Experimental investigation on size-dependent higher-mode vibration of cantilever microbeams

Published on Aug 1, 2019in Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems1.737
· DOI :10.1007/S00542-018-4244-0
Zhenkun Li10
Estimated H-index: 10
(HUST: Huazhong University of Science and Technology),
Yuming He23
Estimated H-index: 23
(HUST: Huazhong University of Science and Technology)
+ 3 AuthorsDabiao Liu20
Estimated H-index: 20
(HUST: Huazhong University of Science and Technology)
A new perspective is presented to study size-dependent elasticity experimentally within micron scale utilizing dynamic approach. The size-dependent vibration of cantilever microbeams made of nickel is studied for the first three transverse modes. The normalized natural frequency of the first mode manifests strong size effect as reported. Remarkably, the normalized natural frequencies of the second and third mode also increase to 1.9 times as the thickness of microbeams decreases from 15 to 2.1 μm. Similarly the normalized bending rigidity increases to about 3.5 times. It is the first time that elastic size effect is observed in vibration of higher modes. Moreover, the size-dependent vibration of the first mode is interpreted in light of the modified couple stress theory, and the theoretical prediction also fit the experimental results of high modes very well. Hence it is confirmed that modified couple stress theory is valid for vibration of higher modes too.
📖 Papers frequently viewed together
1,932 Citations
2,056 Citations
20161.34AIP Advances
5 Authors (Jian Lei, ..., Dabiao Liu)
103 Citations
#1Chien H. Thai (Ton Duc Thang University)H-Index: 31
#2António Ferreira (University of Porto)H-Index: 70
Last. Hung Nguyen-Xuan (Sejong University)H-Index: 69
view all 4 authors...
Abstract We present a non-classical model for bending, free vibration and buckling analyses of functionally graded (FG) isotropic and sandwich microplates based on the modified couple stress theory (MCST) and the refined higher order shear deformation theory. Unlike the classical higher order shear deformation theory, the present model retains four variables and contains a single material length scale parameter which can be considered as the size-dependent effect. Effective material properties o...
25 CitationsSource
#1Armagan KaramanliH-Index: 10
#2Thuc P. Vo (Northumbria University)H-Index: 36
Abstract This paper presents the flexural behaviour of two directional functionally graded (2D-FG) microbeams subjected to uniformly distributed load with various boundary conditions. A four-unknown shear and normal deformation theory or quasi-3D one is employed based on the modified couple stress theory, Ritz method and finite element formulation. The material properties are assumed to vary through the thickness and longitudinal axis and follow the power-law distribution. Firstly, the static de...
38 CitationsSource
#1Zhenkun Li (HUST: Huazhong University of Science and Technology)H-Index: 10
#2Yuming He (HUST: Huazhong University of Science and Technology)H-Index: 23
Last. Lin Wang (HUST: Huazhong University of Science and Technology)H-Index: 61
view all 6 authors...
Abstract A standard experimental method for determining the intrinsic material length scale of modified couple stress theory is proposed based on a non-contact laser Doppler vibration measurement system. The first-order resonant frequencies of two different cantilever microbeams made of copper and titanium with thickness ranging from 15 to 2 µm are measured, respectively. The elastic size effects are obviously observed from the experimental results. The length scale parameters are obtained by fi...
67 CitationsSource
#1Zhu Su (NUAA: Nanjing University of Aeronautics and Astronautics)H-Index: 2
#1Zhu Su (NUAA: Nanjing University of Aeronautics and Astronautics)H-Index: 4
Last. Tiangui Ye (HEU: Harbin Engineering University)H-Index: 26
view all 3 authors...
Abstract This paper describes a unified approach for free vibration and transient response of functionally graded piezoelectric plates with different boundary conditions on the basis of first order shear deformation theory. Both effective electrical and mechanical properties of the plate are estimated by the Voigt model combined with a simple power-law distribution. The formulation is derived by variational principle in conjunction with penalty function method which relaxes the requirement of ad...
37 CitationsSource
Abstract In this paper, a size-dependent continuum-based model is presented for the coupled nonlinear dynamics of extensible functionally graded (FG) microbeams with viscoelastic properties. The length-scale effect is incorporated based on the modified couple stress theory (MCST). Moreover, employing the Kelvin–Voigt viscoelastic model, viscous components are taken into consideration in both stress and deviatoric segments of the symmetric couple stress tensors. The variation of the material prop...
