However, the critical area occurs on the main roll bar instead of on the frame structure itself. It was found that in the bended frame, the maximum Von Misses stress occurs at the rear section of the frame structure, which indicates possible chassis failure at given frequency of 62.16 Hz. The results indicate that there is only slight difference in the natural frequencies for both frames and the modeshape of both frames starts with torsional mode. For the second modeshape of the frames, the non-bended frame still remain having the torsional mode while the bended frame start to have the bending mode. The results presented here may facilitate improvements in the race car frame where the non-bended frame is having better structural frame than the bended frame. This was proved by the bended frame had a changed of modeshape from torsional mode to bending mode. The significance of the results indicates that the bended frame has less stiffness than the non-bended frame and it is not permittable for a race car frame.

Power Spectra Density Replication Control Strategy for 2-Axis Hydraulic Shaker Based on HV Estimator

2014 ◽  
Vol 596 ◽  
pp. 610-615
Author(s):  
Yu Chen ◽  
Qiang Li Luan ◽  
Zhang Wei Chen ◽  
Hui Nong He
Keyword(s):  
Response Function ◽  
Control Algorithm ◽  
Power Spectra ◽  
Time History ◽  
Good Effect ◽  
System Response ◽  
Power Spectral ◽  
Iterative Correction ◽  
Replication Control ◽  
The Given

Hydraulic shaker, equipment of simulating laboratory vibration environment, can accurately replicate the given power spectral density (PSD) and time history with an appropriate control algorithm. By studying method Hv estimator of frequency response function (FRF) estimation, a FRF identification strategy based on the Hv estimator is designed to increase the convergence rapidity and improve the system response function specialty. The system amplitude-frequency characteristics in some frequency points or frequency bands have large fluctuation. To solve this issue, a step-varying and frequency-sectioning iterative correction control algorithm is proposed for the control of 2-axial exciter PSD replication tests and the results show that the algorithm has a good effect on the control of hydraulic shaker, and can achieve reliable and high-precision PSD replication.

Nonrandom variability in respiratory cycle parameters of humans during stage 2 sleep

1990 ◽  
Vol 69 (2) ◽  
pp. 630-639 ◽  
Author(s):  
M. Modarreszadeh ◽  
E. N. Bruce ◽  
B. Gothe
Keyword(s):  
High Frequency ◽  
Minute Ventilation ◽  
Power Spectra ◽  
Low Frequency ◽  
Neural Mechanism ◽  
Normal Subjects ◽  
Feedback Loops ◽  
Low Frequency Oscillations ◽  
Stage 2 Sleep ◽  
Correlated Components

We analyzed breath-to-breath inspiratory time (TI), expiratory time (TE), inspiratory volume (VI), and minute ventilation (Vm) from 11 normal subjects during stage 2 sleep. The analysis consisted of 1) fitting first- and second-order autoregressive models (AR1 and AR2) and 2) obtaining the power spectra of the data by fast-Fourier transform. For the AR2 model, the only coefficients that were statistically different from zero were the average alpha 1 (a1) for TI, VI, and Vm (a1 = 0.19, 0.29, and 0.15, respectively). However, the power spectra of all parameters often exhibited peaks at low frequency (less than 0.2 cycles/breath) and/or at high frequency (greater than 0.2 cycles/breath), indicative of periodic oscillations. After accounting for the corrupting effects of added oscillations on the a1 estimates, we conclude that 1) breath-to-breath fluctuations of VI, and to a lesser extent TI and Vm, exhibit a first-order autoregressive structure such that fluctuations of each breath are positively correlated with those of immediately preceding breaths and 2) the correlated components of variability in TE are mostly due to discrete high- and/or low-frequency oscillations with no underlying autoregressive structure. We propose that the autoregressive structure of VI, TI, and Vm during spontaneous breathing in stage 2 sleep may reflect either a central neural mechanism or the effects of noise in respiratory chemical feedback loops; the presence of low-frequency oscillations, seen more often in Vm, suggests possible instability in the chemical feedback loops. Mechanisms of high-frequency periodicities, seen more often in TE, are unknown.

scholarly journals Temporal Properties of Posterior Parietal Neuron Discharges During Working Memory and Passive Viewing

