Flutter Suppression of a Heated Panel in Supersonic Airflow Using Energy Harvesters

Heated curved panels flutter in supersonic air flow will affect fatigue life and flight performance of aircrafts, thus the research on heated curved panels flutter was an important problem in flight design. A nonlinear aero-elastic partial differential equation for two-dimensional heated curved panels in supersonic flow was established based on the von-Karman nonlinear strain-displacement relation and aerodynamic force model of supersonic flow, which was described by improved piston theory. The aero-elastic partial differential equation was derived to a four-dimensional ordinary differential equation system by using second order Galerkin discretization method. The algebraic criterion of the Hopf bifurcation was utilized in the equation system to derive the Hopf bifurcation point of the system (also the flutter critical value).Therefore, analytical expressions of flutter critical dynamic pressure and vibration frequency were theoretically derived. Then, a numerical experiment was established, and the agreement of numerical result and theoretical value was validated. The result showed that flutter dynamic pressure decreased and then increased with initial curvature rising. For small curvature panel, flutter dynamic pressure also first decreased and then increased with temperature rising, while for large curvature panel flutter dynamic pressure always increased with temperature rising. The established equation system and analytical expression of Hopf bifurcation point can provide some guidance for heated curved panel in supersonic air flow.

Time-sharing orbit jump and energy harvesting in nonlinear piezoelectric energy harvesters using a synchronous switch circuit

The nonlinear energy harvester has become a hot topic due to its broad bandwidth and lower resonant frequency. Based on the preliminary test and analyses in our previous work, further analyses and tests on the influence of parameters, including the nonlinear magnetic force of the hybrid energy harvesting structure on its output performance under harmonic excitation, are performed in this paper, which will provide powerful support for structural optimization. For designing a nonlinear piezoelectric-electromagnetic hybrid energy harvester, the state equation of electromechanical coupling, the harmonic response and average output power, voltage, and current of a nonlinear hybrid energy harvester under harmonic excitation are derived by the harmonic balance method. The effects of the excitation acceleration and the external load on the output performance of the nonlinear hybrid energy harvester are verified through experimental tests. The results showed that the output power of the nonlinear hybrid energy harvester increases with the increase in the acceleration of harmonic excitation, and the increase is affected by external load. When the piezoelectric-electromagnetic hybrid harvester operates at the optimal load and the resonant frequency, the average output power reaches its maximum value and the increase of the load of the piezoelectric unit makes the resonant frequency of the energy harvesting system increase. Compared with linear harvesting structures, the nonlinear hybrid harvester has better flexibility of environmental adaptability and is more suitable for harvesting energy in low-frequency environments.

In this paper, we design and experimentally validate a new auxetic nonlinear piezoelectric energy harvester for broad working bandwidth and high power output, which combines a clamped-clamped beam with multiple rotating square unit cells. On one hand, the key structural parameter of the square rotating unit cell is adjusted to obtain desired broad working bandwidth. On the other hand, the number of the unit cells is increased to improve the power output of the energy harvester with minor influence on the working bandwidth. Therefore, based on the parameter adjustment and unit cell number increment, the proposed energy harvester can obtain both broad working bandwidth and high power output, which can solve the trade-off between these two aspects in previous auxetic nonlinear energy harvesters. Finite element analysis is performed to analyse the characteristics of the energy harvester. The lumped parameter model is utilized to predict the performance of the energy harvester, which matches well with the experimental results. In the experimental validation, under 0.3g base acceleration, the working bandwidth and power output of the auxetic nonlinear energy harvester are increased by 14% and 268%, respectively, compared with the conventional nonlinear energy harvester.

Multi-solution phenomena and nonlinear characteristics of tristable galloping energy harvesters with magnetic coupling nonlinearity

Over the past decade, there has been special interest in developing nonlinear energy harvesters capable of operating over a wideband frequency spectrum. Chief among the nonlinear energy harvesting techniques is magnetic levitation–based energy harvesting. Nonetheless, current nonlinear magnetic levitation–based energy harvesting approaches encapsulate design challenges. This work investigates some of the design issues and limitations faced by traditional magnetic levitation–based energy harvesters such as damping schemes and stiffness nonlinearities. Both experiment and model are used to quantify and evaluate damping regimes and stiffness nonlinearities present in magnetic levitation–based energy harvesters. Results show that dry friction, mostly ignored in magnetic levitation–based energy harvesting literature, contributes to the overall energy dissipation. Measured and modeled magnetic forces–displacement curves suggest that stiffness nonlinearities are weak over moderate distances. An enhanced design utilizing a combination of mechanical and magnetic springs is introduced to overcome some of these limitations. A non-dimensional model of the proposed design is developed and used to investigate the enhanced architecture. The unique potential energy profile suggests that the proposed nonlinear energy harvester outperforms the linear version by steepening the displacement response and shifting the resonance frequency, resulting in a larger bandwidth for which power can be harvested.

Harmonic balance analysis of nonlinear tristable energy harvesters for performance enhancement

Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems

This paper reports electromagnetically transduced multistable non-linear vibrational energy harvesters to exploit the combined dynamical effects of monostable and bistable non-linear potential energies in a single system, by utilizing the stretching of specially designed cascaded tapered spring topology along with repulsive magnetic levitation. Using comprehensive (analytical and numerical) simulations and experimental validations, we reveal the signature of coupling and its key characteristics present in multimodal non-linear wideband energy harvesters. Here, a dynamical root-tracking technique is employed to trace stable, unstable, and hidden solution branches systematically, which enables predictive configuring of physical experimental parameters to realize previously inaccessible high response dynamical regimes along with a higher normalized power integral density metric. Thus, by tuning the powerful interplay between the numerical continuation framework and available physical parameters, we offer a robust technique for optimizing design and output performances in all such types of energy harvesting systems (independent of the scale and transduction) for their enhanced figure of merit.

