Size and Foundation Effects on the Vibration of Buckled Functionally Graded Microplates Within the Modified Couple Stress Theory Framework

2018 ◽  
Vol 10 (06) ◽  
pp. 1850068 ◽  
Author(s):  
Jia Lou ◽  
Liwen He ◽  
Jie Yang ◽  
Sritawat Kitipornchai ◽  
Huaping Wu
Keyword(s):  
Elastic Foundation ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Linear Perturbation ◽  
Governing Equations ◽  
Stress Theory ◽  
Post Buckling ◽  
Modified Couple Stress

In the present paper, the vibration behavior of a buckled functionally graded (FG) microplate lying on a nonlinear elastic foundation is studied. The modified couple stress theory is utilized to capture the size effect of the FG microplate, and the Mindlin plate theory with the von Karman’s geometric nonlinearity is adopted to describe its deflection behavior. Based on these assumptions and Hamilton’s principle, the governing equations and associated boundary conditions are derived for the FG microplate. By linearizing the governing equations around a pre-buckling/post-buckling state, linear perturbation equations are obtained. After substituting the pre-buckling/post-buckling deformation and assumed vibration mode into the linear perturbation equations and applying the Galerkin method, an eigenvalue problem is obtained, from which the free vibration frequency of the FG microplate around its pre-buckling/post-buckling state can be determined analytically. Based on the obtained closed-form solutions, numerical examples are also presented to investigate the effects of the material length scale parameter to thickness ratio, the power law index, and the stiffness of the elastic foundation on the vibration behavior of the buckled FG microplate.

Buckling and Post-Buckling of Symmetric Functionally Graded Microplate Lying on Nonlinear Elastic Foundation Based on Modified Couple Stress Theory

2018 ◽  
Vol 18 (09) ◽  
pp. 1850110 ◽  
Author(s):  
Chengyang Wu ◽  
Jia Lou ◽  
Liwen He ◽  
Jianke Du ◽  
Huaping Wu
Keyword(s):  
Elastic Foundation ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Equilibrium Equations ◽  
Stress Theory ◽  
Post Buckling ◽  
Modified Couple Stress ◽  
Nonlinear Elastic

This paper is concerned with the buckling and post-buckling behaviors of a simply supported symmetric functionally graded (FG) microplate lying on a nonlinear elastic foundation. The modified couple stress theory is used to capture the size effects of the FG microplate, and the Mindlin plate theory with von Karman’s geometric nonlinearity taken into account is adopted to describe its deflection behavior. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the FG microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the power law index, the material length scale parameter to thickness ratio, the stiffness of the elastic foundation, and in-plane boundary conditions on the buckling and post-buckling behaviors of the FG microplate are discussed in detail.

Magnetic field effect on free vibration of smart rotary functionally graded nano/microplates: A comparative study on modified couple stress theory and nonlocal elasticity theory

2018 ◽  
Vol 29 (11) ◽  
pp. 2492-2507 ◽  
Author(s):  
Mohammad Hassan Shojaeefard ◽  
Hamed Saeidi Googarchin ◽  
Mohammad Mahinzare ◽  
Seyed Ahmad Eftekhari
Keyword(s):  
Elastic Material ◽  
Nonlocal Elasticity ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Nonlocal Elasticity Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

In this article, free vibration behavior of a rotating nano/microcircular plate constructed from functionally graded magneto-elastic material is simulated with the first-order shear deformation theory. For the sake of comparison, the nonlocal elasticity theory and the modified couple stress theory are employed to implement the small size effect in the natural frequencies behavior of the nano/microcircular plate. The governing equations of motion for functionally graded magneto-elastic material nano/microcircular plates are derived based on Hamilton’s principle; comparing the obtained results with those in the literature, they are in a good agreement. Finally, the governing equations are solved using the differential quadrature method. It is shown that the vibrational characteristics of functionally graded magneto-elastic material nano/microcircular plates are significantly affected by non-dimensional angular velocity, size dependency of the Eringen’s and the modified couple stress theories, and power law index for clamped and hinged boundary conditions. Results show that a critical point occurs by increasing the angular velocity and the effect of several parameters are changed after this point.

Vibration of size-dependent functionally graded sandwich microbeams with different boundary conditions based on the modified couple stress theory

2017 ◽  
Vol 22 (2) ◽  
pp. 220-247 ◽  
Author(s):  
Nuttawit Wattanasakulpong ◽  
Arisara Chaikittiratana ◽  
Sacharuck Pornpeerakeat
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Slenderness Ratio ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

This paper investigates flexural vibration of functionally graded sandwich microbeams supported by different axially immovable boundary conditions. The governing equations of free vibration problem are based on Timoshenko beam theory and the modified couple stress theory which are taking into account the important effects of shear deformation, rotary inertia and material length scale parameter. To solve the governing equations presented in the forms of coupled differential equations for vibration analysis of the beams with various boundary conditions, an effective tool, namely Chebyshev collocation method, is employed to find out accurate solutions with many important parametric studies. The effects of material volume fraction index, layer thickness ratio, slenderness ratio, boundary condition, temperature rise, etc. on natural frequencies of the beams are taken into account and discussed in details. The numerical results of the beams in ambient temperature and high thermal environment are presented in several tables and figures that can serve as benchmarks for further investigations in the field of FG sandwich microbeam analysis.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

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