Harmonic Actuation Research Articles

Active Vibration Suppression of Lift-Offset Coaxial Rotorcraft Using Multicyclic Control

This study explores the best vibration reduction method using a multicyclic controller with an individual blade control (IBC) actuation scheme for a lift-offset coaxial helicopter during high-speed flight. The rotorcraft dynamics model consists of coaxial three-bladed counter-rotating rotors and a finite element fuselage stick model constructed based on the measured data of the XH-59A helicopter. The two-way coupled rotor–body vibration analysis results exhibited excellent correlation with the test data for the rotor hub loads and airframe vibrations. The best actuation scenarios are sought for the minimum vibration of the vehicle using either an open- or closed-loop control scheme. IBC actuation is shown to effectively reduce the vibrations of the rotorcraft. Coreduction of the three per rotor revolution (3P) and 6P vibrations of the rotorcraft is achieved using multicyclic control with offline system identification. Multicyclic harmonic IBC actuation enables the suppression of rotorcraft vibration at the rotor hub and pilot seat by 81.4%, and 3P cockpit vibration by 92% compared with the uncontrolled case, leading to a significantly reduced vibration level (below 0.05g) of the rotorcraft. The closed-loop multicyclic control using the identified system and aircraft model shows good correlation, ensuring the suitability of the present optimal control simulations.

Underwater dynamic modeling and experiments of flexible structure with harmonic actuation of macro fiber composites

Flexible structures driven by smart actuators are promising alternatives for aquatic bionic propulsion vehicles. However, the hydrodynamic effects induced by viscous fluids on the dynamic response of flexible structures remain an ongoing challenge. Thus, this article presents a fluid-structure interaction dynamic model of a flexible underwater structure actuated by macro fiber composite actuators, and the underwater multimodal vibration characteristics are studied. The model is based on the extended Hamilton’s principle, which considers the effects of hydrodynamic forces. The segmented mode shape functions of the flexible structure are derived using the assumed mode method. The study shows that the first two mode shapes of the beam predicted by the model agrees with the experimental results. The underwater dynamic responses of the flexible structure in a board band covering the first two resonance frequencies are also investigated at different actuation levels. The underwater results indicate that the first two resonance frequencies are 1.05 and 6.1 Hz respectively, basically consistent with the simulation ones (1.07 and 6.61 Hz). Correspondingly, the maximum transverse deflections at the end of the beam are 4.81 and 1.31 mm respectively, which are slightly lower than the predicted values of 5.75 and 1.62 mm. Therefore, the validity of the proposed coupled dynamic model is verified, which can be utilized to predict the multimodal dynamic responses of underwater flexible structures actuated by MFC or other smart actuators.

Rotor Power Savings and Pitch-Link Load Reductions with Spanwise-Varying Active Camber Morphing

The effect of spanwise-varying active-camber morphing on helicopter rotor power and pitch-link loads was investigated computationally for advance ratios ranging from hovering to high-speed forward flight (μ=0.35) and was compared to results obtained with spanwise uniform camber actuation. Different actuation strategies were applied, such as constant (0P) deflection and superimposed harmonic actuation based on a 0P deflection combined with 1P (one per revolution) and 2P harmonics. A comprehensive rotor aeromechanics model of an isolated Bo-105 rotor, including elastic blade modeling and free vortex wake aerodynamics, was used for this analysis. Two different active-camber section sizes were investigated, one ranging from 0.22R to 0.9R and one from 0.5R to 0.9R. The greatest benefits from active-camber actuation were found in hover and high-speed flight. It was possible to reduce both the rotor power consumption and the peak-to-peak pitch-link loads. A relevant contribution of the spanwise variability to these power gains was obtained in hovering flight. Toward higher flight speeds, the effect of spanwise variable camber morphing became less important in terms of rotor power savings. However, it allowed a notable reduction of the actuation amplitude far outboard on the rotor blade.

