A C1 continuous hexahedral element for nonlinear vibration analysis of nano-plates with circular cutout based on 3D strain gradient theory

2018 ◽  
Vol 205 ◽  
pp. 69-85 ◽  
Author(s):  
Jalal Torabi ◽  
Reza Ansari ◽  
Mansour Darvizeh
Keyword(s):  
Nonlinear Vibration ◽  
Strain Gradient ◽  
Vibration Analysis ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Hexahedral Element ◽  
Circular Cutout

Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells

2021 ◽  
pp. 095440622110458
Author(s):  
Vahid Movahedfar ◽  
Mohammad M Kheirikhah ◽  
Younes Mohammadi ◽  
Farzad Ebrahimi
Keyword(s):  
Nonlinear Vibration ◽  
Material Properties ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Scale Parameters ◽  
Functionally Graded Piezoelectric ◽  
Doubly Curved

Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes.

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