Tetsuhiko Ueda

Aeroelastic analysis considering structural uncertainty

Abstract Uncertainties in aero elastic analysis are investigated. In aero elastic analysis, we usually find divergence speed or flutter speed by using deterministic equations of motion for elastic wings of aircraft. If any parameter in these equations is sensitive to the critical speed, we should treat it carefully since inaccuracy is inevitable in the production process. Tragic failure may occur if the margin is small. Therefore, it is important to know in the analysis the effects of uncertainties of the critical values when they play a critical role in the design. The sensitivity of parameters in aero elastic analysis is not simple even in linear analysis. It is not always possible to have an analytic form of the sensitivity of uncertainty. In order to evaluate the structural sensitivity of aero elastic phenomena, we have to resort to numerical calculations with uncertain parameters having some random deviations, i.e. the so‐called Monte Carlo simulation. In the present study, the divergence speed and f...

Deformation of a Beam with Partially Debonded Piezoelectric Actuators

A linear and a non-linear mathematical models for analyzing the deformation behavior of a beam with a pair of partially debonded piezoelectric actuators are developed on the basis of the Timoshenko beam theory. Effect of buckling is considered in the linear model, where the debonded actuator region is assumed to generate the Euler buckling load when the axial force in the region is larger than the load. The static behavior of the beam is investigated for extension and bending deformation. When the actuator debonds from its edge, the performance deteriorates; in contrast, the debonding in the middle of the actuator does not show any performance degradation until the debonded region buckles. The deformation behavior obtained from the linear model has been found to have good agreement with that from the non-linear model. The non-linear analysis shows that after the buckling the debonded actuator region maintains an axial force of the order of the Euler buckling load of a fix—fix column for the extending actuation, although for the bending actuation, it retains nearly 75% of the Euler buckling load. Further, the strain distribution in the debonded region shows that the buckling may occur before cracks begin in the actuator.

A constitutive model for temperature dependent behavior of ferroelectric materials

A simple constitutive model for temperature dependent behavior of ferroelectric materials is developed. This model is based on the one-dimensional phase transformation model of shape memory alloys. To model the temperature dependent behavior of the ferroelectric materials, a paraelectric phase is considered in addition to four ferroelectric variants in a ferroelectric phase. These ferroelectric variants are connected in series to each other, whereas the paraelectric phase is connected in parallel to the ferroelectric phase. The internal stress is induced in the material due to this parallel connection, which increases or decreases the driving energy for the switching depending on the switching direction. As the temperature increases up to the Curie temperature, the volume fraction of the paraelectric phase is assumed to increase and the required switching energy is assumed to decrease as observed in experiments. The temperature dependence of the relationships among the electric field, electric displacement, stress, and strain are simulated and compared with published experimental data for a soft PZT. The comparison indicates that the present constitutive model can predict the temperature dependent behavior well. This implies that the proposed model can provide a convenient tool to understand the physical mechanism of the ferroelectric materials and to design smart structures containing the ferroelectric materials.

Smart vortex generator transformed by change in ambient temperature and aerodynamic force

A Smart Vortex Generator (SVG) concept has been proposed, where the SVG is autonomously transformed between an upright vortex-generating position in take-off and landing and a flat drag-reducing position in a cruise. This SVG is made of a Shape Memory Alloy (SMA), which is in the austenite phase and memorizes the upright position at high temperatures of the take-off and landing. At low temperatures during ascent the SVG is transformed into a martensite phase, and it lies flat against a base structure due to external or/and internal forces. In this paper, we examine whether the SVG can be transformed into the drag-reducing position by an aerodynamic force. To this end, numerical simulations are carried out with a simple line element model. The aerodynamic force applied on the SVG is calculated by a commercial CFD program. Result reveals that this SVG can be transformed from the upright vortex-generating position into the drag-reducing position by just an airplane climbing, and vice versa, if the SMA applied to the SVG has the two-way shape memory effect. If the SMA has the one-way shape memory effect, it is necessary to reduce the stiffness of the SVG or/and use a counter spring.

