Interaction of fundamental parametric resonances with subharmonic resonances of order one-half

The interaction of fundamental parametric resonances with subharmonic resonances of order one-half in a single-degree-of-freedom system with quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to derive two first-order ordinary differential equations that describe the modulation of the amplitude and the phase of the response with the non-linearity and both resonances. These equations are used to determine the steady state solutions and their stability. Conditions are derived for the quenching or enhancement of a parametric resonance by the addition of a subharmonic resonance of order one-half. The degree of quenching or enhancement depends on the relative amplitudes and phases of the excitations. The analytical results are verified by numerically integrating the original governing differential equation.     

Acoustic propagation in partially choked converging-diverging ducts

A computer model based on the wave-envelope technique is used to study acoustic propagation in converging-diverging hard walled and lined circular ducts carrying near sonic mean flows. The influences of the liner admittance, boundary layer thickness, spinning mode number, and mean Mach number are considered. The numerical results indicate that the diverging portion of the duct can have a strong reflective effect for partially choked flows.     

Silicon nanoparticle charge trapping memory cell

A charge trapping memory with 2 nm silicon nanoparticles (Si NPs) is demonstrated. A zinc oxide (ZnO) active layer is deposited by atomic layer deposition (ALD), preceded by Al₂O₃ which acts as the gate, blocking and tunneling oxide. Spin coating technique is used to deposit Si NPs across the sample between Al₂O₃ steps. The Si nanoparticle memory exhibits a threshold voltage (V_t) shift of 2.9 V at a negative programming voltage of –10 V indicating that holes are emitted from channel to charge trapping layer. The negligible measured V_t shift without the nanoparticles and the good re‐ tention of charges (>10 years) with Si NPs confirm that the Si NPs act as deep energy states within the bandgap of the Al₂O₃ layer. In order to determine the mechanism for hole emission, we study the effect of the electric field across the tunnel oxide on the magnitude and trend of the V_t shift. The V_t shift is only achieved at electric fields above 1 MV/cm. This high field indicates that tunneling is the main mechanism. More specifically, phonon‐assisted tunneling (PAT) dominates at electric fields between 1.2 MV/cm < E < 2.1 MV/cm, while Fowler–Nordheim tunneling leads at higher fields (E > 2.1 MV/cm). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flight dynamics and control of flapping-wing MAVs: a review

This paper provides a thorough review of the significant work done so far in the area of flight dynamics and control of flapping-wing micro-air-vehicles (MAVs). It provides the background necessary to do research in that area. Furthermore, it raises questions that need to be addressed in the future. The three main blocks constituting the flight dynamic framework of flapping MAVs are reviewed. These blocks are the flapping kinematics, the aerodynamic modeling, and the body dynamics. The design and parametrization of the flapping kinematics necessary to produce high-control authority over the MAV, as well as design of kinematics suitable for different flight conditions, are reviewed. Aerodynamic models used for analysis of flapping flight are discussed. Particular attention is given to the physical aspects captured by these models. The issues and consequences of averaging the dynamics and neglecting the wing inertia are discussed. The dynamic stability analysis of flapping MAVs is usually performed by either averaging, linearization and subsequent analysis or using Floquet theory. Both approaches are discussed. The linear and nonlinear control design techniques for flapping MAVs are also reviewed and discussed.     

Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler–Lagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester’s behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation.     

Modeling and analysis of electrostatic MEMS filters

We present an analytical model and closed-form expressions describing the response of a tunable MEMS filter made of two electrostatic resonators coupled by a weak microbeam. The model accounts for the filter geometric and electric nonlinearities as well as the coupling between them. It is obtained by discretizing the distributed-parameter system to produce a reduced-order model. We predict the filter deflection and static pull-in voltage by solving a boundary-value problem (BVP). We also solve an eigenvalue problem (EVP) to determine the filter poles (the natural frequencies delineating the filter bandwidth). We found a good agreement between the results obtained using our model and published experimental results. We found that, when the input and output resonators are mismatched, the first mode is localized in the softer resonator whereas the second mode is localized in the stiffer resonator. We demonstrated that mismatch between the resonators can be countermanded by applying different DC voltages to the resonators. As the effective nonlinearities of the filter grow, multi-valued responses appear and distort the filter performance. Once again, we found that the filter can be tuned to operate linearly by choosing a DC voltage that makes the effective nonlinearities vanish.     

Combination Internal Resonances in Heated Annular Plates

Nonlinear modal interactions in the forced vibrations of a thermally loaded pre-buckled annular plate with clamped–clamped immovable boundary conditions are investigated. The mechanism responsible for the interaction is a combination internal resonance involving the natural frequencies of the three lowest axisymmetric modes. The in-plane thermal load acting on the plate is assumed to be axisymmetric and the plate is externally excited by a harmonic force. The nonlinear von Kármán plate equations along with the heat conduction equation are combined to model the behavior of the system. An analytical/numerical approach is used to examine the plate vibrations to a harmonic excitation near primary resonance of one of the modes.     

Effects of a non-linear energy sink (NES) on vortex-induced vibrations of a circular cylinder

We investigate in detail the passive control of vortex-induced vibrations of a freely oscillating circular cylinder using a non-linear energy sink consisting of a secondary system having linear damping and an essential non-linear cubic stiffness. The loads on the cylinder are calculated using a direct numerical simulation of the incompressible flow over the cylinder using a parallel computational fluid dynamics code. A strongly coupled fluid structure control numerical model is used to determine the responses of the cylinder and the sink as well as the flow. We vary the sink parameters (mass and damping) and determine their effects on the response of the coupled system. We find multiple stable responses of the coupled system for different mass ratios and damping coefficient of the sink, depending on the initial conditions.     

Resonant non-linear normal modes. Part I: analytical treatment for structural one-dimensional systems

Approximations of the resonant non-linear normal modes of a general class of weakly non-linear one-dimensional continuous systems with quadratic and cubic geometric non-linearities are constructed for the cases of two-to-one, one-to-one, and three-to-one internal resonances. Two analytical approaches are employed: the full-basis Galerkin discretization approach and the direct treatment, both based on use of the method of multiple scales as reduction technique. The procedures yield the uniform expansions of the displacement field and the normal forms governing the slow modulations of the amplitudes and phases of the modes. The non-linear interaction coefficients appearing in the normal forms are obtained in the form of infinite series with the discretization approach or as modal projections of second-order spatial functions with the direct approach. A systematic discussion on the existence and stability of coupled/uncoupled non-linear normal modes is presented. Closed-form conditions for non-linear orthogonality of the modes, in a global and local sense, are discussed. A mechanical interpretation of these conditions in terms of virtual works is also provided.     

Non-linear propagation of directional spherical waves

The method of renormalization is used to determine a uniformly valid expansion for the problem of non-linear waves produced in a fluid by spatially non-uniform simple harmonic motion of the surface of a sphere. The effect of dimensionless quantities upon the acoustic shock-formation distance is examined.