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No description available.

Dynamics of a beam-based micro-electromechanical resonator is investigated theoretically and experimentally. The resonant structure comprises a micro-beam and two electrostatic comb-drives, one for exciting the vibration, and the other for detecting the response. Two identical resonators of this type can form a double-ended tuning fork. An analytical linear model of these resonators is developed by assuming the beam to obey the thin beam theory subjected to an axial force. The comb-drives are initially treated as a point mass. The point mass is free to be placed anywhere along the beam span. The exact natural frequencies and mode shapes of vibration are obtained. Further, the mass is considered to have rotary inertia. The influence of the rotary inertia on the natural frequencies and mode shapes of vibration are investigated. Subsequently, the model of a beam with a guided mass is studied to determine the upper limit of the natural frequencies of the resonator. The advantage of this model over the previous ones is in providing detailed insight into the dynamics of the resonator, particularly when the comb-drives are placed at locations other than the mid-point of the beam. It has been shown that the mode shapes of vibration of these resonators are not orthogonal to each other under its classic definition. The orthogonality condition of the mode shapes of the beam-lumped mass system is introduced, and used for studying the forced vibration response. The nonlinear vibration of the system due to stretching is considered for the case of free vibration and the primary resonance. The nonlinear model is used to investigate the effect of damping on the resonator response. The interaction of the electrostatic governing equations and the mechanical model is studied. This model is employed for designing the experiment circuits for testing fabricated resonators. The fabrication processes used are explained, and the design parameters of each resonator are provided. The experimental results are reported, and used to find the axial force and stress of the resonant beams. The model and results of this dissertation can be used in the design of beam-based micromachined resonators for different applications.

Dynamics of a beam-based micro-electromechanical resonator is investigated theoretically and experimentally. The resonant structure comprises a micro-beam and two electrostatic comb-drives, one for exciting the vibration, and the other for detecting the response. Two identical resonators of this type can form a double-ended tuning fork. An analytical linear model of these resonators is developed by assuming the beam to obey the thin beam theory subjected to an axial force. The comb-drives are initially treated as a point mass. The point mass is free to be placed anywhere along the beam span. The exact natural frequencies and mode shapes of vibration are obtained. Further, the mass is considered to have rotary inertia. The influence of the rotary inertia on the natural frequencies and mode shapes of vibration are investigated. Subsequently, the model of a beam with a guided mass is studied to determine the upper limit of the natural frequencies of the resonator. The advantage of this model over the previous ones is in providing detailed insight into the dynamics of the resonator, particularly when the comb-drives are placed at locations other than the mid-point of the beam. It has been shown that the mode shapes of vibration of these resonators are not orthogonal to each other under its classic definition. The orthogonality condition of the mode shapes of the beam-lumped mass system is introduced, and used for studying the forced vibration response. The nonlinear vibration of the system due to stretching is considered for the case of free vibration and the primary resonance. The nonlinear model is used to investigate the effect of damping on the resonator response. The interaction of the electrostatic governing equations and the mechanical model is studied. This model is employed for designing the experiment circuits for testing fabricated resonators. The fabrication processes used are explained, and the design parameters of each resonator are provided. The experimental results are reported, and used to find the axial force and stress of the resonant beams. The model and results of this dissertation can be used in the design of beam-based micromachined resonators for different applications.

In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction.

