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

2002 ◽  
Vol 257 (1) ◽  
pp. 19-62 ◽  
Author(s):  
M. EL KADIRI ◽  
R. BENAMAR
Keyword(s):  
Analytical Method ◽  
Linear Response ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Linear Mode ◽  
Non Linear

scholarly journals Non-Linear Forced Vibration of Fully Clamped FGM Skew Plates using Homogenization Technique

2019 ◽  
Vol 286 ◽  
pp. 03002
Author(s):  
H. Moulay Abdelali ◽  
R. Benamar
Keyword(s):  
Forced Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Skew Angle ◽  
Linear Mode ◽  
Homogenization Technique ◽  
Skew Plate ◽  
Non Linear ◽  
Excitation Force ◽  
The Right

The present work concerns the geometrically non-linear forced vibration of fully clamped functionally graded skew plates (FGSP). The theoretical model based on Hamilton’s principle and spectral analysis previously applied to obtain the non-linear mode shapes of thin straight structures is used. A homogenization technique is developed to reduce the FGSP problem under consideration to that of an equivalent isotropic homogeneous skew plate. Results are given for the linear and non-linear fundamental frequency of fully clamped FGSP, considering different parameters, such as the skew angle, the excitation force level. The results show a non linearity of the hardening type with a shift to the right of the bent non linear frequency response function, in the neighbourhood of the fundamental mode.

Geometrically Non-Linear Free Vibration of Fully Clamped FGM Skew Plates Using Homogenization Technique

2015 ◽  
Vol 1105 ◽  
pp. 370-380
Author(s):  
Moulay Abdelali Hanane ◽  
Khalid El Bikri ◽  
Benamar Rhali
Keyword(s):  
Free Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Skew Angle ◽  
Linear Mode ◽  
Homogenization Technique ◽  
Skew Plate ◽  
Non Linear ◽  
Good Agreement

The present work concerns the geometrically non-linear free vibration of fully clamped functionally graded skew plates (FGSP). The theoretical model based on Hamilton’s principle and spectral analysis is used. A homogenization technique has been developed to reduce the FGSP problem under consideration to that of an isotropic homogeneous skew plate. The material properties of the skew plate examined herein are assumed to be graded in the thickness direction of the plate according to the power-law distribution in terms of volume fractions of the constituents. Results are given for the linear and non-linear fundamental frequency considering different parameters. The non-linear mode shapes exhibit a maximum value in the bending stress at the centre of the plate. It is found also that the non-linear frequencies increase with increasing the amplitude of vibration and increasing the skew angle, which corresponds to the hardening type effect. A good agreement is found with published results.

Flow velocity and light level drive non-linear response of seagrass Zostera noltei to ammonium enrichment

2016 ◽  
Vol 545 ◽  
pp. 109-121 ◽  
Author(s):  
B Villazán ◽  
FG Brun ◽  
V González‑Ortiz ◽  
F Moreno‑Marín ◽  
TJ Bouma ◽  
...  
Keyword(s):  
Flow Velocity ◽  
Linear Response ◽  
Light Level ◽  
Zostera Noltei ◽  
Non Linear

Non-linear response of stomata in Pinus koraiensis to tree age and elevation

Trees ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 1389-1396 ◽  
Author(s):  
Yumei Zhou ◽  
Marcus Schaub ◽  
Lianxuan Shi ◽  
Zhongling Guo ◽  
Anan Fan ◽  
...  
Keyword(s):  
Linear Response ◽  
Tree Age ◽  
Pinus Koraiensis ◽  
Non Linear
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