Numerical and experimental investigation of the in-phase and out-phase plasma actuation effects on the wake flow for Re = 1000

The aim is to characterize the role of symmetry pattern on the flow control induced by dielectric barrier discharge plasma actuators. Two DBD actuators are employed for in-phase excitation with duty cycle 50% leading to symmetric wake pattern and out-phase excitation for two pulsing frequencies St=0.2 and St=1 at Re=1000 which forms quasi-symmetric and asymmetric flow structures respectively. The modes deduced from POD and DMD methods represent the competition between symmetric (S) and asymmetric mode (K) in all cases. The harmonic in-phase plasma actuation with 50% duty cycle is the most effective flow control method with lowest power consumption. The harmonic out-phase excitation is not much effective; however adjustment of the actuator position can form the symmetric pattern with minimum power consumption. The superharmonic out-phase plasma actuation reduces the wake region however is not effective in lift reduction significantly and consumes high amount of energy. This indicates that phase difference and plasma location influence on the size and symmetry of the vortical structure. Then, based on the symmetry properties of the designed wake pattern created by frequency and phase difference of the plasma actuator, the effective active flow control can be performed. The numerical results are validated with experiments.

Generation of phononic high-order sidebands via intra- and inter-mode couplings in interconnected electromechanical resonators

To efficiently manipulate parametric mode mixing is an intriguing physical issue for phonon-cavity electromechanics, which is also crucial for various technological applications ranging from frequency synthesis to nonlinear spectroscopy. Here, we theoretically investigate the dependence of phononic high-order sidebands on intra- and inter-mode couplings in two interconnected electromechanical resonators. When the system operates in a strong inter-mode coupling regime, we report that two inter-mode phonon-scattering pathways allow us to selectively obtain either odd- or even-order sidebands at different output ports. The signal intensities of the separated sidebands can be independently modulated by introducing harmonic actuation forces acting on the interconnected resonators. Once the intra-mode coupling becomes totally dominant, the direct transition between intra-mode phonons only triggers the emergence of full-order sidebands in the nonlinear responses. In this case, increasing the quality factor of the resonators is beneficial for amplifying a few low order sidebands nearby the principal modes of the resonators but sacrificing the order of the sidebands.

Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements

In the presented work, a model of a microelectromechanical accelerometer with two microbeam sensing elements located between two fixed electrodes is proposed. The action of the inertia forces in the longitudinal direction affects the spectral properties of the system. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of in-phase and anti-phase oscillations with small changes in the applied acceleration. Diagrams of equilibrium positions are obtained varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is concluded that the amplitude sensitivity of the proposed sensor is orders of magnitude higher than frequency shift sensitivity. Peculiarities of the sensor nonlinear dynamics is investigated in case of external harmonic electrostatic actuation. Principal difference in the characteristics of mode localization phenomenon is revealed between the linearized model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear effects.

High Dynamic Range Nanowire Resonators.

Dynamic range quantifies the linear operation regime available in nanomechanical resonators. Nonlinearities dominate the response of flexural beams in the limit of very high aspect ratio and very small diameter, which leads to expectation of low dynamic range for nanowire resonators in general. However, the highest achievable dynamic range for nanowire resonators with practical dimensions remains to be determined. We report dynamic range measurements on singly clamped silicon nanowire resonators reaching remarkably high values of up to 90 dB obtained with a simple harmonic actuation scheme. We explain these measurements by a comprehensive theoretical examination of dynamic range in singly clamped flexural beams including the effect of tapering, a usual feature of semiconductor nanowires. Our analysis reveals the nanowire characteristics required for broad linear operation, and given the relationship between dynamic range and mass sensing performance, it also enables analytical determination of mass detection limits, reaching atomic-scale resolution for feasible nanowires.

