The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system（FOMEMRS）.Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exh...The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system（FOMEMRS）.Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exhibits chaos.Strange attractors of the system are plotted to validate its chaotic behavior.Afterward,a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time.Using the latest version of the fractional Lyapunov theory,the finite time stability and robustness of the proposed scheme are proved.Finally,we present some computer simulations to illustrate the usefulness and applicability of the proposed method.展开更多
The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not...The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. Nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.展开更多
Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, ...Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.展开更多
A new method to detect the magnetic field direction by using a silicon structure is presented in this paper. The structure includes a micro beam and an in-plane coil electrode. When the electrode under a magnetic fiel...A new method to detect the magnetic field direction by using a silicon structure is presented in this paper. The structure includes a micro beam and an in-plane coil electrode. When the electrode under a magnetic field is applied with an alternating current, the micro beam is actuated under the effect of the Lorentz forces. Magnetic fields of different directions cause different vibration profiles. The direction of the magnetic field is obtained by measuring the vibration amplitudes of the micro beam, which is driven to work at first- and second-order resonant modes. A micro structure has been fabricated using the bulk microma^hined silicon process. A laser Doppler vibrometer system is implemented to measure the vibration amplitudes. The experimental results show that the amplitude of the structure, which depends on the different modes, is a sine or cosine function of the angle of the magnetic field. It agrees well with the simulation result. Currently a resolution of 10~ for the magnetic field direction measurement can be obtained using the detecting principle.展开更多
This paper presents a bulk acoustic wave piezoelectric disk resonator based on a special pair of degenerative modes, to detect z-axis angular velocity. A single piezoelectric disk is operated in its appropriate modes ...This paper presents a bulk acoustic wave piezoelectric disk resonator based on a special pair of degenerative modes, to detect z-axis angular velocity. A single piezoelectric disk is operated in its appropriate modes in the k Hz frequency range to achieve this function. This design combines the bulk acoustic wave drive/sense mode with lead zirconate titanate resonator which improves device's performance and simplifies its structural complexity. The operation principle of piezoelectric disk resonator is given and validated by finite element method,and the scale factor of piezoelectric disk resonator is 0.977 μV/[(°) · s-1] without any amplification section.The results of impedance analysis for the prototype in the air, which is fabricated on lead zirconate titanate wafer by Micro-Electro-Mechanical System process, show that the resonant frequency of the piezoelectric disk resonator is about 190 k Hz. Moreover, the measured frequency split between drive and sense mode is about290 Hz without any tuning methods. At last, a closed-loop driving and detecting circuit system is designed and its modulation/demodulation method is studied, preliminary experiments show that this device is not sensitive to acceleration, but is sensitive to angular velocity, its performance parameters need follow-up experiments.展开更多
文摘The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system（FOMEMRS）.Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exhibits chaos.Strange attractors of the system are plotted to validate its chaotic behavior.Afterward,a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time.Using the latest version of the fractional Lyapunov theory,the finite time stability and robustness of the proposed scheme are proved.Finally,we present some computer simulations to illustrate the usefulness and applicability of the proposed method.
基金This project is supported by Shanghai Municipal Science and Technique Committee Foundation, China (No. 03QF14019, No. 0452nm023, No. AM0420).
文摘The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. Nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.
文摘Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No.61076071)
文摘A new method to detect the magnetic field direction by using a silicon structure is presented in this paper. The structure includes a micro beam and an in-plane coil electrode. When the electrode under a magnetic field is applied with an alternating current, the micro beam is actuated under the effect of the Lorentz forces. Magnetic fields of different directions cause different vibration profiles. The direction of the magnetic field is obtained by measuring the vibration amplitudes of the micro beam, which is driven to work at first- and second-order resonant modes. A micro structure has been fabricated using the bulk microma^hined silicon process. A laser Doppler vibrometer system is implemented to measure the vibration amplitudes. The experimental results show that the amplitude of the structure, which depends on the different modes, is a sine or cosine function of the angle of the magnetic field. It agrees well with the simulation result. Currently a resolution of 10~ for the magnetic field direction measurement can be obtained using the detecting principle.
基金the Special New Century Excellent Talents Support Program of Ministry of Education(No.NCET-10-0583)the National Key Laboratory of Science and Technology on Nano/Micro Fabrication(No.9140C790405110C7904)+2 种基金Preresearch Fund(No.9140A09010312JW03104)Fund(No.2013ZC57003)the Graduate Innovation Program of Shanghai Jiao Tong University(No.Z-340-014)
文摘This paper presents a bulk acoustic wave piezoelectric disk resonator based on a special pair of degenerative modes, to detect z-axis angular velocity. A single piezoelectric disk is operated in its appropriate modes in the k Hz frequency range to achieve this function. This design combines the bulk acoustic wave drive/sense mode with lead zirconate titanate resonator which improves device's performance and simplifies its structural complexity. The operation principle of piezoelectric disk resonator is given and validated by finite element method,and the scale factor of piezoelectric disk resonator is 0.977 μV/[(°) · s-1] without any amplification section.The results of impedance analysis for the prototype in the air, which is fabricated on lead zirconate titanate wafer by Micro-Electro-Mechanical System process, show that the resonant frequency of the piezoelectric disk resonator is about 190 k Hz. Moreover, the measured frequency split between drive and sense mode is about290 Hz without any tuning methods. At last, a closed-loop driving and detecting circuit system is designed and its modulation/demodulation method is studied, preliminary experiments show that this device is not sensitive to acceleration, but is sensitive to angular velocity, its performance parameters need follow-up experiments.
