Cheng-Chi Wang

Nonlinear analysis and control of the uncertain micro-electro-mechanical system by using a fuzzy sliding mode control design

This study analyzes the chaotic behavior of a micromechanical resonator with electrostatic forces on both sides and investigates the control of chaos. A phase portrait, maximum Lyapunov exponent and bifurcation diagram are used to find the chaotic dynamics of this micro-electro-mechanical system (MEMS). To suppress chaotic motion, a robust fuzzy sliding mode controller (FSMC) is designed to turn the chaotic motion into a periodic motion even when the MEMS has system uncertainties.

Analyzing the free vibrations of a plate using finite difference and differential transformation method

This paper analyses the free vibrations of clamped and simply supported rectangular thin plates. A hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations of the plate to a set of algebraic equations. The investigative parameters include the order of the differential transformation, the number of sub-domain spaces, the variable conditions and the type of initial condition. The numerical simulation results indicate that the solution of the natural frequency is more accurate when calculated using a higher number of sub-domains. The effect of the difference transformation order value (k) on the solution of the natural frequency is not significant when the combined T spectra method and differential transformation method is applied. The initial mode shape of the plate has a significant influence on the solution of the natural frequency. The current modeling results confirm the viability of using the hybrid method proposed in this paper to solve the free vibrations and natural frequency of clamped and simply supported plates.

Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem

This paper analyses the large deflections of an orthotropic rectangular clamped and simply supported thin plate. A hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations describing the large deflections of the orthotropic plate to a set of algebraic equations. The simulation results indicate that significant errors are present in the numerical results obtained for the deflections of the orthotropic plate in the transient state when a step force is applied. The magnitude of the numerical error is found to reduce, and the deflection of the orthotropic plate to converge, as the number of sub-domains considered in the solution procedure increases. The deflection of the simply supported orthotropic plate is great than the clamped orthotropic plate. The current modeling results confirm the applicability of the proposed hybrid method to the solution of the large deflections of a rectangular orthotropic plate.

A NUMERICAL INVESTIGATION INTO ELECTROOSMOTIC FLOW IN MICROCHANNELS WITH COMPLEX WAVY SURFACES

This study investigates the flow characteristics of electroosmotic flow in a microchannel with complex wavy surfaces. A general method of coordinate transformation is used to solve the governing equations describing the electroosmotic flow in the microchannel. Numerical simulations are performed to analyze the effects of wave amplitude on the electrical field, flow streamlines, and flow fields in the microchannel. The simulation results show that, compared to a traditional pressure-driven flow, flow recirculation is not developed in the electroosmotic flow in a microchannel with complex wavy surfaces. The simulations also show that the electrical field and velocity profiles change along the channel in the region of wavy surfaces. Non-flat velocity profiles are observed in different cross-sections of the channel in the region of wavy surfaces.

Application of the differential transformation method to bifurcation and chaotic analysis of an AFM probe tip

The AFM (atomic force microscope) has become a popular and useful instrument for measuring intermolecular forces with atomic resolution, that can be applied in electronics, biological analysis, and studying materials, semiconductors etc. This paper conducts a systematic investigation into the bifurcation and chaotic behavior of the probe tip of an AFM using the differential transformation (DT) method. The validity of the analytical method is confirmed by comparing the DT solutions for the displacement and velocity of the probe tip at various values of the vibrational amplitude with those obtained using the Runge-Kutta (RK) method. The behavior of the probe tip is then characterized utilizing bifurcation diagrams, phase portraits, power spectra, Poincare maps, and maximum Lyapunov exponent plots. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the tip motion changes first from subharmonic to chaotic motion, then from chaotic to multi-periodic motion, and finally from multi-periodic motion to subharmonic motion with windows of chaotic behavior as the non-dimensional vibrational amplitude is increased from 1.0 to 5.0.

Bifurcation and nonlinear dynamic analysis of united gas-lubricated bearing system

This paper studies the bifurcation and nonlinear behaviors of a united gas-lubricated bearing (UGB) system by a hybrid numerical method combining the differential transformation method and the finite difference method. The analytical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, quasi-periodic and chaotic responses of the rotor center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of UGB systems.

Theoretical analysis of high speed spindle air bearings by a hybrid numerical method

To study the behavior of the high speed spindle air bearing (HSSAB) system, we conduct the research by means of a hybrid numerical method which combines the differential transformation method and the finite difference method in this paper. According to the results of the research, the flexible rotor center is found to include a complex dynamic behavior that comprises periodic, sub-harmonic and quasi-periodic responses. In addition, as the rotor mass and the bearing number are increased, there will be some changes taking place in the dynamic behavior of the bearing system. The results are proven to have no conflict with those of the other numerical methods, which enables an effective means in gaining insights into the nonlinear dynamics of HSSAB systems.

Transient Analysis of Forced Convection Along a Wavy Surface in Micropolar Fluids

Numerical results for transient laminar-forced convection along a wavy surface in micropolar fluids are presented. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate, and the obtained nonsimilarity boundary layer equation is solved numerically by the spline alternating-direction implicit method. The effects of micropolar parameter and wavy geometry on the velocity and temperature fields are examined. The transient skin friction and transient local and averaged heat-transfer rates decrease with time. Their axial distributions have a frequency equal to the frequency of the wavy surface, but their crests and troughs do not occur just at the crests and troughs of the wavy surface. The amplitudes of the transient local skin-friction coefficient and the transient local Nusselt number tend to increase as the wavy length and the wavy amplitude-wavelength ratio increases. Furthermore, the transient Nusselt number of a micropolar fluid is smaller than that of a Newtonian fluid everywhere, whereas the transient local skin-friction coefficient of a micropolar fluid is larger than that of a Newtonian fluid just near the leading edge

Chaotic Analysis and Control of Microcandilevers with PD feedback Using Differential Transformation Method

This paper investigates the nonlinear dynamic behavior of the probe tip of an atomic force microscope with a PD (proportional-plus-derivative) feedback control using the differential transformation method (DTM). The dynamic behavior of the probe tip with PD control law is characterized by reference to phase portraits, power spectra, Poincare maps, and maximum Lyapunov exponent plots produced using the timeseries data obtained from differential transformation method. Furthermore, the detailed transitions in the dynamic response of the probe tip are examined using bifurcation diagrams of the tip displacement and the tip velocity, respectively. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the proportional and derivative control gain. Specifically, the probe tip motion includes subharmonic, multi-periodic, and chaotic motion. Numerical results show that the dynamic behavior will leave chaotic motion to periodic motion at Kp= -0.45 in the steady state by changing the control loop gain Kv from -0.1 to -1.0. Furthermore, it is demonstrated that the differential transformation method is in good agreement for the considered system.

Real-time measurement of glucose concentration using position sensing detector

This study develops a high-precision, non-destructive measurement technique based on a PSD for determining the glucose concentration of a liquid solution from its refractive index. The optical metrology system is employed to measure the refractive indexes of samples with known glucose concentrations ranging from 10 ~ 100 g/l. By applying regressional analysis to the experimental results, an analytical expression is derived to describe the linear relationship between the refractive index and the glucose concentration. As the glucose concentration 50 g/l is applied, the error between the measured value of the refractive index and the analytically derived value is just 0.0004437627. An excellent agreement is observed between the experimentally determined values of the glucose concentration and the analytically predicted results.