22MAR

Nexte issue of the journal ICAMOP

The next issue of the journal ICAMOP will be published by January 20, 2021. Submit your articles by email to: rabatuniv@gmail.com
The next issue will deal with issues related to engineering studies and system design.

ICAMOP journal
http://www.icamop.periodikos.com.br/article/5c93b1660e88250545122986
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Case study

Experimental investigation on amplitude-frequency dependence of C-S-C-S rectangular plate 2nd mode shape

El Mehdi ABDEDDINE, Abdelfattah MAJID, Khalid ZARBANE & Zitouni BEIDOURI

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Abstract

The theoretical of Benamar’s method that based on Hamilton’s principle and spectral analysis, has extended to study first and second mode shape of clamped-clamped beams in order to investigate dependence between the nonlinear fundamental frequencies, nonlinear mode shapes and the nonlinear bending stress. This model used and applied to investigate the dynamic behavior of fully clamped rectangular plates and of C-S-C-S and C-S-S-S rectangular plates, which published previously by Z.Beidouri. The amplitude frequency dependence has been investigated experimentally in part I carefully in case of C-S-C-S of the first mode shape and compared with those obtained numerically. This paper will explain the identification of the second mode shape and discuss the results obtained experimentally of the amplitude frequency dependence in the case of C-S-C-S rectangular plate. The transverse harmonic vibration has been provided by an electrodynamic exciter that excited the rectangular plate at the center near the second resonance frequency which allowing to identify the second mode shape and investigate the amplitude frequency dependence.

Keywords

second mode shape, resonance frequency, experimental study, geometrically nonlinear, nonlinear dynamic behavior

References

[1]     M. Amabili, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York, 2008.

[2]     R. Benamar, M.M.K. Bennouna, R.G. White, The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures part I: Simply supported and clamped-clamped beams, Journal of Sound and Vibration. 149 (1991) 179–195.

[3]     R. Benamar, M.M.K. Bennouna, R.G. White, The Effects Of Large Vibration Amplitudes On The Mode Shapes And Natural Frequencies Of Thin Elastic Structures, Part II: Fully Clamped Rectangular Isotropic Plates, Journal of Sound and Vibration. 175 (1992) 377–395.

[4]     R. Benamar, M.M.K. Bennouna, R.G. White, The Effects Of Large Vibration Amplitudes On The Mode Shapes And Natural Frequencies Of Thin Elastic Structures, Part III: Fully Clamped Rectangular Isotropic Plates—Measurements Of The Mode Shape Amplitude Dependence And The Spatial Distribution Of Harmonic Distortion, Journal of Sound and Vibration. 175 (1993) 377–395.

[5]     M. El Kadiri, R. Benamar, R.G. White, the non-linear free vibration of fully clamped rectangular plates: second non-linear mode for various plate aspect ratios, journal of sound and vibration. 228 (1999) 333–358.

[6]     M. El Kadiri, R. Benamar, improvement of the semi-analytical method, for determining the geometrically non-linear response of thin straight structures: part ii—first and second non-linear mode shapes of fully clamped rectangular plates, journal of sound and vibration. 257 (2001) 19–62.

[7]     Z. Beidouri, R. Benamar, M. El Kadiri, Geometrically non-linear transverse vibrations of C–S–S–S and C–S–C–S1 rectangular plates, International Journal of Non-Linear Mechanics. 41 (2006) 57–77.

[8]     BEIDOURI, Zitouni. “Contribution to a non-linear modal analysis theory, application to continuous structures and discrete systems with localized non-linearities”, Thesis of doctorate in science technology. Mohammadia School of Engineering, Rabat, 2006.

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