Unsteady Aerodynamic Modeling and Prediction of Loads for Rotary Wings in Forward Flight

In this effort, a new approach in aerodynamic modeling that accounts for unsteady wake effects as well as viscous friction drag, Leading edge suction effect and post stall behavior for rotary wings in forward flight is proposed. The adopted approach commingles the unsteadiness with the problem of helicopter rotor blade in forward flight. The results of the local normal force coefficients were compared with experimental results of the 7A rotor case study in high speed test point 312 at five non-dimensional radial positions. A CFD solver, HOST/elsA, results are compared with the obtained results at five radii locations. The results show a good agreement between the experimental results and the proposed model preserving the same pattern of variation along the azimuth angle with a slight discrepancy for amplitude and phase angle. Of particular interest, the presented model showed better agreement with the experimental for higher radii locations.

Acoustic Non-Reciprocal Band Structure in a Passive, Nonlinear, 1D Material

Acoustic non-reciprocity, referring to the phenomenon of path-dependent propagation, has diverse applications in mechanical devices. This paper presents a numerical study on a periodic triangle-shape structure that breaks reciprocity in a passive manner over a broad range of frequency and energy. The proposed structure contains strong nonlinearity and geometric asymmetry, which contributes to a direction-dependent dispersion relationship. When the signal frequency falls in the band pass in one direction, and band gap in the other, a unidirectional wave propagation results. The system achieves giant non-reciprocity with minimal distortion in the frequency content of the signal.

Evaluation of the ISHM Method Applied for Composite Rotors

The use of SHM (structural health monitoring) techniques has shown promising results for fault detection in rotating machines, making possible to identify various malfunctions. SHM methods provide maintainability and safe operation for these systems. The objective of the present work is to evaluate the SHM method based on the electromechanical impedance (ISHM) to detect faults in a composite rotor shaft. Composite materials present complex damage mechanisms due to their anisotropy and heterogeneity. Moreover, the process of damage detection in these materials is more challenging than in metallic structures. The ISHM approach uses piezoelectric (PZT – Lead Zirconate Titanate) patches as sensors and actuators coupled to the monitored structure. Variations in their electrical impedance are associated with changes in the mechanical integrity of the system. The electrical impedance of the PZT sensor is directly related to the mechanical impedance of the structure, which changes according to variations in the mass, stiffness, and damping properties of the structure. Damage metrics are used to quantify variations in the electrical impedance (impedance signatures) of the PZT patches. Despite the ISHM approach be able to detect incipient faults, it presents some disadvantages. For instance, the impedance signatures are susceptible to temperature variation. In the present contribution, to detect damages in the considered composite rotor shaft, the ISHM technique was implemented based on a data normalization methodology. Thus, an optimization procedure based on hybrid optimization was used to avoid false diagnostics.

Frequency Response of Parametric Resonance of Electrostatically Actuated Circular Plates Under Hard Excitations

In this paper, the Method of Multiple Scales, and the Reduced Order Model method of two modes of vibration are used to investigate the amplitude-frequency response of parametric resonance of electrostatically actuated circular plates under hard excitations. Results show that the Method of Multiple Scales is accurate for low voltages. However, it starts to separate from the Reduced Order Model results as the voltage values are larger. The Method of Multiple Scales is good for low amplitudes and weak non-linearities. Furthermore the Reduced Order Model running with AUTO 07p is validated and calibrated using the 2 Term ROM time responses.

