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

A unified approximation method is derived to illustrate the effect of electro-mechanical coupling on vibration-based energy harvesting systems caused by variations in damping ratio and excitation frequency of the mechanical subsystem. Vibrational energy harvesters are electro-mechanical systems that generate power from the ambient oscillations. Typically vibration-based energy harvesters employ a mechanical subsystem tuned to resonate with ambient oscillations. The piezoelectric or electromagnetic coupling mechanisms utilized in energy harvesters, transfers some energy from the mechanical subsystem and converts it to an electric energy. Recently the focus of energy harvesting community has shifted toward nonlinear energy harvesters that are less sensitive to the frequency of ambient vibrations. We consider the general class of hybrid energy harvesters that use both piezoelectric and electromagnetic energy harvesting mechanisms. Through using perturbation methods for low amplitude oscillations and numerical integration for large amplitude vibrations we establish a unified approximation method for linear, softly nonlinear, and bi-stable nonlinear energy harvesters. The method quantifies equivalent changes in damping and excitation frequency of the mechanical subsystem that resembles the backward coupling from energy harvesting. We investigate a novel nonlinear hybrid energy harvester as a case study of the proposed method. The approximation method is accurate, provides an intuitive explanation for backward coupling effects and in some cases reduces the computational efforts by an order of magnitude.     

Regularization of jump points in applying the adaptive spatial resolution technique

The performance of the adaptive spatial resolution technique is improved by making the resolution function of the coordinate transformation as smooth as possible. To this end, the smoothness of the resolution function is probed and a quantitative criterion is proposed to make the jump points; which were conventionally equidistant from each other, regularized. The here-proposed regularization is applied to two different recent formulations and its effects on the overall convergence rate and on the presence of numerical artifacts in analysis of highly conducting gratings are studied. Dielectric and metallic gratings at optical and microwave frequencies are considered and the helpfulness of the proposed technique is discussed.     

Weak and strong coupling theories for polarizable colloids and nanoparticles

A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nanoparticles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far field. All the results are compared with the Monte?Carlo simulations, showing an excellent agreement between the theory and the simulations.     

Milling time and BPR dependence on permeability and losses of Ni0.5Zn0.5Fe2O4 synthesized via mechanical alloying process

Ni_0.5Zn_0.5Fe₂O₄ has been synthesized using mechanical alloying method with two variables (milling time and ball-to-powder weight ratio (BPR)) were varied in order to study its effect on the magnetic properties of the material. The effects of these two variables were studied using XRD, SEM, TEM and later by impedance analyzer with the frequency range from 1 MHz to 1.8 GHz. The results obtained however show that there are no significant trends to relate the milling time and BPR with the permeability and losses of the material studied. After being sintered at 1150 °C, all the effects of alloying process seem to diminish.     

Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory

Graphene-polymer nano-composites are one of the most applicable engineering nanostructures with superior mechanical properties. In the present study, a finite element (FE) approach based on the size dependent nonlocal elasticity theory is developed for buckling analysis of nano-scaled multi-layered graphene sheets (MLGSs) embedded in polymer matrix. The van der Waals (vdW) interactions between the graphene layers and graphene-polymer are simulated as a set of linear springs using the Lennard-Jones potential model. The governing stability equations for nonlocal classical orthotropic plates together with the weighted residual formulation are employed to explicitly obtain stiffness and buckling matrices for a multi-layered super element of MLGS. The accuracy of the current finite element analysis (FEA) is approved through a comparison with molecular dynamics (MD) and analytical solutions available in the literature. Effects of nonlocal parameter, dimensions, vdW interactions, elastic foundation, mode numbers and boundary conditions on critical in-plane loads are investigated for different types of MLGS. It is found that buckling loads of MLGS are generally of two types namely In-Phase (INPH) and Out-of-Phase (OPH) loads. The INPH loads are independent of interlayer vdW interactions while the OPH loads depend on vdW interactions. It is seen that the decreasing effect of nonlocal parameter on the OPH buckling loads dwindles as the interlayer vdW interactions become stronger. Also, it is found that the small scale and polymer substrate have noticeable effects on the buckling loads of embedded MLGS.     

Instability of the stationary solutions of generalized dissipative Boussinesq equation

In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.     

An algebraic closure for the DNS of fiber-induced turbulent drag reduction in a channel flow

An algebraic closure for the non-Newtonian Navier–Stokes equations is presented which accounts for the effect of a dilute fiber suspension. The model is intended to be used in simulations of turbulent drag reduction by fiber additives, and can be considered as a computationally efficient alternative to the existing rheological models for fiber suspensions in turbulent wall-bounded flows. It is based on the assumption that the suspended elongated particles are aligned with the local velocity fluctuation vector. The model is proved to be Galilean invariant. One-way coupled simulations and comparison with a direct solution of the underlying Fokker–Planck equation show a considerable improvement over an existing and comparable model. Finally, two-way coupled simulations demonstrate that the model predicts flow statistics that are in very good agreement with those obtained by the moment approximation approach. Interestingly, the model is realistic in terms of the polymer concentration. Using the proposed model, the cost of simulating a drag-reduced flow in terms of CPU-time is slightly more than that of a Newtonian flow.     

Synthesis of Nitroalkanes from Alkylhalides under Mild and Nonaqueous Conditions by Using Polymer Supported Nitrites

Alkyl halides are efficiently converted to their corresponding nitroalkanes under mild and nonaqueous conditions by using polymer supported nitrites. The polymeric reagent is regenerable.     

Visualization of spontaneous aggregates by diblock poly(styrene)‐b‐poly(L‐lactide)/poly(D‐lactide) pairs in solution with new fluorescent CdSe quantum dot labels

Spontaneous stereocomplex aggregation of diblock poly(styrene)‐b‐poly(L ‐lactide) PS‐b‐PLLA/poly(D ‐lactide) PDLA pairs has been investigated under ambient temperature in tetrahydrofuran solution. First, diblock PS₂₆₀‐b‐PLLA₁₆₅ and PS₂₆₀‐b‐PDLA₁₆₂ bearing similar lengths of respective PLLA and PDLA blocks were synthesized through controlled atom‐transfer radical polymerization of styrene, and a subsequent living ring‐opening polymerization of optically pure lactides, and their structures were further characterized by nuclear magnetic resonance spectroscopy (NMR) and gel‐permeation chromatography (GPC). Subsequently, new enantiomeric poly(D ‐lactide) stabilized core‐shell fluorescent CdSe quantum dots (CdSe/PDLA QD) were designed and prepared as sensitive fluorescence labels to shed new lights on the spontaneous stereocomplex aggregation in THF, which was mediated by stereocomplexation of the PLLA and PDLA chains. Upon simply mixing two individual THF solution of diblock PS₂₆₀‐b‐PLLA₁₆₅ and HO‐PDLA₃₀‐SH, spontaneous stereocomplex aggregation was studied, and the aggregated uniform spherical particles were observed by scanning electronic microscopy (SEM) to exhibit average particle diameters of 2.0 μm. Finally, utilizing the prepared CdSe/PDLA QDs as new fluorescent labels, morphologies of the spontaneous aggregates by new diblock PS₂₆₀‐b‐PLLA₁₆₅/HO‐PDLA₃₀‐SH pair were for the first time directly visualized by a confocal laser scanning fluorescence microscopy (CLSFM). These results might suggest alternative ways to simply prepare functional fluorescent particles with tunable diameter sizes and would be helpful to understand the mechanism of stereocomplex particle aggregation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1393–1405, 2009