Vibration Control of H-Shaped Planar Frames Based on the Classical Euler-Bernoulli and the Advanced Timoshenko Bending Theories

Coupled bending and longitudinal vibrations in H-shaped planar frames are controlled from a wave standpoint, in which vibrations are described as waves traveling along uniform structural waveguides, and being reflected and transmitted at structural discontinuities. Active discontinuities are created using active control forces/moments both along structural elements and at structural joints to control vibration waves. The bending vibrations are modeled and controlled using the classical Euler-Bernoulli as well as the advanced Timoshenko theories. Numerical examples are presented. Comparisons are made between the results obtained using the classical Euler-Bernoulli model and the advanced Timoshenko model. Good agreements have been reached at low frequencies. However, discrepancies are significant at higher frequencies, typically when the transverse dimensions are not negligible with respect to the wavelength. This study addresses the importance of taking into account the effects of rotary inertia and shear distortion at high frequencies.

Robust and Dynamically Consistent Reduced Order Models

The need for reduced order models (ROMs) has become considerable higher with the increasing technological advances that allows one to model complex dynamical systems. When using ROMs, the following two questions always arise: 1) “What is the lowest dimensional ROM?” and 2) “How well does the ROM capture the dynamics of the full scale system model?” This paper considers the newly developed concepts the authors refer to as subspace robustness — the ROM is valid over a range of initial conditions, forcing functions, and system parameters — and dynamical consistency — the ROM embeds the nonlinear manifold — which quanitatively answers each question. An eighteen degree-of-freedom pinned-pinned beam which is supported by two nonlinear springs is forced periodically and stochastically for building ROMs. Smooth and proper orthogonal decompositions (SOD and POD, respectively) based ROMs are dynamically consistent in four or greater dimensions. In the strictest sense POD-based ROMs are not considered coherent whereas, SOD-based ROMs are coherent in roughly five dimesions and greater. Is is shown that in the periodically forced case, the full scale dynamics are captured in a five-dimensional POD and SOD-based ROM. For the randomly forced case, POD and SOD-based ROMs need three dimensions but SOD captures the dynamics better in a lower-dimensional space. When the ROM is developed from a different set of initial conditions and forcing values, SOD outperforms POD in periodic forcing case and are equal in the random forcing case.

Wind Energy Conversion: The Potential of a Novel Ducted Turbine for Residential and Commercial Applications

A novel ducted turbine, referred to as a Wind Tower, for capturing wind power in either residential or commercial scale applications is studied theoretically and experimentally. A mathematical model is developed to predict the flow behavior inside the tower and a velocity coefficient is defined to correct the results at different test conditions. A wind tower prototype, including a four-quadrant-peak wind-catcher rooftop, a tower, a nozzle, and a turbine, is designed and fabricated. The captured wind power values from the mathematical model and the preliminary experimental tests are compared. While the mathematical model provides a good estimation of the output power in some cases, more precise experimental tests and simulation techniques are required to improve the mathematical model in some other cases. Significant changes in the output wind speed due to pressure differences created by the surrounding environment, the tower height, and the number of nozzles are observed. The advantages of being maintenance free, reliable, and sustainable, together with its special design that eliminates bird/bat mortality make the Wind Tower a promising solution for residential, commercial, and even off-grid applications.

Studying the Potential of a Novel Multiple-Generator Drivetrain in Wind Energy Conversion Systems

A novel multiple generator drivetrain (MGD), where a single large generator in a wind turbine is replaced by multiple generators with the same or different rated powers, is proposed along with an automatic switch mechanism as an alternative to an existing MGD. To better understand the advantages and disadvantages of having a MGD in onshore/offshore wind turbines, a MGD with a single or double stage gearbox and multiple generators is compared with a conventional drivetrain with a triple-stage gearbox and a large induction generator. A simple mathematical model for a MGD with an automatic switch is developed, a novel prototype of a MGD is designed and fabricated, and experiments are conducted on the prototype. It is concluded that a multiple-generator drivetrain with generators operating individually or in parallel through an automatic switch mechanism has a better potential of improving the efficiency and the reliability, expanding the operational range, and reducing the cost of offshore and onshore wind turbines than the existing MGD configuration.