Comparison of Frequency Response of Primary Resonance of DWCNT and CNT Resonators Under Electrostatic Actuation

This paper deals with the frequency-amplitude response of primary resonance of electrostatically actuated Double-Walled Carbon Nanotubes (DWCNT) and Single-Walled Carbon Nanotubes (SWCNT) cantilever resonators. Their responses are compared. Both the DWCNT and SWCNT are modeled as Euler-Bernoulli cantilever beams. Electrostatic and damping forces are applied on both types of resonators. An AC voltage provides a soft electrostatic actuation. For the DWCNT, intertube van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes and acting as a nonlinear spring between the two carbon nanotubes. Electrostatic (for SWCNT and DWCNT) and intertube van der Waals (for DWCNT) forces are nonlinear. Both resonators undergo nonlinear parametric excitation. The Method of Multiple Scales (MMS) is used to investigate the systems under soft excitations and weak nonlinearities. A 2-Term Reduced-Order-Model (ROM) is numerically solved for stability analysis using AUTO-07P, a continuation and bifurcation software. The coaxial vibrations of DWCNT are considered in this work, in order to draw comparisons between DWCNT and SWCNT. Effects of damping and voltage of the frequency-amplitude response are reported.

Numerical Study of Superharmonic Resonances in a Mistuned Horizontal-Axis Wind-Turbine Blade-Rotor Set

This paper is on a simplified model of an in-plane blade-hub dynamics of a horizontal-axis wind turbine with a mistuned blade. The model has cyclic parametric and direct excitation due to gravity and aerodynamics. This work follows up a previous perturbation study applied to the blade equations written in the rotor-angle domain and decoupled from the hub, in which superharmonic and primary resonances were analyzed. In this work, the effects of mistuning, damping, and forcing level are illustrated. The first-order perturbation solutions are verified with comparisons to numerical simulations at superharmonic resonance of order two. Additionally, the effect of rotor loading on the rotor speed and blade amplitudes is investigated for different initial conditions and mistuning cases.

Reduced-Order Modeling and Experimental Studies of Two-Way Coupled Fluid-Structure Interaction in Flapping Wings

Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies.

Vibrations of a Double Beam Structure Carrying a High-Pressure Driven Projectile

In this paper, a mathematical model of a double beam structure carrying a high-pressure driven projectile is developed for investigation of the physical behaviors of gun barrels during firing. The dynamic response of such a weapon system is particularly interesting when reduction of muzzle vibrations and relevant dynamic stress in the structure is needed to improve the life cycle of the gun. In the model presented, the Timoshenko beam theory is implemented, and realistic characteristics of the physical system are considered. Numerical simulation results are presented for the displacement and rotation of the two beams, and the rigid-body projectile mass.

A SPICE Sub-Circuit Model for Backward Diode

Backward diode and tunnel diode were formerly used in communication systems and now considered obsolete. Recently, because of their ultra-low threshold voltage at reverse bias condition, the backward diode is used as a rectifier diode for ultra-low power energy harvester. Unfortunately, there are few models available for SPICE simulation or any other computation analysis. The challenge of modeling backward diode and tunnel diode is their negative differential resistance (NDR) and result in a high probability of having numerical instabilities. This paper will first investigate several available mathematical models such as the polynomial model and Ray’s Empirical model, then, a less complex SPICE model based on discrete components sub-circuit will be proposed. All the unknown parameters of this proposed model are optimized based on measurement data using the Levenberg-Marquardt (LM) algorithm. This discrete SPICE model can be easily modified to model other elements with similar negative resistance behavior.

A Non-Traditional Variant Nonlinear Energy Sink: Transient Responses

In this paper, a non-traditional variant nonlinear energy sink (NES) is developed for simultaneous vibration suppression and energy harvesting in a broad frequency band. The non-traditional variant NES consists of a cantilever beam attached by a pair of magnets at its free end, a pair of the so-called continuous-contact blocks, and a pair of coils. The beam is placed between the continuous-contact blocks. The constraint of the continuous-contact blocks forces the beam to deflect nonlinearly. Each of the magnet-coil pairs forms an electromagnetic energy harvester. Different from a traditional way that attaches the coils to the primary mass, the developed setup has the coils fixed to the base. First, the developed apparatus is described. Subsequently, the system modeling and parameter identification are addressed. The performance of the apparatus under transient responses is examined by using computer simulation. The results show that the proposed apparatus behaves similarly as the NES with the following features: 1:1 resonance, targeted energy transfer, initial energy dependence, etc.