INTEGRABILITY THEOREMS FOR FOURIER-JACOBI TRANSFORMS

Abstract. In this paper, we prove the Hardy-Littlewood-Paley inequality for the generalized Fourier transform on Chébli-Trimèche hypergroups and we study in the particular case of the Jacobi hypergroup the integrability of this transform on Besov-type spaces

Incident flow effects on the performance of piezoelectric energy harvesters from galloping vibrations

AbstractIn this paper, we investigate experimentally the concept of energy harvesting from galloping oscillations with a focus on wake and turbulence effects. The harvester is composed of a unimorph piezoelectric cantilever beam with a square cross-section tip mass. In one case, the harvester is placed in the wake of another galloping harvester with the objective of determining the wake effects on the response of the harvester. In the second case, meshes were placed upstream of the harvester with the objective of investigating the effects of upstream turbulence on the response of the harvester. The results show that both wake effects and upstream turbulence significantly affect the response of the harvester. Depending on the spacing between the two squares and the opening size of the mesh, wake and upstream turbulence can positively enhance the level of the harvested power

Effective design of vibro-impact energy harvesting absorbers with asymmetric stoppers

An investigation is carried out for the purpose of simultaneously controlling a base-excited dynamical system and enhancing the effectiveness of a piezoelectric energy harvesting absorber. Amplitude absorbers are included to improve the energy harvested by the absorber with the possibility of activating broadband resonant regions to increase the operable range of the absorber. This study optimizes the stoppers’ ability for the energy harvesting absorber to generate energy by investigating asymmetric gap and stiffness configurations. Medium stiffnesses of $$5\times {10}^{4}\, {\text {N/m}}$$ and $$1\times {10}^{5}\, {\text {N/m}}$$ show significant impact on the primary system’s dynamics and improvement in the level of the harvested power for the absorber. A solo stopper configuration when the gap distance is $$0.02\, {\text {m}}$$ improves 29% in peak power and 9% in average power over the symmetrical case. Additionally, an asymmetric stiffness configuration when one of the stiffnesses is $$1\times {10}^{5}\, {\text {N/m}}$$ and a gap size of $$0.02\, {\text {m}}$$ indicates an improvement of 25% and 8% for peak and average harvested power, respectively, and the second stopper’s stiffness is $$5\times {10}^{3}\, {\text {N/m}}$$. Hard stopper configurations shows improvements with both asymmetric cases, but not enough improvements to outperform the system without amplitude stoppers

Investigations on the stability and effectiveness of wing-based piezoaeroelastic systems with combined nonlinearities

An investigation on the effects of the existence of freeplay, polynomial stiffness and aerodynamic nonlinearities on the dynamical responses of flutter-based piezoaeroelastic energy harvesting systems is performed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived including structural and aerodynamic nonlinearities, namely stall effects. The aerodynamic loading used in this study is the unsteady representation, based on the Duhamel formulation. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay combined with structural hardening nonlinearities before and after the linear onset of flutter. Such nonlinearities must be considered in the modeling and design of piezoaeroelastic energy harvesters, the combination of it can result in the presence of several secondary bifurcations and multiple solution regions and, therefore, affect the overall efficiency of the system. It is shown that the existence of freeplay nonlinearity leads to the possibility of harvesting energy at lower speeds than the linear onset speed of instability. As the gap size of the freeplay nonlinearity increases, the polynomial quadratic term in structural nonlinearity minimally affects the performance of the energy harvester. Further, it is shown that the stall effect should be considered when the angle of attack is higher than 2$$^{\circ }$$ which significantly affect the higher Hopf bifurcations in the pitch degree of freedom

Insights on the Effects of Magnetic Forces on the Efficiency of Vibration Energy Harvesting Absorbers in Controlling Dynamical Systems