154 CitationsSource
#1Jianshi Fang (NJIT: Nanjing Institute of Technology)H-Index: 1
#2Jianping Gu (NJIT: Nanjing Institute of Technology)H-Index: 2
Last. Hongwei Wang (NJIT: Nanjing Institute of Technology)H-Index: 1
view all 3 authors...
Abstract A size-dependent three-dimensional dynamic model of rotating functionally graded (FG) microbeams is developed based on the Euler–Bernoulli beam theory. A two-constituent material varying along the thickness is considered following the power law. In addition, Poisson's ratio is assumed constant in the present model. Hamilton's principle is adopted in conjunction with a modified couple stress theory to derive the governing equations with the von Karman geometric nonlinearity incorporated....
67 CitationsSource
#1Raheb Gholami (IAU: Islamic Azad University)H-Index: 39
#2Reza Ansari (University of Gilan)H-Index: 69
6 CitationsSource
#1Mergen H. Ghayesh (University of Adelaide)H-Index: 67
#2Hamed Farokhi (McGill University)H-Index: 35
The nonlinear bending and vibrations of tapered beams made of axially functionally graded (AFG) material are analysed numerically. For a clamped–clamped boundary conditions, Hamilton’s principle is employed so as to balance the potential and kinetic energies, the virtual work done by the damping, and that done by external distributed load. The nonlinear strain–displacement relations are employed to address the geometric nonlinearities originating from large deflections and induced nonlinear tens...
16 CitationsSource
#1Wanli Yang (SAU: Shenyang Aerospace University)H-Index: 7
#1Wanli Yang (SAU: Shenyang Aerospace University)H-Index: 2
Last. Wanji Chen (SAU: Shenyang Aerospace University)H-Index: 5
view all 3 authors...
Abstract This study developed a new composite laminated size-dependent beam model based on a re-modified couple stress theory and a refined zigzag theory. Unlike the classical theory, the proposed model only includes one internal material length scale parameter and can capture the scale effects. In addition, the current model satisfies a priori interlaminar continuity conditions and can accurately predict the displacements and stresses, particularly the interlaminar stresses. Reissner’s Mixed Va...
13 CitationsSource
#1Anton V. Krysko (Saratov State Technical University)H-Index: 19
#2Jan Awrejcewicz (Warsaw University of Technology)H-Index: 37
Last. V.A. Krysko (Saratov State Technical University)H-Index: 15
view all 5 authors...
Abstract In this work, a size-dependent model of a Sheremetev-Pelekh-Reddy-Levinson micro-beam is proposed and validated using the couple stress theory, taking into account large deformations. The applied Hamilton's principle yields the governing PDEs and boundary conditions. A comparison of statics and dynamics of beams with and without size-dependent components is carried out. It is shown that the proposed model results in significant, both qualitative and quantitative, changes in the nature o...
35 CitationsSource
Cited By19
#1Moeen Radgolchin (FUM: Ferdowsi University of Mashhad)H-Index: 4
#2Masoud Tahani (FUM: Ferdowsi University of Mashhad)H-Index: 24
The objective of this paper is to present a novel nonlocal strain gradient formulation for dynamic analysis of microgyroscopes. Taking into account the effect of nonlocal and gradient strains, the coupled equations of motion and the corresponding boundary conditions are derived using the Hamilton’s principle. Reduced order models for electrostatic and electrodynamic performance of the gyroscope are presented based on Galerkin projection technique. First, the influence of nonlocal and length-scal...
#1Tran Quoc ThaiH-Index: 3
#2Xiaoying ZhuangH-Index: 55
Last. Timon Rabczuk (Ton Duc Thang University)H-Index: 101
view all 3 authors...
Abstract We present a nonlinear Kirchhoff-Love micro-shell element based on isogeometric analysis (IGA) and couple stress theory. Higher-order NURBS functions are exploited for analyzing the strain gradient effect which automatically fulfill the higher-order continuity requirements. We express the strain gradient elastic formulation in natural curvilinear coordinates, which leads to an efficient numerical tool to examine geometric nonlinearities of thin micro-shell structures. The presented IGA ...
