Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment

Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting piezoelectric or other transduction mechanisms) for performance enhancement.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Classical and quantum signatures of competing chi((2)) nonlinearities

We report the observation of the quantum effects of competing chi((2)) nonlinearities. We also report classical signatures of competition, namely, clamping of the second-harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various chi((2)) up-conversion and down-conversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.

Initialisation of Nonlinearities for PNL and Wiener systems Inversion

This paper proposes a very fast method for blindly initial- izing a nonlinear mapping which transforms a sum of random variables. The method provides a surprisingly good approximation even when the basic assumption is not fully satis¯ed. The method can been used success- fully for initializing nonlinearity in post-nonlinear mixtures or in Wiener system inversion, for improving algorithm speed and convergence.

Power semiconductor nonlinearities in active du/dt output filtering

This doctoral thesis introduces an improved control principle for active du/dt output filtering in variable-speed AC drives, together with performance comparisons with previous filtering methods. The effects of power semiconductor nonlinearities on the output filtering performance are investigated. The nonlinearities include the timing deviation and the voltage pulse waveform distortion in the variable-speed AC drive output bridge. Active du/dt output filtering (ADUDT) is a method to mitigate motor overvoltages in variable-speed AC drives with long motor cables. It is a quite recent addition to the du/dt reduction methods available. This thesis improves on the existing control method for the filter, and concentrates on the lowvoltage (below 1 kV AC) two-level voltage-source inverter implementation of the method. The ADUDT uses narrow voltage pulses having a duration in the order of a microsecond from an IGBT (insulated gate bipolar transistor) inverter to control the output voltage of a tuned LC filter circuit. The filter output voltage has thus increased slope transition times at the rising and falling edges, with an opportunity of no overshoot. The effect of the longer slope transition times is a reduction in the du/dt of the voltage fed to the motor cable. Lower du/dt values result in a reduction in the overvoltage effects on the motor terminals. Compared with traditional output filtering methods to accomplish this task, the active du/dt filtering provides lower inductance values and a smaller physical size of the filter itself. The filter circuit weight can also be reduced. However, the power semiconductor nonlinearities skew the filter control pulse pattern, resulting in control deviation. This deviation introduces unwanted overshoot and resonance in the filter. The controlmethod proposed in this thesis is able to directly compensate for the dead time-induced zero-current clamping (ZCC) effect in the pulse pattern. It gives more flexibility to the pattern structure, which could help in the timing deviation compensation design. Previous studies have shown that when a motor load current flows in the filter circuit and the inverter, the phase leg blanking times distort the voltage pulse sequence fed to the filter input. These blanking times are caused by excessively large dead time values between the IGBT control pulses. Moreover, the various switching timing distortions, present in realworld electronics when operating with a microsecond timescale, bring additional skew to the control. Left uncompensated, this results in distortion of the filter input voltage and a filter self-induced overvoltage in the form of an overshoot. This overshoot adds to the voltage appearing at the motor terminals, thus increasing the transient voltage amplitude at the motor. This doctoral thesis investigates the magnitude of such timing deviation effects. If the motor load current is left uncompensated in the control, the filter output voltage can overshoot up to double the input voltage amplitude. IGBT nonlinearities were observed to cause a smaller overshoot, in the order of 30%. This thesis introduces an improved ADUDT control method that is able to compensate for phase leg blanking times, giving flexibility to the pulse pattern structure and dead times. The control method is still sensitive to timing deviations, and their effect is investigated. A simple approach of using a fixed delay compensation value was tried in the test setup measurements. The ADUDT method with the new control algorithm was found to work in an actual motor drive application. Judging by the simulation results, with the delay compensation, the method should ultimately enable an output voltage performance and a du/dt reduction that are free from residual overshoot effects. The proposed control algorithm is not strictly required for successful ADUDT operation: It is possible to precalculate the pulse patterns by iteration and then for instance store them into a look-up table inside the control electronics. Rather, the newly developed control method is a mathematical tool for solving the ADUDT control pulses. It does not contain the timing deviation compensation (from the logic-level command to the phase leg output voltage), and as such is not able to remove the timing deviation effects that cause error and overshoot in the filter. When the timing deviation compensation has to be tuned-in in the control pattern, the precalculated iteration method could prove simpler and equally good (or even better) compared with the mathematical solution with a separate timing compensation module. One of the key findings in this thesis is the conclusion that the correctness of the pulse pattern structure, in the sense of ZCC and predicted pulse timings, cannot be separated from the timing deviations. The usefulness of the correctly calculated pattern is reduced by the voltage edge timing errors. The doctoral thesis provides an introductory background chapter on variable-speed AC drives and the problem of motor overvoltages and takes a look at traditional solutions for overvoltage mitigation. Previous results related to the active du/dt filtering are discussed. The basic operation principle and design of the filter have been studied previously. The effect of load current in the filter and the basic idea of compensation have been presented in the past. However, there was no direct way of including the dead time in the control (except for solving the pulse pattern manually by iteration), and the magnitude of nonlinearity effects had not been investigated. The enhanced control principle with the dead time handling capability and a case study of the test setup timing deviations are the main contributions of this doctoral thesis. The simulation and experimental setup results show that the proposed control method can be used in an actual drive. Loss measurements and a comparison of active du/dt output filtering with traditional output filtering methods are also presented in the work. Two different ADUDT filter designs are included, with ferrite core and air core inductors. Other filters included in the tests were a passive du/dtfilter and a passive sine filter. The loss measurements incorporated a silicon carbide diode-equipped IGBT module, and the results show lower losses with these new device technologies. The new control principle was measured in a 43 A load current motor drive system and was able to bring the filter output peak voltage from 980 V (the previous control principle) down to 680 V in a 540 V average DC link voltage variable-speed drive. A 200 m motor cable was used, and the filter losses for the active du/dt methods were 111W–126 W versus 184 W for the passive du/dt. In terms of inverter and filter losses, the active du/dt filtering method had a 1.82-fold increase in losses compared with an all-passive traditional du/dt output filter. The filter mass with the active du/dt method was 17% (2.4 kg, air-core inductors) compared with 14 kg of the passive du/dt method filter. Silicon carbide freewheeling diodes were found to reduce the inverter losses in the active du/dt filtering by 18% compared with the same IGBT module with silicon diodes. For a 200 m cable length, the average peak voltage at the motor terminals was 1050 V with no filter, 960 V for the all-passive du/dt filter, and 700 V for the active du/dt filtering applying the new control principle.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Long duration stimuli and nonlinearities in the neural–haemodynamic coupling