Optical coherence elastography of bilayer soft tissue based on harmonic surface wave spectroscopy

Diseases often initiate from a certain layer of the biological tissue, thus simultaneous measurement of the elastic modulus of each layer is important for early diagnosis and treatment of various diseases. A surface wave spectroscopy (SWS) optical coherence elastography (OCE) technique based on harmonic wave excitation was proposed. An actuator consisting of a piezoelectric stack with a pin was designed to generate harmonic surface waves. A B-mode OCT data acquisition and phase analysis method was proposed to image the wave forms, and calculate the surface wave velocity. By exciting the sample with different frequencies, the surface wave dispersion curves were obtained. A total variation (TV) regularization iterative algorithm was proposed to obtain the elastic modulus distribution along the depth. Effectiveness of the proposed method was evaluated by both finite element simulation and experimental measurement of a bi-layer phantom. The mechanically driven harmonic wave actuation based OCE method is simple and cost-effective in experimental setup. Based on B-mode OCT scans, data analysis can be very fast, which is possible to realize real-time elastography imaging. This study provides an effective method for biomechanical properties study of layered tissue.

Active Flow Control Utilizing an Adaptive Blade Geometry and an Extremum Seeking Algorithm at Periodically Transient Boundary Conditions

Abstract As a consequence of constant volume combustion in gas turbines, pressure waves propagating upstream the main flow into the compressor system are generated leading to incidence variations. Numerical and experimental investigations of stator vanes have shown that active flow control (AFC) by means of adaptive blade geometries is beneficial when such periodic incidence variations occur. A significant risk reduction in a compressor facing disturbances can thereby be achieved concerning stall or choke. Experimental investigations on such an AFC method with simultaneous application of a closed-loop control are missing in order to demonstrate its potential. This work investigates a linear compressor cascade that is equipped with a 3D-manufactured piezo-adaptive blade structure. The utilized actuators are piezoelectric macro-fiber-composites. A throttling device is positioned downstream the trailing edge plane to emulate an unsteady combustion process. Periodic transient throttling events with a frequency of up to 20 Hz cause incidence changes to the blade’s leading edge. Consequently, pressure fluctuations on the blade’s surface occur, having a significant impact on the pressure recovery downstream of the stator cascade. Experimental results of harmonically actuating the piezo-adaptive blade with the corresponding disturbance frequency show that the impact of disturbances can be reduced to approximately 50%. However, this is only effective if the phase shift of the harmonic actuation is adjusted correctly. Using an inadequate phase shift reverses the positive effects, causing the aforementioned stall, choke, or significant losses. In order to find the optimum phase shift, even under varying, possibly unpredictable operating conditions, an extremum seeking controller is presented. This gradient-based approach is minimizing the pressure variance over time by carefully adjusting the phase shift of the harmonic actuation of the AFC system.

Micro thrust measurement experiment and pressure field evolution of bionic robotic fish with harmonic actuation of macro fiber composites

The design and realization of underwater bionic robots actuated by smart materials have attracted growing attention in recent years. The experimental acquisition of the dynamic thrust force is crucial for the development of underwater robots. A simple micro thrust measurement system based on a decoupled lever mechanism is designed for a macro fiber composite (MFC)-actuated bionic robotic fish. The pressure field distribution and evolution associated with the thrust variation induced by the oscillating caudal fin of the robotic fish are visualized using computational fluid dynamics (CFD) technologies. A miniature MFC-actuated robotic fish that mimics the koi fish is designed. A simple decoupled lever mechanism with excellent linearity, high precision and resolution, and the ability to minimize the interference from the lateral force is proposed. Calibration results indicate that the output sensitivity of the designed measurement apparatus is 5.48 mN/V. The dynamic variations in the micro thrust generated by the robotic fish at different actuation levels are effectively captured using the proposed measurement system. Experimental results show that the MFC-actuated robotic fish obtains a maximum mean thrust of −2.95 mN in the case of the greatest tip oscillating velocity, which is consistent with Lighthill’s elongated-body theory. Moreover, for the robotic fish, the maximum instant thrust grows with an increase in the oscillating frequency. The maximum instant drag first decreases, and then increases as the actuation frequency increases. It reaches its minimum value of 0.37 mN in the case of the maximum oscillating velocity. In contrast, the variation behavior of the thrust pattern/oscillating period is the reverse to that of the maximum instant drag, and it obtains a maximum of 85.7%. The propulsion performance indexes of the robotic fish in the CFD simulations match those of experimental results for different oscillating cases. Furthermore, the distribution and evolution mechanisms of the steady pressure fields around the oscillating robotic fish are revealed. The CFD simulations demonstrate that the variations in the instant thrust could be fully determined by the distributions and intensities of the concentrated pressure regions induced by the oscillating caudal fin. The cycle-averaged velocity fields around the caudal fin are closely related to the mean thrust generated by the MFC-actuated robotic fish. Accordingly, these results may be helpful in the development of underwater bionic robots actuated by smart actuators.

Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation

• Nonlinear dynamics, vibration and stability analysis of cylindrical nanoshell resonator is studied. • Electro-elastic Gurtin–Murdoch surface/interface theory with von-Karman–Donnell's shell model are used. • The effects of different parameters on nonlinear frequency response and stability analysis are investigated. • Effects of electrostatic and harmonic excitation on nonlinear frequency response and stability analysis are studied. In this paper, nonlinear dynamics, vibration and stability analysis of piezo-visco medium nanoshell resonator (PVM-NSR) based on functionally graded (FG) cylindrical nanoshell integrated with two piezoelectric layers subjected to visco-pasternak medium, electrostatic and harmonic excitations is investigated. Nonclassical method of the electro-elastic Gurtin–Murdoch surface/interface theory with von-Karman–Donnell's shell model as well as Hamilton's principle, the assumed mode method combined with Lagrange–Euler's are considered. Complex averaging method combined with arc-length continuation is used to achieve a numerical solution for the steady state vibrations of the system. The stability analysis of the steady state response is performed. The parametric studies such as the effects of different boundary conditions, different geometric ratios, structural parameters, electrostatic and harmonic excitation on the nonlinear frequency response and stability analysis are studied. The results indicate that near the natural frequency of the nanoshell, it will lead to resonance and will have large motion amplitude and near the resonant frequency, the nanoshell shows a softening type of nonlinear behavior, and the nanoshell bandwidth increases due to nonlinear factors. In this range, nanoshell has three different ranges of motion, of which two are stable and the other unstable, and so the jump phenomenon and saddle-node bifurcation are visible in the behavior of the system. Also piezoelectric voltage influences on static deformation and resonant frequency but has no significant effect on nonlinear behavior and bandwidth and also system very sensitive to the damping coefficient and due to decrease of nano shell stiffness, natural frequency decreases. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system's instability, nonlinear behavior and bandwidth.

Effects of van der Waals force on nonlinear vibration of electromechanical integrated electrostatic harmonic actuator

An electromechanical integrated electrostatic harmonic actuator is promising for the miniaturization of electromechanical devices. As the dimensions of the actuator decrease, the effects of the van der Waals force become obvious. In this study, by considering the nonlinearity of electrostatic and van der Waals forces, nonlinear vibration equations of the flexible ring of an electrostatic harmonic actuator are deduced. Using these equations, the nonlinear free vibration and nonlinear forced response of the actuator are investigated. The effects of the van der Waals force on the nonlinear vibration of the flexible ring are analyzed. Results show that these effects of the van der Waals force are relatively obvious under some conditions and should be considered.

Control of crossflow instability over a swept wing using dielectric-barrier-discharge plasma actuators

This paper investigates the potential use of dielectric-barrier-discharge (DBD) plasma actuators to control the crossflow instability of the boundary layer on a 45° swept NLF-0415 airfoil at −4∘ angle of attack.The disturbance evolution is resolved using nonlinear parabolized stability equations (NPSEs). Actuators are mounted near the leading edge and generate an electric wind perpendicular to the crossflow vortex axes. The spanwise distance between neighboring actuators is first set to be the fundamental wavelength of the unstable mode. This harmonic actuation reduces the disturbance energy only when the induced body force and the disturbance velocity have reverse sign. At certain different locations, the actuators can actually increase the disturbance energy. The robustness in laminar flow control is improved when two actuators per fundamental wavelength are used. This subharmonic actuation leads to reduction in the energy of the primary unstable mode independent of the actuator locations. Finally, the simulation without baseflow forcing reveals that harmonic modes play important roles in this subharmonic control.

