On-demand Aerodynamics in Integrally Actuated Membranes with Feedback Control

This paper is a numerical investigation on model reduction and control system design of integrally actuated membrane wings. A high-fidelity electro-aeromechanical model is used for the simulation of the dynamic fluid-structure interaction between a low-Reynolds-number flow and a dielectric elastomeric wing. Two reduced-order models with different levels of complexity are then derived. They are based on the projection of the fullorder discretisation of fluid and structure on modal shapes obtained from eigenvalue analysis and Proper Orthogonal Decomposition. The low-order systems are then used for the design of Proportional-Integral-Derivative and Linear Quadratic Gaussian feedback schemes to control wing lift. When implemented in the full-order model, closed-loop dynamics are in very good agreement with the reduced-order model for both tracking and gust rejection, demonstrating the suitability of the approach. The control laws selected in this work were found to be effective only for low-frequency disturbances due to the large phase delay introduced by the fluid convective time-scales, but results demonstrate the potential for the aerodynamic control of membrane wings in outdoor flight using dielectric elastomers

On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

Viscoelastic effects in the aeromechanics of actuated elastomeric membrane wings

AbstractThis work is a numerical investigation on the influence of viscoelastic effects on the aerodynamics of integrally actuated membrane wings. For that purpose, a high-fidelity electro-aeromechanical computational model of wings made of dielectric elastomers has been developed. The structural model is based on a geometrically non-linear description and a non-linear electro-viscoelastic constitutive material law. It is implicitly coupled with a fluid solver based on a finite-volume discretisation of the unsteady Navier–Stokes equations. The resulting framework is used for the evaluation of the dynamics of passive and integrally actuated membrane wings at low Reynolds numbers under hyperelastic and viscoelastic assumptions on the constitutive model. Numerical simulations show that the damping introduced by viscoelastic stresses can significantly reduce the amplitude of membrane oscillations and modify key features in the coupled system dynamics. The estimated wing performance metrics are in good agreement with previous experimental observations and demonstrate the need of including rate-dependent effects to correctly capture the coupled system dynamics, in particular, for highly compliant membranes

Reduced-order modelling and feedback control of integrally actuated membrane wings

This paper presents a numerical investigation on aerodynamic control of integrally-actuated membrane wings made of dielectric elastomers. They combine the advantages of membrane shape adaptability with the benefits of the simple, lightweight but high-authority control mechanism offered by integral actuation. For that purpose, high-fidelity numerical models have been developed to predict their performance. They include a fluid solver based on the direct numerical integration of the unsteady Navier-Stokes equations, an electromechanical constitutive material model and a non-linear three-dimensional membrane structural model. In addition, using the Eigensystem Realization Algorithm, it is obtained a very low order model description of the fully coupled aero-electromechanical system to aid the design of a simple PID control scheme for the feedback control of the wing. The resulting regulator is then implemented in the high-fidelity model and used for the mitigation of flow disturbances

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

'Candidatus Phytoplasma solani' interferes with the distribution and uptake of iron in tomato

Background: \u2018Candidatus Phytoplasma solani\u2019 is endemic in Europe and infects a wide range of weeds and cultivated plants. Phytoplasmas are prokaryotic plant pathogens that colonize the sieve elements of their host plant, causing severe alterations in phloem function and impairment of assimilate translocation. Typical symptoms of infected plants include yellowing of leaves or shoots, leaf curling, and general stunting, but the molecular mechanisms underlying most of the reported changes remain largely enigmatic. To infer a possible involvement of Fe in the host-phytoplasma interaction, we investigated the effects of \u2018Candidatus Phytoplasma solani\u2019 infection on tomato plants (Solanum lycopersicum cv. Micro-Tom) grown under different Fe regimes. Results: Both phytoplasma infection and Fe starvation led to the development of chlorotic leaves and altered thylakoid organization. In infected plants, Fe accumulated in phloem tissue, altering the local distribution of Fe. In infected plants, Fe starvation had additive effects on chlorophyll content and leaf chlorosis, suggesting that the two conditions affected the phenotypic readout via separate routes. To gain insights into the transcriptional response to phytoplasma infection, or Fe deficiency, transcriptome profiling was performed on midrib-enriched leaves. RNA-seq analysis revealed that both stress conditions altered the expression of a large (> 800) subset of common genes involved in photosynthetic light reactions, porphyrin / chlorophyll metabolism, and in flowering control. In Fe-deficient plants, phytoplasma infection perturbed the Fe deficiency response in roots, possibly by interference with the synthesis or transport of a promotive signal transmitted from the leaves to the roots. Conclusions: \u2018Candidatus Phytoplasma solani\u2019 infection changes the Fe distribution in tomato leaves, affects the photosynthetic machinery and perturbs the orchestration of root-mediated transport processes by compromising shoot-to-root communication