Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures

Ebrahimi, Farzad; Barati, Mohammad Reza; Cívalek, Ömer

doi:10.1007/s00366-019-00742-z

Cited by 142 publications

(32 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Besides, Civalek et al [27] have studied the free vibration analyses of embedded carbon and silica carbide nanotubes lying on an elastic matrix based on Eringen's nonlocal elasticity theory. Also, they found that in the continuous systems especially like beam and rod, the decrease in vibration frequency appears with the reducing of the rigidity of structure [28]. Therefore, the interdigital electrode is modelled as a rod.…”

Section: Structural Design Of the Sensormentioning

confidence: 99%

Flexible carbon monoxide sensor for environmental detection of small‐scale robot

Zhang

Lin

Wang

et al. 2020

Micro & Nano Letters

View full text Add to dashboard Cite

Section: Structural Design Of the Sensormentioning

confidence: 99%

Flexible carbon monoxide sensor for environmental detection of small‐scale robot

Zhang

Lin

Wang

et al. 2020

Micro & Nano Letters

View full text Add to dashboard Cite

“…In the design of electrostatic driven microstructures, the energy domain coupling of electrical and mechanical energies is a very important issue. Vibration analysis of microstructures based on different composite materials is the focus of current research [7][8][9][10]. Vibration analysis of microstructures is different from macrostructures because the force proportional to the area plays a leading role [11].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of Microring Driven by the Symmetrically Distributed Electrostatic Force

et al. 2021

View full text Add to dashboard Cite

This paper aims at investigating the dynamic characteristics of a microring driven by dual arch electrodes because they are basic elements of microelectrostatic motors. The dual arch electrodes surround the periphery of the microring and are arranged symmetrically to the center of the ring. The electrodes are fixed while the microring is flexible. The electrostatic force will deform the microring, while the deflection of the microring changes the gap between the microring and the electrodes, thereby changing the electrostatic force. Therefore, this is an electromechanical coupling effect. The nonlinear partial-differential equation that governs the motion of the microring is derived based on thin shell theory. Then, based on the assumption of small deflection, the nonlinear governing equation is linearized by truncating the higher-order terms of the Taylor series expansion of the nonlinear electrostatic force. After that, the linearized governing equation is discretized into a set of ordinary differential equations using Galerkin method in which the mode shape functions of the ring are adopted. The influences of the structural damping of the microring and the span of the arch electrodes on the forced response and dynamical stabilities of the microring are investigated. The results show that the damping ratio has a great influence on the system instability during high-frequency excitation. The unstable region of the system can increase with the increase of the electrode span; the response amplitude can also be increased within a certain range.

show abstract

“…Ebrahimi et al. [22] applied the Chebyshev–Ritz method to investigating the static stability and vibration characteristics of FG nanostructures with various boundary conditions. Demir and Civalek [23] investigated the size‐effects in the axial and torsional response of microtubules through utilizing the nonlocal continuum rod model.…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Zhang

Ullah

et al. 2020

Z Angew Math Mech

View full text Add to dashboard Cite

This paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving boundary value problems of governing partial differential equations of plate. Based on the integral transform theory, the title problem is transformed into solving regular linear algebraic simultaneous equations, which provides a more rational and theoretical solution process than traditional inverse/semi‐inverse approaches. The acquired comprehensive results of critical buckling load factors and mode shapes are in excellent agreement with the ones obtained by finite element method, which verifies the validity and accuracy of the present approach. In addition, classical boundary conditions, such as simply supported and clamped edges, can be investigated by choosing different rotational fixity factors. Furthermore, the features of the employed method that no preselection of trial function and the generality for various boundary conditions enable one to analytically solve static problems for moderately thick plates and thick plates.

show abstract

Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures

Cited by 142 publications

References 43 publications

Flexible carbon monoxide sensor for environmental detection of small‐scale robot

Flexible carbon monoxide sensor for environmental detection of small‐scale robot

Dynamic Characteristics of Microring Driven by the Symmetrically Distributed Electrostatic Force

Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Contact Info

Product

Resources

About