Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates

R Ansari,R Gholami,V Mohammadi,M A Darabi,M Faghihshojaei

doi:10.1590/s1679-78252014001300003

R Ansari, R Gholami + Show 3 more

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https://doi.org/10.1590/s1679-78252014001300003

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Abstract

In this paper, the free vibration behavior of post-buckled functionally graded (FG) Mindlin rectangular microplates are described based on the modified couple stress theory (MCST). This theory enables the consideration of the size-effect through introducing material length scale parameters. The FG microplates made of a mixture of metal and ceramic are considered whose volume fraction of components is expressed by a power law function. By means of Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-plates in the postbuckling domain. The governing equations and boundary conditions are then discretized by using the generalized differential quadrature (GDQ) method before solving numerically by the pseudo-arclength continuation technique. In the solution procedure, the postbuckling problem of microplates is investigated first. Afterwards, the free vibration of microplates around the buckled configuration is discussed. The effects of dimensionless length scale parameter, material gradient index and aspect ratio on the on the postbuckling path and frequency of FG microplates subject to arbitrary edge supports are thoroughly discussed.

Highlights

Graded (FG) materials are increasingly being used in microstructures because of their potentiality in acquiring desired performance
The numerical results obtained from the modified couple stress theory (MCST) for the size-dependent vibration analysis of post-buckled functionally graded (FG) Mindlin microplates with various edge supports are represented
The effects of the length scale parameter h l, gradient index n, and length-to-thickness ratio a h on the free vibration characteristics of postbuckled FG microplates are discussed in detail

Summary

INTRODUCTION

Graded (FG) materials are increasingly being used in microstructures because of their potentiality in acquiring desired performance. The modified form of this theory (MCST) was proposed by Yang et al (2002); they considered only one additional material length scale parameter besides two classical material constants and facilitated incorporating the size effect This theory has been employed to develop several size-dependent microbeams and microplates. The free vibration behavior of post-buckled FG Mindlin rectangular microplates is investigated To this end, firstly, the MCST and Hamilton’s principle are used to obtain the nonlinear governing equations and associated boundary conditions of FG microplates in the postbuckling configuration. The GDQ method and the pseudo-arclength continuation technique are employed to discretize and solve the governing equations and boundary conditions

GOVERNING EQUATIONS OF SIZE-DEPENDET FG MINDLIN RECTANGULAT MICROPLATES

SOLUTION STRATEGY

F X X Xs

RESULTS AND DISCUSSION

CONCLUSION