Free flexural vibration of geometrically imperfect functionally graded microbeams

Dehrouyeh-Semnani, Amir Mehdi; Mostafaei, Hasan; Nikkhah‐Bahrami, Mansour

doi:10.1016/j.ijengsci.2016.05.002

Cited by 100 publications

(13 citation statements)

References 84 publications

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“…The initial imperfection also has a major effect on the resonance frequencies of a resonator. An increase of the initial deflection leads to a divergence of the odd resonance frequencies also known as frequency veering [ 19 , 20 , 21 , 22 ]. This phenomenon was reported in several studies such as the effect of varying the ratio of the side lengths of a rectangular plate [ 23 ] and the effect of varying the sagging levels on cables [ 24 ].…”

Section: Introductionmentioning

confidence: 99%

Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

2018

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In order to investigate the effects of geometric imperfections on the static and dynamic behavior of capacitive micomachined ultrasonic transducers (CMUTs), the governing equations of motion of a circular microplate with initial defection have been derived using the von Kármán plate theory while taking into account the mechanical and electrostatic nonlinearities. The partial differential equations are discretized using the differential quadrature method (DQM) and the resulting coupled nonlinear ordinary differential equations (ODEs) are solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). It is shown that the initial deflection has an impact on the static behavior of the CMUT by increasing its pull-in voltage up to 45%. Moreover, the dynamic behavior is affected by the initial deflection, enabling an increase in the resonance frequencies and the bistability domain and leading to a change of the frequency response from softening to hardening. This model allows MEMS designers to predict the nonlinear behavior of imperfect CMUT and tune its bifurcation topology in order to enhance its performances in terms of bandwidth and generated acoustic power while driving the microplate up to 80% beyond its critical amplitude.

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Section: Introductionmentioning

confidence: 99%

Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

2018

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“…However, he used the Galerkin and He's variational method to obtain approximate solutions for the beams with simply supported and clamped BCs. Dehrouyeh-Semnani et al [214] included initial geometric imperfections on the free vibration analysis of FG microbeams.…”

Section: Beam Models 321 Modified Couple Stress Models Based On Thmentioning

confidence: 99%

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

Thai

Nguyen

et al. 2017

Composite Structures

304

109

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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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“…Ke et al [12] also incorporated the geometric nonlinearity effects in the free vibration of FG beams. Dehrouyeh-Semnani et al [13] investigated the free vibration of geometrically imperfect FG beams under various BCs based on the Rayleigh-Ritz's method. Reddy [14] examined the static bending, vibration and buckling behaviours of simply supported FG beams using both CBT and FOBT, which included the geometric nonlinearity effect.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions

Trinh

Thai

et al. 2018

Composites Part B: Engineering

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In this paper, the free vibration behaviour of bi-dimensional functionally graded (BDFG) microbeams under arbitrary boundary conditions (BCs) is studied. Based on the frame work of the modified couple stress theory and Hamilton's principle, governing equations of motion are developed for the BDFG microbeams using a quasi-3D theory. The formula then can be reduced to a higher-order beam theory (HOBT) of conventional functionally graded (FG) microbeams with the material properties varying along the thickness direction only. Two types of BDFG microbeams with different patterns of material volume distribution are considered. The material properties used in this study are assumed to vary exponentially along both longitudinal and thickness directions of microbeams. Based on the state-space concept, the governing equations are solved for natural frequencies and vibration mode shapes of microbeams under various BCs. The effects of material distribution, geometric parameters and BCs are also investigated to examine the size-dependent behaviour of BDFG microbeams.

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Free flexural vibration of geometrically imperfect functionally graded microbeams

Cited by 100 publications

References 84 publications

Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

Investigations of the Effects of Geometric Imperfections on the Nonlinear Static and Dynamic Behavior of Capacitive Micomachined Ultrasonic Transducers

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

Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions

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