This study investigates the effects of magnetic constraints on a piezoelectric energy harvesting absorber while simultaneously controlling a primary structure and harnessing energy. An accurate forcing representation of the magnetic force is investigated and developed. A reduced-order model is derived using the Euler–Lagrange principle, and the impact of the magnetic force is evaluated on the absorber’s static position and coupled natural frequency of the energy harvesting absorber and the coupled primary absorber system. The results show that attractive magnet configurations cannot improve the system substantially before pull-in occurs. A rigorous eigenvalue problem analysis is performed on the absorber’s substrate thickness and tip mass to effectively design an energy harvesting absorber for multiple initial gap sizes for the repulsive configurations. Then, the effects of the forcing amplitude on the primary structure absorber are studied and characterized by determining an effective design of the system for a simultaneous reduction in the primary structure’s motion and improvement in the harvester’s efficiency

High-Fidelity Modeling and Investigation on Blade Shape and Twist Angle Effects on the Efficiency of Small-Scale Wind Turbines

A high-fidelity analysis is carried out in order to evaluate the effects of blade shape, airfoil cross-section. as well as twist angle distribution on the yielded torque and generated power of a horizontal axis Small-Scale Wind Turbine (SSWT). A computational modeling and an effective design for a small turbine with a blade length of 25 cm subject to a 4 m/s freestream velocity are presented, in which a segregated RANS solver is utilized. Four airfoil profiles are assessed, namely NACA0012, NACA0015, NACA4412, and NACA4415, and two blade shape configurations, rectangular and tapered, are evaluated. The flow around the rotating turbines is investigated along with blade stresses and performance output for each configuration. Subsequently, the impact of various linear and nonlinear twist distributions on SSWT efficiency is also examined. Results show that for the studied operating conditions corresponding to low-speed flows, the rectangular blade configuration outperforms the tapered blade shape from the generated torque and power perspectives, while the tapered shape configuration represents an attractive design choice from the yielded stresses point of view. Additionally, while the nonlinear twist configuration results in the best performance among the configurations studied, an SSWT blade design implementing a linear twist distribution can be highly competitive provided that a good slope is carefully selected

Modeling and Design Enhancement of Electrothermal Actuators for Microgripping Applications

Microgrippers are miniature tools that have the capability to handle and manipulate micro- and nano-scale objects. The present work demonstrates the potential impact of the incorporation of perforations on a ‘hot and cold arm’ electrothermal actuation mechanism in order to improve the operation of microgrippers in terms of arm opening and operating temperature. By applying a voltage to one arm and setting the other as a ground, the current passes through the electrothermal actuator and induces its displacement along the in-plane direction. The difference in the geometry of the two arms causes one arm to expand more than the other and this results in transverse bending. A computational model was developed using a finite element analysis tool to simulate the response of the thermal actuators with varying geometries and investigate the impact of incorporating perforations on the arms of the thermal actuators to enhance its performance in terms of deflection and operating temperature. The simulation results were compared to their experimental counterparts reported in the literature. A good agreement between the numerical and experimental data was obtained. A novel design of a microgripper, made of perforated electrothermal actuators, was introduced. Its main characteristics, including the tip opening of the gripper arms, the applied voltage, and the stress and temperature distributions, were analyzed using the developed computational model. Different perforation shape and distribution were investigated. The present study demonstrates the capability of perforations to enhance the operation of microgrippers as manifested by the obtained higher tip displacement and lower tip temperature in comparison to conventional microgripper designs made of non-perforated thermal actuators. Furthermore, the highest stress generated on the microgripper elements was found to be much lower than the yield strength of the constituent material, which indicates proper functioning without any mechanical failure

Role of Active Morphing in the Aerodynamic Performance of Flapping Wings in Formation Flight