Basic resonator structures for frequency-selective capacitive vibration sensors which exploit their mechanical resonance peak for spectral selectivity are developed and analyzed. As an important capability, the stuctures offer voltage-controlled frequency tuning realized by electrostatic principles. Direct electrostatic tuning based on displacement-dependent electrostatic forces as well as tuning by stress-stiffening based on constant electrostatic forces are discussed. The sensor structures are designed for fabrication using common silicon surface microtechnologies. Experimental tests of both mentioned tuning principles are carried out at structures fabricated using a surface technology known as SCREAM. A considerable part of the work focusses on nonlinear oscillations of the mechanical resonator at large amplitudes arising in resonance. Dimensioning rules for minimum nonlinear disturbance are derived from a detailed analysis of the Duffing oscillator. Various capacitive principles for signal detection and electrostatic frequency tuning are evaluated in terms of nonlinearity. A novel type of specially shaped electrode systems offering linear properties within an amplitude range of 10 micrometers, so-called curved comb capacitors, is developed for fabrication in SCREAM technology. / In der vorliegenden Arbeit werden Grundstrukturen frequenzselektiver kapazitiver Vibrationssensoren entwickelt und analysiert, deren spektrale Selektionswirkung durch Ausnutzung ihrer mechanischen Resonanzüberhöhung entsteht. Wesentliches Merkmal der Strukturen ist ihre spannungsgesteuerte Abstimmbarkeit, die auf elektrostatischen Prinzipien beruht. Es werden die direkte elektrostatische Frequenzabstimmung, basierend auf positionsabhängigen Feldkräften, sowie das Prinzip des Stress-Stiffening, basierend auf einer konstanten elektrostatischen Kraft, diskutiert. Die Entwicklung konzentriert sich auf Sensorstrukturen, die in klassischen Oberflächentechnologien gefertigt werden können. Experimentelle Tests der beiden genannten Abstimmprinzipien werden anhand von Strukturen in oberflächennaher Silizium-bulk-Mikromechanik (SCREAM) durchgeführt. Schwerpunkt der Arbeit sind nichtlineare Schwingungen der mechanischen Resonatorkomponente bei großen Amplituden, die durch die Resonanzüberhöhung entstehen. Für den Sonderfall des Duffing-Schwingers werden Dimensionierungsregeln zur Minimierung der Nichtlinearitäten entwickelt. Kapazitive Prinzipien zur Detektion bzw. elektrostatischen Abstimmung werden hinsichtlich ihrer Linearität geprüft. Es werden neuartige Elektrodensysteme für die SCREAM-Technologie, sogenannte Kurvenkammsysteme entwickelt, die bei Schwingamplituden bis zu 10 Mikrometer linear arbeiten.

Basic resonator structures for frequency-selective capacitive vibration sensors which exploit their mechanical resonance peak for spectral selectivity are developed and analyzed. As an important capability, the stuctures offer voltage-controlled frequency tuning realized by electrostatic principles. Direct electrostatic tuning based on displacement-dependent electrostatic forces as well as tuning by stress-stiffening based on constant electrostatic forces are discussed. The sensor structures are designed for fabrication using common silicon surface microtechnologies. Experimental tests of both mentioned tuning principles are carried out at structures fabricated using a surface technology known as SCREAM. A considerable part of the work focusses on nonlinear oscillations of the mechanical resonator at large amplitudes arising in resonance. Dimensioning rules for minimum nonlinear disturbance are derived from a detailed analysis of the Duffing oscillator. Various capacitive principles for signal detection and electrostatic frequency tuning are evaluated in terms of nonlinearity. A novel type of specially shaped electrode systems offering linear properties within an amplitude range of 10 micrometers, so-called curved comb capacitors, is developed for fabrication in SCREAM technology. / In der vorliegenden Arbeit werden Grundstrukturen frequenzselektiver kapazitiver Vibrationssensoren entwickelt und analysiert, deren spektrale Selektionswirkung durch Ausnutzung ihrer mechanischen Resonanzüberhöhung entsteht. Wesentliches Merkmal der Strukturen ist ihre spannungsgesteuerte Abstimmbarkeit, die auf elektrostatischen Prinzipien beruht. Es werden die direkte elektrostatische Frequenzabstimmung, basierend auf positionsabhängigen Feldkräften, sowie das Prinzip des Stress-Stiffening, basierend auf einer konstanten elektrostatischen Kraft, diskutiert. Die Entwicklung konzentriert sich auf Sensorstrukturen, die in klassischen Oberflächentechnologien gefertigt werden können. Experimentelle Tests der beiden genannten Abstimmprinzipien werden anhand von Strukturen in oberflächennaher Silizium-bulk-Mikromechanik (SCREAM) durchgeführt. Schwerpunkt der Arbeit sind nichtlineare Schwingungen der mechanischen Resonatorkomponente bei großen Amplituden, die durch die Resonanzüberhöhung entstehen. Für den Sonderfall des Duffing-Schwingers werden Dimensionierungsregeln zur Minimierung der Nichtlinearitäten entwickelt. Kapazitive Prinzipien zur Detektion bzw. elektrostatischen Abstimmung werden hinsichtlich ihrer Linearität geprüft. Es werden neuartige Elektrodensysteme für die SCREAM-Technologie, sogenannte Kurvenkammsysteme entwickelt, die bei Schwingamplituden bis zu 10 Mikrometer linear arbeiten.