Influence of Nonlinearities in Boundary Conditions on the Free Vibrations of Plates Under Geometrically Nonlinear Deformation

2013 ◽  
Vol 194 (2) ◽  
pp. 213-224
Author(s):  
I. D. Breslavsky ◽  
K. V. Avramov
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Deformation ◽  
Free Vibrations ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Deformation

A Nonlinear Shear Deformable Nanoplate Model Including Surface Effects for Large Amplitude Vibrations of Rectangular Nanoplates with Various Boundary Conditions

2015 ◽  
Vol 07 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Reza Ansari ◽  
Mostafa Faghih Shojaei ◽  
Vahid Mohammadi ◽  
Raheb Gholami ◽  
Mohammad Ali Darabi
Keyword(s):  
Boundary Conditions ◽  
Surface Stress ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Free Vibrations ◽  
Model Parameters ◽  
Geometrically Nonlinear ◽  
Residual Surface Stress ◽  
Various Boundary Conditions ◽  
Shear Deformable

In this paper, a geometrically nonlinear first-order shear deformable nanoplate model is developed to investigate the size-dependent geometrically nonlinear free vibrations of rectangular nanoplates considering surface stress effects. For this purpose, according to the Gurtin–Murdoch elasticity theory and Hamilton's principle, the governing equations of motion and associated boundary conditions of nanoplates are derived first. Afterwards, the set of obtained nonlinear equations is discretized using the generalized differential quadrature (GDQ) method and then solved by a numerical Galerkin scheme and pseudo arc-length continuation method. Finally, the effects of important model parameters including surface elastic modulus, residual surface stress, surface density, thickness and boundary conditions on the vibration characteristics of rectangular nanoplates are thoroughly investigated. It is found that with the increase of the thickness, nanoplates can experience different vibrational behavior depending on the type of boundary conditions.

Geometrically nonlinear deformation and the emergent behavior of polarons in soft matter

Soft Matter ◽  
2015 ◽  
Vol 11 (41) ◽  
pp. 8042-8047 ◽  
Author(s):  
Xiaobao Li ◽  
Liping Liu ◽  
Pradeep Sharma
Keyword(s):  
Quantum Dots ◽  
Electronic Structure ◽  
Soft Matter ◽  
Nonlinear Deformation ◽  
Mechanical Strain ◽  
Emergent Behavior ◽  
Geometrically Nonlinear ◽  
Bulk Semiconductors ◽  
Geometrically Nonlinear Deformation

Mechanical strain can alter the electronic structure of both bulk semiconductors as well as nanostructures such as quantum dots.

Geometrically nonlinear deformation elastoplastic soil

2014 ◽  
Vol 8 ◽  
pp. 6341-6348 ◽  
Author(s):  
D. V. Berezhnoi ◽  
A. A. Sachenkov ◽  
M. K. Sagdatullin
Keyword(s):  
Nonlinear Deformation ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Deformation ◽  
Elastoplastic Soil
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