Micro scale experiments demonstrated that the material deformation behaviors of some metals and polymers deformed elasticity are size dependence, and the modified couple stress theory (MCST), which introduce an additional material length scale parameter, could capture the size dependences. The article reviews the available size-dependent models of micro-beam and micro-plate based on the MCST. For the representative micro-beams and micro-plates, the relevant mechanical models of micro-structures ...
The main objective of this study is to investigate the post-buckling thermal load–deflection path of rotating pre-twisted microblades/beams made of temperature-dependent functionally graded materials (FGMs) via nonlinear non-classical first-order shear deformation theory (FSDT). To this end, modified strain gradient theory (MSGT) as well as the von Karman geometric nonlinearity is used to develop the size-dependent nonlinear beam theory. Thermal loading is exerted by providing nonlinear (non-uni...
1 CitationsSource
#1Oscar Zi Shao Ong (University of Adelaide)H-Index: 1
#2Mergen H. Ghayesh (University of Adelaide)H-Index: 67
Last. Shahid Hussain (UC: University of Canberra)H-Index: 20
view all 3 authors...
This article examines the free size-dependent vibration behaviour of an Euler–Bernoulli type double-microbeam system, made of two microbeams elastically connected, with simply supported, clamped–clamped and clamped–pinned boundary conditions using an assumed-mode expansion technique (AMET) along with finite-element verifications; effects of altering the couple-stress-tensor-related parameter and the stiffness coefficient of the elastic connection are studied. The double-microbeam problem is form...
1 CitationsSource
#1Amir Mehdi Dehrouyeh-Semnani (UT: University of Tehran)H-Index: 18
#2Hasan Mostafaei (IUT: Isfahan University of Technology)H-Index: 3
Abstract The current article presents a thorough investigation into the natural frequencies and mode shapes of thin doubly curved shallow microshells by taking into account the influence of material length scale parameter. The mathematical model of system is obtained by applying the Hamilton's principle along with the modified couple stress theory and the Kirchhoff-Love's shell theory. In order to extract the free vibration characteristics of system, the finite element method is employed. Severa...
6 CitationsSource
#1Mohamed A. Attia (Zagazig University)H-Index: 14
#2S.A. Mohamed (Zagazig University)H-Index: 12
In the present study, the nonlinear thermal buckling, postbuckling, and snap-through phenomenon of higher-order shear deformable tapered bidirectional functionally graded (BDFG) microbeams are comprehensively investigated under different types of thermal loading, for the first time. The thermomechanical properties of the BDFG microbeam are assumed to be functions of temperature, axial, and thickness directions. Reddy’s parabolic shear deformation beam theory with the von Karman nonlinearity is e...
9 CitationsSource
#1Bo Zhang (Southwest Jiaotong University)H-Index: 22
#1Bo Zhang (Southwest Jiaotong University)H-Index: 17
Last. Huoming Shen (Southwest Jiaotong University)H-Index: 10
view all 5 authors...
Abstract This paper constructs a four-node Kirchhoff plate element considering dilatation, deviatoric stretch and rotation gradient effects to address the general boundary value problems of size-dependent isotropic thin micro-plates. This element benefits from the merits of differential quadrature method (DQM) and finite element method (FEM) and possesses four nodal displacement parameters at each node, i.e., deflection, its two first partial derivatives and one second mixed partial derivative w...
8 CitationsSource
#1Zhang Nan (NUAA: Nanjing University of Aeronautics and Astronautics)H-Index: 1
#2Zhao Xie (NUAA: Nanjing University of Aeronautics and Astronautics)H-Index: 2
Last. Chen Dejin (NUAA: Nanjing University of Aeronautics and Astronautics)H-Index: 1
view all 4 authors...
According to electric enthalpy variation and Hamilton's principle, governing differential equations and boundary conditions of functionally gradient piezoelectric nanobeams with porosities are established. The generalized differential quadrature method (GDQM) plays the role of transforming governing differential equations into a group of linear algebraic equations. Based on the strain gradient theory, a size-dependent functionally gradient piezoelectric nanobeam formulation including additional ...
3 CitationsSource