2007 ◽  
Vol 97 (3) ◽  
pp. 2254-2266 ◽  
Author(s):  
Frederik C. Joelving ◽  
Albert Compte ◽  
Christos Constantinidis
Keyword(s):  
Working Memory ◽  
Posterior Parietal Cortex ◽  
Memory Task ◽  
Power Spectra ◽  
Low Frequency ◽  
Spatial Location ◽  
Spike Trains ◽  
Memory Condition ◽  
Temporal Properties ◽  
Posterior Parietal

Working memory is mediated by the discharges of neurons in a distributed network of brain areas. It was recently suggested that enhanced rhythmicity in neuronal activity may be critical for sustaining remembered information. To test whether working memory is characterized by unique temporal discharge patterns, we analyzed the autocorrelograms and power spectra of spike trains recorded from the posterior parietal cortex of monkeys performing a visuospatial working-memory task. We compared the intervals of active memory maintenance and fixation and repeated the same analysis in spike trains from monkeys never trained to perform any kind of memory task. The most salient effect we observed was a decrease of power in the 5- to 10-Hz frequency range during the presentation of visual stimuli. This pattern was observed both in the working-memory condition and the control condition, although it was more prominent in the former, where it persisted after cue presentation when the monkeys actively remembered the spatial location of the stimulus. Low-frequency power suppression resulted from relative refractory periods that were significantly longer in the working-memory condition and presumably emerged from local-circuit inhibition. We also detected a spectral peak in the 15- to 20-Hz range, although this was more prominent during fixation than during the stimulus and working-memory periods. Our results are in line with previous reports in prefrontal cortex and indicate that unique temporal patterns of single-neuron firing characterize persistent delay activity, although these do not involve the appearance of enhanced oscillations.

Aerodynamic Drag Measurement in a High-Enthalpy Shock Tunnel

2018 ◽  
Author(s):  
Yunpeng Wang ◽  
Zonglin Jiang ◽  
Honghui Teng
Keyword(s):  
Natural Frequencies ◽  
Aerodynamic Drag ◽  
Aerodynamic Force ◽  
Mechanical Vibration ◽  
Low Frequency ◽  
Shock Tunnel ◽  
Test Time ◽  
Test Duration ◽  
Flow State ◽  
High Enthalpy

Shock tunnels create very high temperature and pressure in the nozzle plenum and flight velocities up to Mach 20 can be simulated for aerodynamic testing of chemically reacting flows. However, this application is limited due to milliseconds of its test duration (generally 500 μs–20 ms). For the force test in the conventional hypersonic shock tunnel, because of the instantaneous flowfield and the short test time [1–4], the mechanical vibration of the model-balance-support (MBS) system occurs and cannot be damped during a shock tunnel run. The inertial forces lead to low frequency vibrations of the model and its motion cannot be addressed through digital filtering. This implies restriction on the model’s size and mass as its natural frequencies are inversely proportional the length scale of the model. As to the MBS system, sometimes, the lowest natural frequency of 1 kHz is required for the test time of typically 5 ms in order to get better measurement results [2]. The higher the natural frequencies, the better the justification for the neglected acceleration compensation. However, that is very harsh conditions to design a high-stiffness MBS structure, particularly a drag balance. Therefore, it is very hard to carried out the aerodynamic force test using traditional wind tunnel balances in the shock tunnel, though its test flow state with the high-enthalpy is closer to the real flight condition.

The infrared spectrum of di-imide near 7.6 μm

1981 ◽  
Vol 59 (5) ◽  
pp. 663-672 ◽  
Author(s):  
K-E. J. Hallin ◽  
J. W. C. Johns ◽  
A. Trombetti
Keyword(s):  
Infrared Spectrum ◽  
Gas Phase ◽  
Type A ◽  
Phase Spectrum ◽  
The Other ◽  
Mode Analysis ◽  
Simultaneous Presence ◽  
Torsional Mode ◽  
Bending Mode ◽  
Type C

The gas phase spectrum of N2H2 has been investigated in the region of 7.6 μm at a resolution of about 0.06cm−1. Two bands have been identified; one, near 1288 cm−1, is a type C band and must correspond to ν4 (the hitherto unidentified Au torsional mode), and the other, near 1317 cm−1, is a type A–B hybrid and corresponds to ν6 (the Bu bending mode). Analysis of the spectrum is complicated by the simultaneous presence of strong A-type and B-type Coriolis interactions which couple the observed levels.

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