Multiscale Functional Imaging of Interfaces through Atomic Force Microscopy Using Harmonic Mixing.

The spatial resolution of atomic force microscopy (AFM) needed to resolve material interfaces is limited by the tip-sample separation ( d) dependence of the force used to record an image. Here, we present a new multiscale functional imaging technique that allows for in situ tunable spatial resolution, which can be applied to a wide range of inhomogeneous materials, devices, and interfaces. Our approach uses a multifrequency method to generate a signal whose d-dependence is controlled by mixing harmonics of the cantilever's oscillation with a modulated force. The spatial resolution of the resulting image is determined by the signal's d-dependence. Our measurements using harmonic mixing (HM) show that we can change the d-dependence of a force signal to improve spatial resolution by up to a factor of two compared to conventional methods. We demonstrate the technique with both Kelvin probe force microscopy (KPFM) and bimodal AFM to show its generality. Bimodal AFM with harmonic mixing actuation separates conservative from dissipative forces and is used to identify the regions of adhesive residue on exfoliated graphene. Our electrostatic measurements with open-loop KPFM demonstrate that multiple force modulations may be applied at once. Further, this method can be applied to any tip-sample force that can be modulated, for example, electrostatic, magnetic, and photoinduced forces, showing its universality. Because HM enables in situ switching between high sensitivity and high spatial resolution with any periodic driving force, we foresee this technique as a critical advancement for multiscale functional imaging.

Electrostatically actuated encased cantilevers.

Background: Encased cantilevers are novel force sensors that overcome major limitations of liquid scanning probe microscopy. By trapping air inside an encasement around the cantilever, they provide low damping and maintain high resonance frequencies for exquisitely low tip–sample interaction forces even when immersed in a viscous fluid. Quantitative measurements of stiffness, energy dissipation and tip–sample interactions using dynamic force sensors remain challenging due to spurious resonances of the system.Results: We demonstrate for the first time electrostatic actuation with a built-in electrode. Solely actuating the cantilever results in a frequency response free of spurious peaks. We analyze static, harmonic, and sub-harmonic actuation modes. Sub-harmonic mode results in stable amplitudes unaffected by potential offsets or fluctuations of the electrical surface potential. We present a simple plate capacitor model to describe the electrostatic actuation. The predicted deflection and amplitudes match experimental results within a few percent. Consequently, target amplitudes can be set by the drive voltage without requiring calibration of optical lever sensitivity. Furthermore, the excitation bandwidth outperforms most other excitation methods.Conclusion: Compatible with any instrument using optical beam deflection detection electrostatic actuation in encased cantilevers combines ultra-low force noise with clean and stable excitation well-suited for quantitative measurements in liquid, compatible with air, or vacuum environments.

Detached-Eddy Simulations for Active Flow Control

The present study conducted improved delayed detached-eddy simulations of actively controlled flows with a harmonic actuation on a backward-facing step and pulsed blowing on a pitching airfoil for reattachment and separation controls. Spectra analyses based on the unexcited flowfield data were carried out by using dynamic mode decomposition to identify spatial structures corresponding to the different Strouhal frequencies. The characteristic physical modes have been extracted for both cases. With better understanding of unsteady flow features, effective control practices were illustrated. For the backward-facing step case, the optimal excitation frequency was found to be identical with the step-mode frequency of the baseline flow. Such harmonic actuation enhanced the pairing process, forming the largest-scale spanwise coherent structures in the free shear layer, resulting in a 40% maximum reduction of the bubble length. For the airfoil case, with the optimum excitation frequency determined by the vortex-shedding mode of the baseline flow, a 194% increase of the lift-to-drag ratio was obtained; the pulsed blowing with the jet orifices in an antiphased manner was found to be very effective to damp the fluctuations of the lift around its mean value, though it led to a small decrease in mean lift.

