Geometrically non-linear transverse vibrations of C–S–S–S and C–S–C–S rectangular plates

Beidouri, Zitouni; Benamar, Rhali; Kadiri, M. El

doi:10.1016/j.ijnonlinmec.2005.06.002

Cited by 15 publications

(3 citation statements)

References 18 publications

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“…-Different structures : beams, plates, shells (Beidouri et al, 2006;Moussaoui et al, 2000;Azrar et al, 1999a;Benamar et al, 1994;Benamar et al, 1991;Benamar, 1990). .…”

Section: Presentation and Discussion Of The Benamar's Methodsmentioning

confidence: 99%

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Nonlinear transverse steady-state periodic forced vibration of 2-dof discrete systems with cubic nonlinearities

Eddanguir

Beidouri

Benamar

2011

TECM

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A method based on Hamilton’s principle and spectral analysis has been applied recently to nonlinear transverse vibrations of discrete systems with cubic nonlinearities, leading to calculation of the nonlinear free modes of transverse vibration and their associated nonlinear frequencies. The objective of the present work was the extension of this method to the nonlinear forced transverse steady-state periodic response of 2-dof system leading to nonlinear frequency response function in the neighbourhood of the two modes

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“…-Different structures : beams, plates, shells (Beidouri et al, 2006;Moussaoui et al, 2000;Azrar et al, 1999a;Benamar et al, 1994;Benamar et al, 1991;Benamar, 1990). .…”

Section: Presentation and Discussion Of The Benamar's Methodsmentioning

confidence: 99%

“…-Different types of problems : nonlinear free response, nonlinear forced response (references cited above in addition to (Beidouri et al, 2006;Azrar et al, 2002;Azrar et al, 1999b)).…”

Section: Presentation and Discussion Of The Benamar's Methodsmentioning

confidence: 99%

Nonlinear transverse steady-state periodic forced vibration of 2-dof discrete systems with cubic nonlinearities

Eddanguir

Beidouri

Benamar

2011

TECM

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“…This approach was then used by other co-workers of Benamar such as Rougui and Moussaoui [12] who studied the geometrically non-linear free and forced vibrations of simply supported circular cylindrical shells, Haterbouch [13] who examined the effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates by applying iterative and explicit analytical solutions to non-linear transverse vibrations and non-linear coupled transverse and in-plane vibrations [14]. Beidouri [15] investigated similarly the geometrically non-linear transverse vibrations of C-S-S-S and C-S-C-S rectangular plates. Also, Eddanguir and Beidouri [16] studied the geometrically nonlinear transverse vibrations of discrete multi-degrees of freedom Systems with a localized non-linearity by using the explicit method.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Analytical Approach for the Geometrically Nonlinear Analysis of Skew Plates

Abdelali

Kadiri

Benamar

2014

AMM

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The present work concerns the nonlinear dynamic behaviour of fully clamped skew plates at large vibration amplitudes. A model based on Hamilton’s principle and spectral analysis has been used to study the large amplitude free vibration problem, reducing the non linear problem to solution of a set of non-linear algebraic equations. Two methods of solution have been adopted, the first method uses an improved version of the Newton-Raphson method, and the second leads to explicit analytical expressions for the higher mode contribution coefficients to the first non-linear mode shape of the skew plate examined. The amplitude dependent fundamental mode shape and the associated non-linear frequencies have been obtained by the two methods and a good convergence has been found. It was found that the non-linear frequencies increase with increasing the amplitude of vibration, which corresponds to the hardening type effect, expected in similar cases, due to the membrane forces induced by the large vibration amplitudes. The non-linear mode exhibits a higher bending stress near to the clamps at large deflections, compared with that predicted by linear theory. Numerical details are presented and the comparison made between the results obtained and previous ones available in the literature shows a satisfactory agreement. Tables of numerical results are given, corresponding to the linear and nonlinear cases for various values of the skew angle θ and various values of the vibration amplitude. These results, similar to those previously published for other plates, are expected to be useful to designers in the need of accurate estimates of the non-linear frequencies, the non linear strains and stresses induced by large vibration amplitudes of skew plates.

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Geometrically Non-linear Free Vibrations of Simply Supported Rectangular Plates Connected to Two Distributions of Rotational Springs at Two Opposite Edges

Babahammou

Benamar

2019

Lecture Notes in Mechanical Engineering

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Geometrically non-linear transverse vibrations of C–S–S–S and C–S–C–S rectangular plates

Cited by 15 publications

References 18 publications

Nonlinear transverse steady-state periodic forced vibration of 2-dof discrete systems with cubic nonlinearities

Nonlinear transverse steady-state periodic forced vibration of 2-dof discrete systems with cubic nonlinearities

A Semi-Analytical Approach for the Geometrically Nonlinear Analysis of Skew Plates

Geometrically Non-linear Free Vibrations of Simply Supported Rectangular Plates Connected to Two Distributions of Rotational Springs at Two Opposite Edges

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