Migratory birds have the ability to save energy during flight by arranging themselves in a V-formation. This arrangement enables an increase in the overall efficiency of the group because the wake vortices shed by each of the birds provide additional lift and thrust to every member. Therefore, the aerodynamic advantages of such a flight arrangement can be exploited in the design process of micro air vehicles. One significant difference when comparing the anatomy of birds to the design of most micro air vehicles is that bird wings are not completely rigid. Birds have the ability to actively morph their wings during the flapping cycle. Given these aspects of avian flight, the objective of this work is to incorporate active bending and torsion into multiple pairs of flapping wings arranged in a V-formation and to investigate their aerodynamic behavior using the unsteady vortex lattice method. To do so, the first two bending and torsional mode shapes of a cantilever beam are considered and the aerodynamic characteristics of morphed wings for a range of V-formation angles, while changing the group size in order to determine the optimal configuration that results in maximum propulsive efficiency, are examined. The aerodynamic simulator incorporating the prescribed morphing is qualitatively verified using experimental data taken from trained kestrel flights. The simulation results demonstrate that coupled bending and twisting of the first mode shape yields the highest propulsive efficiency over a range of formation angles. Furthermore, the optimal configuration in terms of propulsive efficiency is found to be a five-body V-formation incorporating coupled bending and twisting of the first mode at a formation angle of 140 degrees. These results indicate the potential improvement in the aerodynamic performance of the formation flight when introducing active morphing and bioinspiration

On the Aerodynamic Analysis and Conceptual Design of Bioinspired Multi-Flapping-Wing Drones

Many research studies have investigated the characteristics of bird flights as a source of bioinspiration for the design of flapping-wing micro air vehicles. However, to the best of the authors’ knowledge, no drone design targeted the exploitation of the aerodynamic benefits associated with avian group formation flight. Therefore, in this work, a conceptual design of a novel multi-flapping-wing drone that incorporates multiple pairs of wings arranged in a V-shape is proposed in order to simultaneously increase the propulsive efficiency and achieve superior performance. First, a mission plan is established, and a weight estimation is conducted for both 3-member and 5-member configurations of the proposed air vehicle. Several wing shapes and airfoils are considered, and aerodynamic simulations are conducted, to determine the optimal planform, airfoil, formation angle, and angle of attack. The simulation results reveal that the proposed bioinspired design can achieve a propulsive efficiency of 73.8%. A stability analysis and tail sizing procedure are performed for both 3-member and 5-member configurations. In addition, multiple flapping mechanisms are inspected for implementation in the proposed designs. Finally, the completed prototypes’ models of the proposed multi-flapping-wing air vehicles are presented, and their features are discussed. The aim of this research is to provide a framework for the conceptual design of bioinspired multi-flapping-wing drones and to demonstrate the sizing, weight estimation, and design procedures for this new type of air vehicles. This work establishes the first multi-flapping-wing drone design which exploits the aerodynamic features of the V-formation flight observed in birds to achieve superior performance in terms of payload and endurance

Nonlinear Analysis and Bifurcation Characteristics of Whirl Flutter in Unmanned Aerial Systems

Aerial drones have improved significantly over the recent decades with stronger and smaller motors, more powerful propellers, and overall optimization of systems. These improvements have consequently increased top speeds and improved a variety of performance aspects, along with introducing new structural challenges, such as whirl flutter. Whirl flutter is an aeroelastic instability that can be affected by structural or aerodynamic nonlinearities. This instability may affect the prediction of potentially dangerous behaviors. In this work, a nonlinear reduced-order model for a nacelle-rotor system, considering quasi-steady aerodynamics, is implemented. First, a parametric study for the linear system is performed to determine the main aerodynamic and structural characteristics that affect the onset of instability. Multiple polynomial nonlinearities in the two degrees of freedom nacelle-rotor model are tested to simulate possible structural nonlinear effects including symmetric cubic hardening nonlinearities for the pitch and yaw degrees of freedom; purely yaw nonlinearity; purely pitch nonlinearity; and a combination of quadratic, cubic, and fifth-order nonlinearities for both degrees of freedom. Results show that the presence of hardening structural nonlinearities introduces limit cycle oscillations to the system in the post-flutter regime. Moreover, it is demonstrated that the inclusion of quadratic nonlinearity introduces asymmetric oscillations and subcritical behavior, where large and potentially dangerous deformations can be reached before the predicted linear flutter speed