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

Ansari, R.; FaghihShojaei, M.; Mohammadi, V.; Gholami, R.; Darabi, Mohammad Ali

doi:10.1590/s1679-78252014001300003

Cited by 15 publications

(7 citation statements)

References 34 publications

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“…The displacement vector field based on Mindlin plate theory through the thickness of the microplate in terms of in-plane displacements is [13,76].…”

Section: Strain and Curvature Tensor Fieldsmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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Using modified couple stress plate and Mindlin theories, the present study is a parametric study for revealing the effect of length scale parameter on postbuckling of saturated poroelastic rectangular microplates with pore distribution being functionally graded across thickness. The microplate postbuckling is a nonlinear eigenvalue problem with coupled partial differential equations of equilibrium. In order to find the mode shapes, the eigenfunctions have been approximated by some complete polynomial series expansions in accordance with the conventional Ritz approximation technique. After discretizing the governing equations throughout the microplate grid points, the assembled difference equations construct a nonlinear eigenvalue problem with coupled algebraic equations. The nontrivial coefficients of the expansions were calculated such that the eigenfunctions extremize the microplate potential energy for satisfying the equilibrium homogeneous equations. Variation of the potential energy have been derived with respect to the expansions coefficients from the vantage of using Maple software. By gradual reduction in the initial end shortening of the movable supports and solving the assembled difference equations via Newton-Raphson iterations, the critical postbuckling displacement imposed to the movable supports are found along with the nontrivial coefficients regarding eigenfunctions. The results of the parametric study have revealed how geometric parameters, pore distribution, the Skempton coefficient, porosity, and different boundary conditions modify the influence of length scale parameter on the microplate postbuckling.

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“…The displacement vector field based on Mindlin plate theory through the thickness of the microplate in terms of in-plane displacements is [13,76].…”

Section: Strain and Curvature Tensor Fieldsmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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“…It is noted that the nonlinear FSDT model developed in [286] considered the physical neutral surface of FG plates and thus the stretching-bending coupling was eliminated. Ansari et al [287] adopted the nonlinear FSDT model to investigate the size effect on the post-buckling path and frequency of FG microplates. Lou and He [288] also presented nonlinear CPT and FSDT models for the nonlinear bending and free vibration analysis of FG microplates.…”

Section: Plate Models 331 Modified Couple Stress Models Based On Tmentioning

confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

316

112

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This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

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“…The MCST has been employed by several researchers to study the size dependency of the static and dynamic mechanical behaviors of materials in small size. For example, the modi ed couple stress theory has been used as a basic formulation to study sizedependent e ect of static and dynamic behaviors of linear and nonlinear micro-beams [28][29][30][31][32][33][34][35], vibration response of rotating FGM micro-beams [36], static and dynamic behaviors of rectangular and annular sectors of microplates [37][38][39][40][41][42][43][44][45], curved micro-tubes [46], and micro/nano spherical shells [47].…”

Section: Introductionmentioning

confidence: 99%

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

Rahi

2018

Scientia Iranica

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In this paper, the modi ed couple stress theory is used to capture size e ect on dynamic behavior of a micro-drill subjected to an axial load and a concentrated mass, which is attached to its free end. Governing equations of lateral vibrations of the system and associated boundary conditions were derived by rst, obtaining the total kinetic and potential energy of the system and then, using Hamilton's principle. The Assumed Modes method was applied for transforming the governing partial di erential equations into a set of in nite ordinary di erential equations. Considering two terms of the equations, the rst two natural frequencies and instability rotational speeds of the micro-drill system were determined semi-analytically. Finally, numerical results of natural frequencies and the threshold of instability speeds of the system were derived with respect to di erent values of the system parameters such as rotational speed, axial load, rotor length, concentrated mass, and material length scale. The results showed that the material length scale parameter was extremely e ective on natural frequencies and the threshold of instability speeds of the micro-drill.

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

Cited by 15 publications

References 34 publications

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

A review of continuum mechanics models for size-dependent analysis of beams and plates

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

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