Molecular forces in electromechanical integrated electrostatic harmonic actuator

Authors invent an electromechanical integrated electrostatic harmonic actuator. It is more favorable for miniaturization of the electromechanical devices. As the dimensions of the actuator decreases, the effects of the Casimir and van der Waals forces become obvious. Here, effects of the molecular forces on the operating behavior of the actuator are investigated theoretically investigated by a parametric study. The equations of the radial displacements of the flexible ring and the output torque for the actuator are deduced for three different situations: only considering electrostatic force, considering electrostatic and van der Waals forces, and considering electrostatic and the Casimir forces. The effects of van der Waals or the Casimir force on the radial displacements of the flexible ring and the output torque for the actuator are analyzed. Results show that van der Waals or the Casimir forces has obvious effects on the output torque of the actuator for small structure dimension. The results are useful in theory and technique studies on further miniaturization of the actuator.

Optimal deployment schedule of an active twist rotor for performance enhancement and vibration reduction in high-speed flights

The best active twist schedules exploiting various waveform types are sought taking advantage of the global search algorithm for the reduction of hub vibration and/or power required of a rotor in high-speed conditions. The active twist schedules include two non-harmonic inputs formed based on segmented step functions as well as the simple harmonic waveform input. An advanced Particle Swarm assisted Genetic Algorithm (PSGA) is employed for the optimizer. A rotorcraft Computational Structural Dynamics (CSD) code CAMRAD II is used to perform the rotor aeromechanics analysis. A Computation Fluid Dynamics (CFD) code is coupled with CSD for verification and some physical insights. The PSGA optimization results are verified against the parameter sweep study performed using the harmonic actuation. The optimum twist schedules according to the performance and/or vibration reduction strategy are obtained and their optimization gains are compared between the actuation cases. A two-phase non-harmonic actuation schedule demonstrates the best outcome in decreasing the power required while a four-phase non-harmonic schedule results in the best vibration reduction as well as the simultaneous reductions in the power required and vibration. The mechanism of reduction to the performance gains is identified illustrating the section airloads, angle-of-attack distribution, and elastic twist deformation predicted by the present approaches.

Electro-mechanical response to the harmonic actuation of the pneumatically coupled dielectric elastomer based actuators with and without load

Pneumatically Coupled Dielectric Elastomer (PCDE) based actuators with air as an intervening medium, were developed. Fabrication of these actuators have been carried out using dielectric elastomer membrane on both sides of an insulating annular holder of diameter 10 mm. The membrane at the bottom side acts as an active membrane which consists of ultrathin metal electrode on it’s both sides, whereas top membrane acts as a passive membrane. Mechanical performance of PCDE actuators were studied using bulge test method. Initially, high voltage performance of both active and passive membranes with electric field strength upto 40 MV/m were characterized by sweeping the frequency from 0 to 2 kHz and their frequencies responses were analyzed. With fixing a cylindrical magnet as a load at the center of the passive membrane, further experimental studies on several harmonics along with their phase shift were performed using an indigenously developed magnetoresistive sensor and the detailed analysis on these observations are presented.

Investigation of the coherent structures in flow behind a backward-facing step

Purpose – The purpose of this paper is to investigate the characteristic flow structures behind a backward-facing step. With better understanding of unsteady features, effective control practice with harmonic actuation is illustrated. Design/methodology/approach – The present study employs Improved Delayed Detached Eddy Simulation to resolve flow turbulence with a finite-volume approach on structured grid mesh. The coherent structure is displayed through temporal- and spatial-evolution of pressure fluctuations. Characteristic frequencies in different flow regions are extracted using fast Fourier transform. Dynamic mode decomposition method is applied to uncover the critical dynamic modes. Findings – The time- and spanwise-averaged quantities agree well with experimental data. It is observed that two distinct modes exist: shear layer mode and shedding mode. The former is related to Kelvin-Helmholtz instability mechanism, vortex pairing and step mode with non-dimensional frequency, Sth,st at around 0.2. The latter is of multi-scale, with a typical coherent structure shedding frequency, Sth,st at 0.074. Step mode interacts with shedding mode in the reattachment region, resulting in the low-frequency characteristics. Originality/value – An optimal excitation frequency to reduce recirculation bubble length is obtained at about Sth,st =0.2 with an explanation.