Recent studies have shown that the haemodynamic responses to brief (<2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (>2 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depth-resolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).

Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros

In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations when the continuous non-linearity has a positive zero and it satisfies a p-linear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities. (C) 2009 Elsevier Masson SAS. All rights reserved.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Mesoscopic structure evidenced by AC dielectric nonlinearities in Sr(0.75)Ba(0.25)Nb(2)O(6) relaxor ferroelectric thin films

The AC electric field and temperature dependences of the dielectric permittivity for strontium barium niobate (Sr(0.75)Ba(0.25)Nb(2)O(6)) relaxor ferroelectric thin films have been investigated. The results indicate the existence of a true mesoscopic structure evidenced by the nonlinear dielectric response of these films, which is similar to those observed for bulk relaxor ferroelectrics. A tendency for a temperature dependent crossover from a linear to a quadratic behaviour of the dielectric nonlinearity was observed, indicating an evolution from paraelectric to glass-like behaviour on cooling the samples towards the freezing temperature transition.

A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration

Some dynamical properties of a bouncing ball model under the presence of an external force modelled by two nonlinear terms are studied. The description of the model is made by the use of a two-dimensional nonlinear measure-preserving map on the variable's velocity of the particle and time. We show that raising the straight of a control parameter which controls one of the nonlinearities, the positive Lyapunov exponent decreases in the average and suffers abrupt changes. We also show that for a specific range of control parameters, the model exhibits the phenomenon of Fermi acceleration. The explanation of both behaviours is given in terms of the shape of the external force and due to a discontinuity of the moving wall's velocity.

Wide localized solitons in systems with time- and space-modulated nonlinearities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)