Simplified Procedure to Estimate the Wind Turbine Blade Aerodynamic Loadings Without Using CFD

The aerodynamic loadings that act on the blade of a horizontal axis wind turbine change as a function of time due to the instantaneous change of the wind speed, the wind direction and the blade position. The new contribution in this study is the introduction of a simplified non CFD based procedure for the calculation of all the aerodynamic loadings acting on a wind turbine blade. The premise of the current simplified model is that (a) the forces can be modeled by a set of point loads rather than distributed pressures, and (b) the magnitudes of these point loads can be estimated using the below load formulas, (c) an interpolation scheme needed to have all computed forces and moments as a function of the blade lengthwise x. Considering a 14m blade length and utilizing a time dependent set of parameters such as angle of attack, material and air density, wind and blade speed, flow angle, yaw, pitch angles, the centrifugal forces (along x-direction of the blade length), the cross-sectional forces (Fy and Fz) and the twisting moment of the blade (about the x-direction) were calculated for each of all the given time steps. After that the authors explain how to interpolate the calculated loadings (forces and twisting moment) and the right formulas to compute the aerodynamic load vector (the right side of the dynamic equations of motion).

Sliding Mode Control in Ziegler’s Pendulum With Tracking Force: Novel Modeling Considerations

Ziegler’s pendulum is an appropriate model of a non-conservative dynamic system. By considering gravity effect, new equations of motion are extracted from Newton’s motion laws. The instability of equilibriums is determined by linear stability analysis. Chaotic behavior of the model is shown by numerical simulations. Sliding mode controller is used for eliminating chaos and for stabilizing the equilibriums.

Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.

Periodicities Changes of Nonlinear Oscillatory Behavior of a Fluttering Plate With Periodicity Ratio and Periodicity Change Rate

This study focuses on diagnosing the periodicity change of nonlinear dynamic responses of a fluttering plate excited by high-velocity air flow. The number and changing multiple-periodicities of the system with the implementation of Periodicity Ratio (PR) are investigated. The multiple-periodicity diagram is generated such that the periodicities and nonlinearity of the systems with respect to the system parameters can be graphically studied. The results of the research show that the number of period of periodicity of the systems increases when certain system parameters increase. Transitional characteristics of the systems are also investigated with Periodicity Change Rate as well.

Parametric Stability of a Nonlinear Rotating Blade

The stability of period-1 motions of a rotating blade with geometric nonlinearity is studied. The roles of cubic stiffening geometric term are considered in the study of nonlinear periodic motions and its stability and bifurcations of a rotating blade. The nonlinear model of a rotating blade is reduced to the ordinary differential equations through the Galerkin method, and the gyroscopic systems with parametric excitations are obtained. The generalized harmonic balance method is employed to determine the period-1 solutions and the corresponding stability and bifurcations.

Vibration Control for Parallel Manipulator Based on the Feed Forward Control Strategy

Due to the high stiffness, high dynamic performance, the parallel manipulator presents great advantages in the industrial manufacture. However in the machining process, the external low frequency disturbance, e.g. the varying cutting force, has a significant effect on the control system of parallel manipulator, which presents a chatter phenomenon on the end-effector of manipulator. In this paper, a feed forward control strategy is proposed to eliminate the effect of the random external disturbance on the control system of parallel manipulator. By applying the external disturbance force on the inverse dynamic model, the compensation torque is calculated and fed forward into the manipulator driving joints to cancel out the effect of the disturbance acting on the manipulator end-effector. The key issue herein is to be able to establish the accurate dynamic model for the parallel manipulator. Furthermore, in order to guarantee the position precision of the manipulator, a feed forward model-based control strategy combined with the feedback loop PV (position and velocity) control has been developed based on the reference trajectory, which could relatively simplify the highly nonlinear control system of the parallel manipulator and obtain a stable tracking error model. The whole research has been carried out on a parallel manipulator named CaPaMan which has been built in the laboratory of robotics and mechatronics in university of Cassino and South Latium. The results show that the chatter phenomenon could be utterly depressed by the force compensation from the feed forward path of the external disturbance; meanwhile the model-based controller can guarantee the trajectory tracking accuracy within a stable error by choosing the suitable PV gains.