Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory

2019 ◽  
Vol 47 (5) ◽  
pp. 521-545 ◽  
Author(s):  
Zanyar Esmailpoor Hajilak ◽  
Johar Pourghader ◽  
Davoud Hashemabadi ◽  
Farzaneh Sharifi Bagh ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Reinforced Composites ◽  
Modified Strain Gradient Theory ◽  
Scale Parameters ◽  
Number Of Layers ◽  
Resonance Frequencies

In this paper, influence of modified strain gradient theory (MSGT) on buckling, free and forced vibration characteristics of the composite cylindrical nanoshell reinforced with graphene nanoplatelet (GPL) in thermal environment is investigated. The material properties of piece-wise functionally graded graphene-reinforced composites GPLRC are assumed to be graded in the thickness direction of a cylindrical nanoshell and are estimated through a nanomechanical model. The results show that GPL distribution pattern, three length scale parameters, number of layers and GPL weight function have important role on resonance frequencies, buckling load, relative frequency and dynamic deflections of the GPLRC cylindrical nanoshell.

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.

Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers

2019 ◽  
Vol 30 (4) ◽  
pp. 593-605 ◽  
Author(s):  
Mohammad Hosseini ◽  
Reza Bahaadini ◽  
Zahra Khalili-Parizi
Keyword(s):  
Functionally Graded Material ◽  
Strain Gradient ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Stress Theory ◽  
Graded Material

This investigation aims to explore the non-conservative instability of a functionally graded material micro-beam subjected to a subtangential force. The functionally graded material micro-beam is integrated with piezoelectric layers on the lower and upper surfaces. To take size effect into account, the mathematical derivations are expanded in terms of three length scale parameters using the modified strain gradient theory in conjunction with the Euler–Bernoulli beam model. However, the modified strain gradient theory includes modified couple stress theory and classical theory as special cases. Applying extended Hamilton’s principle and Galerkin method, the governing equation and corresponding boundary conditions are obtained and then solved numerically by the eigenvalue analysis, respectively. The results illustrated effects of non-conservative parameter, length scale parameter, different material gradient index, and various values of piezoelectric voltage on the natural frequencies, flutter and divergence instabilities of a cantilever functionally graded material micro-beam. It is found that both the material gradient index and applied piezoelectric voltage have significant influence on the vibrational behaviors, divergence and flutter instability regions. Furthermore, a comparison between the various micro-beam theories on the basis of modified couple stress theory, modified strain gradient theory, and classical theory are presented.

Study of Small Scale Effects on the Nonlinear Vibration Response of Functionally Graded Timoshenko Microbeams Based on the Strain Gradient Theory

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
S. Sahmani
Keyword(s):  
Strain Gradient ◽  
Beam Theory ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Scale Parameters ◽  
Linear And Nonlinear ◽  
Material Length Scale ◽  
Material Length

In the current study, the nonlinear free vibration behavior of microbeams made of functionally graded materials (FGMs) is investigated based on the strain gradient elasticity theory and von Karman geometric nonlinearity. The nonclassical beam model is developed in the context of the Timoshenko beam theory which contains material length scale parameters to take the size effect into account. The model can reduce to the beam models based on the modified couple stress theory (MCST) and the classical beam theory (CBT) if two or all material length scale parameters are taken to be zero, respectively. The power low function is considered to describe the volume fraction of the ceramic and metal phases of the FGM microbeams. On the basis of Hamilton’s principle, the higher-order governing differential equations are obtained which are discretized along with different boundary conditions using the generalized differential quadrature method. The dimensionless linear and nonlinear frequencies of microbeams with various values of material property gradient index are calculated and compared with those obtained based on the MCST and an excellent agreement is found. Moreover, comparisons between the various beam models on the basis of linear and nonlinear types of strain gradient theory (SGT) and MCST are presented and it is observed that the difference between the frequencies obtained by the SGT and MCST is more significant for lower values of dimensionless length scale parameter.

Forced vibration of porous functionally graded nanoplates under uniform dynamic load using general nonlocal stress–strain gradient theory

2017 ◽  
Vol 24 (20) ◽  
pp. 4700-4715 ◽  
Author(s):  
Mohammad Reza Barati ◽  
Hossein Shahverdi
Keyword(s):  
Strain Gradient ◽  
Dynamic Load ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Resonance Frequencies ◽  
Forced Vibration Analysis

Forced vibration analysis of porous functionally graded nanoplates under uniform dynamic loads is performed based on generalized nonlocal strain gradient theory. In this model, both stiffness-softening and stiffness-hardening effects are considered for more reliable forced vibration analysis of nanoplates. The present model is based on a vibrating higher order nanoscale plate subjected to transverse uniform dynamic load. Nanopores or nanovoids are incorporated to the model based on a modified rule of mixture. According to t Hamilton’s principle, the formulation of dynamically loaded nanoplate is derived. Applying Galerkin’s method, the resonance frequencies and dynamic deflections are obtained. It is indicated that the forced vibration characteristics of the nanoplate are significantly influenced by the porosities, excitation frequency, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and dynamic load location.

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