Vibration energy harvesting devices have shown potential applications to power many devices such as electronic self-sustainable units. Most traditional linear energy harvesters exploit the phenomenon of resonance to produce electric power. Nonlinear energy harvesters, however, present more interesting alternatives and there is potential for them to work well over relatively wider bandwidths due to characteristics such as bifurcation. The aim of this study is to introduce an alternative design to a nonlinear electromagnetic energy harvesting device to improve the power production of the unit. The configuration presented in the following work has demonstrated higher power efficiency over a wider range of frequencies compared to the previous design. The numerical power outputs for both designs are compared and validated against their experimental values. Finally, the validated numerical model is used to find the optimal design to produce the maximum power for the unit.

A nonlinear aeroelastic model for a two-dimensional heated curved panel in supersonic air flow is established by using Galerkin method. The von Karman large deflection theory and the third-order piston theory appended with the static aerodynamic loading are used in the governing equations. The static aero-thermal deflection of the curved panel is firstly obtained by using Newton iterative approach. Then the stability boundary under different temperature elevations is achieved by using Lyapunov’s indirect method. Lastly, the motion equations of a heated curved panel in supersonic air flow are solved by a fourth-order Runge–Kutta numerical scheme. Time history responses, phase plots, Poincare maps and bifurcation diagrams are used for better understanding of the pre/post-flutter responses of a curved panel by varying parameters, including curvatures, dynamic pressures and temperature elevations. The results demonstrate that the flutter boundary drops significantly with increasing temperature elevation for panels with small curvatures. However, the flutter boundary almost keeps the same for panels with large curvatures. The nonlinear flutter characteristics of the curved panel differs from those of flat panels significantly, the nonlinear flutter response of heated curved panels changes from static equilibrium point or LCO to chaos with the increase of temperature elevation or dynamic pressure and the static, LCO motions also exist in the chaotic area. For panels with large curvatures, the chaotic motions cannot occur, and the amplitude of LCO is limited in a certain range.

The vibrations of mechanical systems and structures are often a combination of periodic and random motions. Emerging interest to exploit nonlinearities in vibration energy harvesting systems for charging microelectronics may be challenged by such reality due to the potential to transition between favorable and unfavorable dynamic regimes for DC power delivery. Therefore, a need exists to devise an optimization method whereby charging power from nonlinear energy harvesters remains maximized when excitation conditions are neither purely harmonic nor purely random, which have been the attention of past research. This study meets the need by building from an analytical approach that characterizes the dynamic response of nonlinear energy harvesting platforms subjected to combined harmonic and stochastic base accelerations. Here, analytical expressions are formulated and validated to optimize charging power while the influences of the relative proportions of excitation types are concurrently assessed. It is found that about a 2 times deviation in optimal resistive loads can reduce the charging power by 20% when the system is more prominently driven by harmonic base accelerations, whereas a greater proportion of stochastic excitation results in a 11% reduction in power for the same resistance deviation. In addition, the results reveal that when the frequency of a predominantly harmonic excitation deviates by 50% from optimal conditions the charging power reduces by 70%, whereas the same frequency deviation for a more stochastically dominated excitation reduce total DC power by only 20%. These results underscore the need for maximizing direct current power delivery for nonlinear energy harvesting systems in practical operating environments.

This study optimizes a linkage-based spring-damped vibration harvester to investigate snap-through dynamics in nonlinear energy harvesting. A Scotch yoke mechanism applies sinusoidal excitation, inducing nonlinear behaviour, while a generator and flywheel integrated at the linkage enable energy conversion. The Euler-Lagrange method establishes governing equations, and stable equilibria are identified via minimum potential energy analysis. Angular displacement responses and phase portraits reveal transitions from small-amplitude periodic to large-amplitude multi-periodic and chaotic motions. Numerical simulations demonstrate stable cross-well oscillations within 4–8 rad/s, with optimal voltage (0–3 V) and power (0–0.2 W) achieved at ω=5.0rad/s. These results highlight the critical role of frequency-dependent snap-through dynamics in enhancing energy harvesting efficiency, providing theoretical guidance for designing nonlinear vibration energy harvesters.

An enhanced nonlinear piezoelectric energy harvester with multiple rotating square unit cells

Harvesting energy from mechanical vibrations via nonlinear energy harvesters has been considered as an effective approach for permanently powering embedded devices and sensors. Many previous studies focused on nonlinear piezoelectric energy harvesters based on cantilever beam structures. This paper presents a novel bistable electromagnetic energy harvester (BEEH) with several permanent magnets (PMs). The bistability is achieved by designing the interaction between magnetic repulsive and attractive forces. The shape of potential wells can be changed by adjusting the distance among the PMs. The theoretical model of the BEEH is established and the analytical solutions are obtained by using the harmonic balance method. The effects of the excitation frequency, excitation amplitude, resistance and shape of potential wells on the energy harvesting performance of the BEEH are investigated numerically and experimentally. The results show that the proposed BEEH has a wide operating bandwidth and high energy harvesting efficiency. The output power can reach up to 28 mW, which is able to power up some low-power consumption devices.