Reduced-Order Modeling of Torque on a Vertical-Axis Wind Turbine at Varying Tip Speed Ratios

2015 ◽  
Vol 10 (4) ◽  
Author(s):  
Muhammad Saif Ullah Khalid ◽  
Tariq Rabbani ◽  
Imran Akhtar ◽  
Naveed Durrani ◽  
M. Salman Siddiqui
Keyword(s):  
Wind Turbine ◽  
Multiple Scales ◽  
Vertical Axis ◽  
Reduced Order Model ◽  
Quadratic Term ◽  
Perturbation Approach ◽  
Vertical Axis Wind Turbine ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order

Vertical-axis wind turbine (VAWT) has received significant attention due to its application in urban environment. Torque produced by VAWT determines its efficiency and power output. In this paper, we develop a reduced-order model of torque VAWT at different tip speed ratios (TSR). We numerically simulate both 2D and 3D flows past a three-bladed Darrieus H-type VAWT and compute overall torque acting on the turbine. We then perform higher-order spectral analysis to identify dominant frequencies and nonlinear couplings. We propose a reduced-order model of torque in the form of modified van der Pol equation with additional quadratic term to allow for even harmonics in addition to odd harmonics present in the system. Using, a perturbation approach of method of multiple scales, we solve the proposed model and compute the coefficients at different TSR. The model not only predicts torque accurately in time domain but also in spectral domain. These reduced-order models provide an accurate and computationally efficient means to predict overall performance and output of the turbine with varying free-stream conditions even in predictive setting.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Frequency Response of Parametric Resonance of Electrostatically Actuated Circular Plates Under Hard Excitations

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Circular Plates ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

Abstract In this paper, the Method of Multiple Scales, and the Reduced Order Model method of two modes of vibration are used to investigate the amplitude-frequency response of parametric resonance of electrostatically actuated circular plates under hard excitations. Results show that the Method of Multiple Scales is accurate for low voltages. However, it starts to separate from the Reduced Order Model results as the voltage values are larger. The Method of Multiple Scales is good for low amplitudes and weak non-linearities. Furthermore the Reduced Order Model running with AUTO 07p is validated and calibrated using the 2 Term ROM time responses.

scholarly journals Reduced order model of offshore wind turbine wake by proper orthogonal decomposition

2020 ◽  
Vol 82 ◽  
pp. 108554 ◽  
Author(s):  
M. Salman Siddiqui ◽  
Sidra Tul Muntaha Latif ◽  
Muhammad Saeed ◽  
Muhammad Rahman ◽  
Abdul Waheed Badar ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Turbine Wake

Reduced Order Model for MEMS Cantilever Resonators Under Soft AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator is investigated. The AC voltage is of frequency near resonator’s natural frequency. A first order fringe correction of the electrostatic force and viscous damping are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for the uniform microresonator are compared with those obtained via the Method of Multiple Scales (MMS).

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Alternating Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Fringe Effect

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

scholarly journals Data-driven Reduced Order Model for prediction of wind turbine wakes

2015 ◽  
Vol 625 ◽  
pp. 012009 ◽  
Author(s):  
G V Iungo ◽  
C Santoni-Ortiz ◽  
M Abkar ◽  
F Porté-Agel ◽  
M A Rotea ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Reduced Order Model ◽  
Data Driven ◽  
Order Model ◽  
Reduced Order

Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Reduced Order Model ◽  
Lagrange Equations ◽  
Order Model ◽  
Reduced Order ◽  
Dc Voltage ◽  
Ground Plate

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.

Reduced Order Model of Parametric Resonance of Electrostatically Actuated CNT Cantilever Resonators

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate ◽  
Phase Behaviors

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model (ROM) method. Forces acting on the CNT cantilever are electrostatic, van der Waals, and damping. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS), and ROM are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behaviors are found in the case of parametric resonance.

Analysis of Vibration of a Tank Caused by an Explosion

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
M. Utsumi ◽  
H. Tazuke
Keyword(s):  
Fluid Motion ◽  
Three Dimensional ◽  
Longitudinal Axis ◽  
Reduced Order Model ◽  
Fe Model ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Large Tank ◽  
The Galerkin Method

The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.

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