An Experimental Investigation of Multimode Responses in a Cantilever Beam

1997 ◽  
Vol 119 (4) ◽  
pp. 532-538 ◽  
Author(s):  
M. Tabaddor ◽  
A. H. Nayfeh
Keyword(s):  
Experimental Investigation ◽  
Cantilever Beam ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Frequency Mode ◽  
Response Curves ◽  
Additive Type ◽  
Low Frequency Mode

An experimental investigation into the planar, multimode response of a cantilever metallic beam to a transverse harmonic excitation is presented. The cantilever beam was tested in both the horizontal and vertical directions. In the vertical configuration, the beam was excited near its fourth natural frequency and energy was transferred from the directly excited fourth mode to a low-frequency mode through both resonant and nonresonant modal interactions. In the latter case, the response contained contributions from the first and fourth modes, whereas in the former case, the response contained contributions from the fourth, second, and fifth modes. The mechanism responsible for the resonant interaction involving the three modes is a subcombination internal resonance of the additive type; that is, Ω ≈ ω4 ≈ 1/2(ω2 + ω5), where the ωi are the natural frequencies of the beam. This type of resonance occurs in systems with a dominant cubic nonlinearity. In the horizontal configuration, the beam was excited near its fourth and sixth natural frequencies. Again, energy was transferred to a low-frequency mode, but in this case only through a resonant interaction due to a subcombination internal resonance of the additive type. Power spectra, time series, and frequency- and amplitude-response curves were obtained for characterization of the dynamic multimode responses.

Modal interactions in a frame under support motions

1998 ◽  
Vol 212 (8) ◽  
pp. 667-686
Author(s):  
M Tabaddor
Keyword(s):  
Experimental Investigation ◽  
Internal Resonance ◽  
Resonant Interaction ◽  
Frequency Interval ◽  
Modal Interactions ◽  
Additive Type ◽  
Portal Frame ◽  
Support Excitation ◽  
Multi Mode ◽  
Mode Response

This paper presents the results from an experimental investigation into the planar, multi-mode response of a metallic portal frame to a harmonic support excitation. Forcing frequency and amplitude sweeps near the frequencies of the eighth and tenth modes of the structure revealed multi-mode responses. In the frequency interval surrounding that of the eighth mode, two additional lower-frequency modes, the fourth and the sixth, were excited. The mechanism responsible for the multimode behaviour of the frame is a combination internal resonance of the additive type. In addition, for a brief interval, a non-resonant interaction involving the eighth mode and the first mode was observed. Forcing amplitude sweeps for forcing frequencies below the eighth linear natural frequency produced a saturation-type phenomenon and a chaotically modulated motion. For the frequency interval surrounding that of the tenth mode, the response contained contributions from seven modes; these modes were excited through the simultaneous satisfaction of several internal resonance conditions.

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.

Observations of a low-frequency mode in a linear multiple mirror

1985 ◽  
Vol 28 (7) ◽  
pp. 2302
Author(s):  
M. A. Makowski ◽  
G. A. Emmert
Keyword(s):  
Low Frequency ◽  
Frequency Mode ◽  
Low Frequency Mode

Light Scattering from Pulsed Laser Deposited BaBi4Ti4O15 Thin Films

2000 ◽  
Vol 623 ◽  
Author(s):  
R.K. Soni ◽  
Anju Dixit ◽  
R. S. Katiyar ◽  
A. Pignolet ◽  
K.M. Satyalakshmi ◽  
...  
Keyword(s):  
Thin Films ◽  
Light Scattering ◽  
Room Temperature ◽  
Layer Structure ◽  
Low Frequency ◽  
Pulsed Laser ◽  
Buffer Layers ◽  
Frequency Mode ◽  
High Frequency Vibrations ◽  
Low Frequency Mode

AbstractLight scattering investigations are carried out on BaBi4Ti4O15 (BBiT) which is a member of the Bi-layer structure ferroelectric oxide with n = 4. The BBiT thin films, thickness ∼ 300 nm, were grown on epitaxial conducting LaNiO3 electrodes on epitaxial buffer layers on (100) silicon by pulsed laser deposition. Micro-Raman measurements performed on these films reveal a sharp low-frequency mode at 51 cm−1 along with broad highfrequeficy modes corresponding to other lattice vibrations including TiO6 octahedra. No temperature dependence of the low frequency mode is seen while a weak dependence of the broad high frequency vibrations are observed in the mixed oriented regions. Raman polarization carried out at room temperature indicates that the prominent modes have Alg and Eg symmetries in the BaBi4Ti4O15 thin films.

scholarly journals Utilization of 2:1 Internal Resonance in Microsystems

Micromachines ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 448 ◽  
Author(s):  
Navid Noori ◽  
Atabak Sarrafan ◽  
Farid Golnaraghi ◽  
Behraad Bahreyni
Keyword(s):  
Internal Resonance ◽  
Mode Coupling ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Beam Structure ◽  
Nonlinear Mode Coupling ◽  
T Beam ◽  
Low Frequency Mode

In this paper, the nonlinear mode coupling at 2:1 internal resonance has been studied both analytically and experimentally. A modified micro T-beam structure is proposed, and the equations of motion are developed using Lagrange’s energy method. A two-variable expansion perturbation method is used to describe the nonlinear behavior of the system. It is shown that in a microresonator with 2:1 internal resonance, the low-frequency mode is autoparametrically excited after the excitation amplitude reaches a certain threshold. The effect of damping on the performance of the system is also investigated.

Interactions between second mode and low-frequency waves in a hypersonic boundary layer

2017 ◽  
Vol 820 ◽  
pp. 693-735 ◽  
Author(s):  
Xi Chen ◽  
Yiding Zhu ◽  
Cunbiao Lee
Keyword(s):  
Boundary Layer ◽  
Parametric Resonance ◽  
Low Frequency ◽  
Frequency Mode ◽  
Linear Stability Theory ◽  
Hypersonic Boundary Layer ◽  
Reynolds Stresses ◽  
Second Mode ◽  
Low Frequency Mode ◽  
Low Frequency Waves

The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.

Observations of low-frequency mode in a multicomponent plasma with negative ions

1999 ◽  
Vol 6 (5) ◽  
pp. 1636-1640 ◽  
Author(s):  
B. Handique ◽  
H. Bailung ◽  
G. C. Das ◽  
Joyanti Chutia
Keyword(s):  
Low Frequency ◽  
Negative Ions ◽  
Frequency Mode ◽  
Multicomponent Plasma ◽  
Low Frequency Mode
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