DYNAMIC ANALYSIS OF A MICRO BEAM BASED ON SUB-HARMONIC PARAMETRIC EXCITATION

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RAHELI AMIR; AZIZI SABER; FAROUGHI SHIRKO

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Journal: Modares Mechanical Engineering Year:2017 | Volume:17 | Issue:5 Page(s): 374-384

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Title

DYNAMIC ANALYSIS OF A MICRO BEAM BASED ON SUB-HARMONIC PARAMETRIC EXCITATION

Author(s)

RAHELI AMIR | AZIZI SABER | FAROUGHI SHIRKO | Issue Writer Certificate

Keywords

MICRO ELECTRO MECHANICAL SYSTEMSQ1

NONLINEAR DAMPED MATHIEU EQUATIONSQ1

SHOOTING METHODQ1

CLAMPED-CLAMPED MICROBEAMQ1

SUBHARMONIC RESONANCEQ1

Abstract

In this research dynamic instability and nonlinear vibration of a clamped-clamped micro-beam sandwiched with piezoelectric layers based on parametric excitation in sub-harmonic region is investigated. The equation of motion is derived based on Hamiltonian principle, and nondimensionalized using appropriate non-dimensional parameters. Applying a harmonic AC voltage to the piezoelectric layers results in the time varying of the linear stiffness of the micro-beam. The resultant motion equation in non-dimensional form is discretized to single degree of freedom model using Galerkin technique. The governing equation is a nonlinear Mathieu type ODE, and the periodic attractors are captured based on the shooting technique. The nonlinearity of governing equation is due to the geometric nonlinearity which originates from the clamped-clamped boundary conditions. The effect of various parameters including magnitude of the nonlinear stiffness, damping coefficient, the frequency and the amplitude of the harmonic excitation on the parametric resonance region is investigated. The results depict that increased damping coefficient leads to the decreased aria of the parametric resonance region. It is concluded that the magnitude of the nonlinear stiffness, does not affect on the area of the resonance region, however it considerably influences on the amplitude of the parametric resonance.

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APA: Copy

RAHELI, AMIR, AZIZI, SABER, & FAROUGHI, SHIRKO. (2017). DYNAMIC ANALYSIS OF A MICRO BEAM BASED ON SUB-HARMONIC PARAMETRIC EXCITATION. MODARES MECHANICAL ENGINEERING, 17(5 ), 374-384. SID. https://sid.ir/paper/179205/en

Vancouver: Copy

RAHELI AMIR, AZIZI SABER, FAROUGHI SHIRKO. DYNAMIC ANALYSIS OF A MICRO BEAM BASED ON SUB-HARMONIC PARAMETRIC EXCITATION. MODARES MECHANICAL ENGINEERING[Internet]. 2017;17(5 ):374-384. Available from: https://sid.ir/paper/179205/en

IEEE: Copy

AMIR RAHELI, SABER AZIZI, and SHIRKO FAROUGHI, “DYNAMIC ANALYSIS OF A MICRO BEAM BASED ON SUB-HARMONIC PARAMETRIC EXCITATION,” MODARES MECHANICAL ENGINEERING, vol. 17, no. 5 , pp. 374–384, 2017, [Online]. Available: https://sid.ir/paper/179205/en

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