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Dynamic modeling of beams under aerodynamic loading is extremely important in many engineering applications. So the objective of this paper is to present a new approach to model and simulate the time domain response of tapered cantilever beams with airfoil cross section to wind excitation. The extended Hamilton’s principles along with the Euler-Bernoulli assumptions are utilized to derive the Partial Differential Equation (PDE) governing the deflection of the beam. A new finite difference based algorithm is proposed for finding the mode-shapes as well as the natural frequencies of the beam. These mode-shapes are then used in a Galerkin projection procedure to convert the PDE governing the system’s behavior into strongly coupled nonlinear Ordinary Differential Equations (ODEs). The aerodynamic loadings are modeled using the open source code of XFOIL. The blade of an under developed 100KW wind turbine is considered as a case study. The results reveal that even a single mode approximation is accurate enough in predicting the beam’s dynamic exposed to wind excitation. It was also observed that the instability speed of beams with higher modal damping is considerably higher than those with lower modal damping. The knowledge resulting from this effort is expected to enable the analysis, optimization, and synthesis of tapered cantilever beams for improved dynamic performance.

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In this study, the effects of frequency, height and wavelength of progressive gravity waves on vibration and energy absorption of the single- and two-degree of freedom Bristol oscillating cylinder systems have been investigated experimentally and numerically in different depth of water. The experiments were carried out in channel equipped with both a paddle-type wave-maker and wave features measurement tools. Numerical simulations were conducted in COMSOL software assigned to simulate interactions between physical environments for turbulent flow. Making a comparison between the numerical and experimental conclusions compared to the other researchers' results demonstrates a desired matching in a wide range of waves' parameters. It can be seen in findings that changing in depth of submerged objects from free surface of water has considerable influence on their vibration behavior, so that by rising in depth, the oscillations amplitude increases to a maximam and then decreases. The obtained results indicate the different effects of relative depth under the submerged buoy on the efficiency of the single- and two-degree of freedom systems; so that increasing water height causes rise in the efficiency of single degree of freedom systems, but it doesn't have considerable influence on two degree of freedom systems. The results also show that expanding the wave-maker frequency for a constant height of water in channel causes to rise in energy and height of the generated waves so that oscillations amplitude of submerged buoy rise in vertical and horizontal line.

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Circular micro-plates are used in microelectromechanical systems (MEMS) such as micro-pumps and ultrasonic transducers due to their special geometry. One of the most important problems with electrostatic micro-actuators is pull-in instability which prevents large displacements. Stabilization in beyond pull-in displacements can be attained using an appropriate controller. This paper presents a position control problem for an electrostatic micro-actuator consisting two circular clamped micro-plates to enhance the stroke and speed up the input commands. To consider the modeling error and geometric uncertainties, a fuzzy controller is applied. First, the equation of the plates vibration is derived using Lagrange equation with single mode assumption. Fuzzy rule-base is constructed according to static and dynamic simulations. Genetic algorithm is utilized for finding the optimum parameters of the controller to accelerate accomplishing the commands. Finally, the maximum voltage of the plates is fitted with a function using the optimization results for full range gap commands. The performance of the fuzzy controller along with this function is depicted applying step, multiple step and chirp commands. The obtained results show that the objective has been met well.