One-dimensional switching model for major and minor hysteresis loops in ferroelectric materials

The one-dimensional phase transformation model of shape memory alloys [Ikeda et al., Smart Materials and Structures, 13, 916-925 (2004)] is applied to expressing the major and minor hysteresis loops in ferroelectric materials. An analogy between the phase transformation in the shape memory alloys and the switching in the ferroelectric materials is involved. The one-dimensional phase transformation model has the following two features. (i) A specimen is assumed to be comprised of grains with infinitesimal sizes, and the order of the energy required for the transformation of the grains is unchanged independently of the transformation directions. Accordingly, the phase transformation occurs onedimensionally. (ii) The required transformation energy is approximated as a sum of two exponential functions of phase volume fraction. To express the ferroelectric behavior, four phases (variants) are considered, namely, the 0° variant, 90° variant, 180° variant, and initial mixed variant. Electro-mechanical behavior of a ferroelectric material is simulated numerically. The result shows the model can approximately duplicate the electro-mechanical behavior observed in the ferroelectric material.

Numerical analysis of deformation of a beam with thin piezoelectric actuators partially debonded and buckling

Deformation of a cantilever beam having thin piezoelectric actuators partially debonded and buckling is analyzed by using a linear mathematical model based on the Timoshenko beam theory. Effects of location and size of the debonding are investigated for passive and active extension and bending. The buckling of the actuators is considered by applying a constant force equal to the buckling load at the boundary between the debonded and the bonded regions. When the actuators are debonded at their edges, only the bonded regions contribute to the deformation of the beam but the debonded regions do not contribute at all. When the actuators are debonded in the middle, both the ends of which are keeping bonded, their performances are almost the same as those for perfectly bonded actuators irrespective of the location and size of the debonded region before the debonded region buckles. However, after it buckles, the performance deteriorates depending on the distance from the clamp and the size of the debonded region.

Flutter Prediction Using Wavelet Transform

[Abstract] The present paper proposes a new methodology to predict flutter. The method is based on the wavelet transform, which transforms time signals into the localized time-frequency domain. A flutter test was conducted at a low speed wind tunnel to obtain experimental data in sub-critical region. The prediction technique was applied to the response signals of a low-aspect-ratio wing model subjected to the windtunnel turbulence. It was found that the linear extrapolation of a new index defined in the transformed domain could well predict the flutter speed. The other prediction methods were also examined with the same signals to compare their predictability.

Numerical simulation for random aeroelastic responses using inverse fourier transform

This paper reports a new simulation technique for an aeroelastic system which responds to random external forces. Since the aeroelastic system including the effects of unsteady aerodynamics is ordinarily described in the frequency domain, the Inverse Discrete Fourier Transform (IDFT) can be utilized to simulate its random response. The response caused by the external random noise is calculated through a transfer function first in the frequency domain and then converted to the time domain. The objective of the present study is to provide mathematical time history data for evaluating the various estimation methods of the flutter boundary from subcritical responses in flight and/or wind tunnel testing. An example application to the method of flutter prediction is shown. The technique can also be used to evaluate the effects of the active control device coping with atmospheric turbulence.

Unsteady transonic aerodynamics during wing flutter

Unsteady pressure distributions of a two-dimensional super-critical wing while it was fluttering were measured in the transonic flow regime. The results were compared with those by the Navier-Stokes code which includes wind-tunnel wall effects. Although there were discrepancies between the experimental results and the analytical model for the pressure phase delay distribution, no disagreements were observed for the pitching first harmonics provided that there was no large flow separation. In the tests, the flutter was forced to be suppressed soon after its onset before it reached a limit cycle oscillation (LCO) where the amplitude of the pitching angle was supposed to be over 2 degrees.

Constitutive model for rate dependent behavior of ferroelectric materials

A constitutive model for rate dependent behavior of ferroelectric materials is developed from a one-dimensional switching model [Ikeda et al., Proc. SPIE, 7289 (2009), 728905]. The one-dimensional switching model has the following three features. (i) Several ferroelectric variants can be considered, such as 0-degree, 90-degree, 180-degree, and initial mixed variants. (ii) Required switching energy is approximated as a sum of two exponential functions of volume fraction of the variants. (iii) A specimen is assumed to be comprised of grains with infinitesimal size, and relationship between two grains regarding the required switching energy is unchanged independently of switching directions. Accordingly, the switching proceeds one-dimensionally. To take into account loading rate effects, a function of volume fraction rate is added to the required switching energy. That makes energy barrier higher at higher rates. To verify validity of the present model, electro-mechanical behavior of a thin PZT plate is measured at various loading rates and simulated using the present model. Result shows the present model can capture the influence of electric loading rate on responses of electric displacement and strain, such that remnant polarization decreases and coercive field increases with increasing the loading rate.