Harmonic Force Research Articles

Motion of localized disturbances in scalar harmonic lattices.

We present analytical and numerical investigations of energy propagation in systems of massive particles that interact via harmonic (linear) forces. The particle motion is described by a scalar displacement, and the particles are arranged in a simple crystal lattice. For the systems under consideration we prove the conservation of the total energy flux analytically. Then, using a sample case of a square lattice, we confirm the analytical results numerically. We create disturbances of a special kind which can move with a predefined velocity with a minor change in their shape. We show that a clot of energy, associated with each disturbance, moves similarly to a free body of matter in classical mechanics. We also numerically study a simultaneous propagation of a number of energy clots as an analogy to the motion of point masses in the conventional mechanics of particles. The obtained results demonstrate that an energy flow in lattices can be described in terms of numerous separated energy bodies, making a step towards a linkage between lattice dynamics and the kinetic theory of heat transfer in solids.

Effect of interaction between polarization direction and inclined force on the dynamic stability of a pre-stressed piezoelectric plate

The current study deals with forced vibration analysis of a pre-stressed piezoelectric plate with finite lengths resting on a rigid foundation, exposed to an inclined time-harmonic force. The present investigation is modeled according to a new theoretical consideration in the context of the three-dimensional linearized theory of elasticity for solids under initial stress (TLTESIS). It is assumed that the plate exhibits a polarization effect in both vertical and horizontal directions to the top surface and there is an exact clamping condition at the interface between the plate and the rigid foundation, that is, no jumping in the quantities. For obtaining the governing and boundary condition equations of our problem, the virtual work principle is used according to Hamilton's principle and the piecewise homogeneous body model. The three-dimensional displacement-based finite element model is developed for solving the system of partial differential equations and analyzing the dynamic behavior of the plate. The reliability of the solution procedure is proved by convergence analysis and comparing the results to the current literature. The target of the paper for surveying the numerical results and findings is divided into two sections. The first one presents the influence of the inclination of the dynamic external force on the forced vibration characteristics of the current model. In the second one, the influence of inclination angle, thickness ratio, aspect ratio, and initial stress parameter on the frequency response of the harmonic force are investigated in detail. As a desirable result for the designer, while a decrease in the angle of the force with the vertical axis exceeds the resonant mode of the stress, increasing values of the initial stress prevents that mode.

Free and forced vibration response of a laminated composite sandwich beam with dual honeycomb core: Numerical and experimental study

AbstractFree and forced vibration characteristics of composite sandwich beams with single‐core (SC) and dual‐core (DC) are investigated in this study. The wet hand‐layup technique is followed to make the composite face sheet, and honeycomb cores are 3D printed using the fused filament fabrication method. The natural frequencies of SC and DC sandwich beams were measured using experimental modal tests and validated through a three‐dimensional finite‐element model. Also, parametric studies on the geometry of composite structures are performed to scrutinize the effect of DC sandwich beams with different ply orientations, length‐to‐breadth ratios, core thickness, and core cell wall thickness. In addition, the transverse vibration responses of SC and DC sandwich beams are examined under harmonic force excitations at different end conditions. The study result shows that the sandwich beam's vibration behavior is enhanced by the inclusion of a core.

Impact of Different Groups on Properties of All Members of the Series of 1-X-Benzotriazole Derivatives (X= H, OH, NH2, Cl and CH3)

Here, the impact of different groups on the geometrical parameters, dipole moments, atomic charges, stabilization and solvation energies, molecular electrostatic potentials, densities rings, positions IR and UV bands and NMR chemical shifts of all members of the series of 1X-benzotriazole derivatives (X= H, CH3, Cl, NH2 and OH) have been investigated by using hybrid B3LYP/6-311++G** calculations because, so far, correlations among their properties neither the vibrational analyses are reported yet. The polarity of N-X bonds, electronegativity, donor/acceptor characteristics of the different X groups were analysed for all members. The polarity of N1-X4 bonds have influence on dipole moments, volumes and on bond lengths of both rings while the chlorinated derivative has a higher reactivity due to its higher global electrophilicity index. NBO and AIM studies reveal the strong influence of Cl on densities of both rings of CBT and, on this derivative. Harmonic force fields evidence very good correlations between stretching force constants and assignments.

Phosphorus fluoride exchange: Multidimensional catalytic click chemistry from phosphorus connective hubs

Phosphorus Fluoride Exchange (PFEx) represents a cutting-edge advancement in catalytic click-reaction technology. Drawing inspiration from Nature's phosphate connectors, PFEx facilitates the reliable coupling of P(V)-F loaded hubs with aryl alcohols, alkyl alcohols, and amines to produce stable, multidimensional P(V)-O and P(V)-N linked products. The rate of P-F exchange is significantly enhanced by Lewis amine base catalysis, such as 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD). PFEx substrates containing multiple P-F bonds are capable of selective, serial exchange reactions via judicious catalyst selection. In fewer than four synthetic steps, controlled projections can be deliberately incorporated along three of the four tetrahedral axes departing from the P(V) central hub, thus taking full advantage of the potential for generating three-dimensional diversity. Furthermore, late-stage functionalization of drugs and drug fragments can be achieved with the polyvalent PFEx hub, hexafluorocyclotriphosphazene (HFP), as has been demonstrated in prior research.

Altering the wake dynamics of a circular cylinder with harmonic forcing

The time-averaged velocity profile in the wake of a circular cylinder resembles a “U” type or a “V” type profile due to a velocity defect. Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020)] showed experimentally that the wake dynamics could be altered with harmonic forcing in such a way that instead of a velocity defect, a “jet-like” profile emerged with a characteristic “W” profile. The harmonic forcing was created by modulating the waveform of a dielectric barrier discharge plasma actuators' supply signal with a frequency twice that of the shedding frequency. However, the reason for the appearance of the “W” profile was not clear in S. Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020).] In this paper, we use numerical simulation to recreate the test conditions implemented by Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020).] We apply large-eddy simulation to study the impact of the pulsed, harmonic forcing on the wake of a circular cylinder at a subcritical Reynolds number of 4700. The plasma actuators are modeled with a body-force approach. The frequency of the driving signal of the plasma actuator is modulated at twice the shedding frequency. The amplitude of the signal is set at 6 kV peak to peak to create a blowing ratio of 0.8. The goal is to understand how the wake changes in three dimensions and the impact on separation on the cylinder surface due to the harmonic forcing. Results show that pulsed forcing causes vortices from one side of the wake to cross the centerline. This crossing creates an effective jet-like velocity along the centerline, resulting in a W velocity profile. Such a W profile is observed at least up to a streamwise distance of five cylinder diameters. Additionally, the pulsed actuation significantly increases the magnitude of primary and secondary frequencies throughout the wake. Forcing caused a 50% increase in the transverse velocity fluctuations at the centerline of the wake at the streamwise location of x/d=5. There was a similar increase in 33% at the centerline in the streamwise velocity fluctuations at the same location.

Quantitive Harmonic Analysis and Force Ripple Suppression of a Parallel Complementary Modular Linear Reluctance Machine

Considering the fluctuating price of permanent magnet, magnetless machine is a new trend in development. Variable reluctance linear machines (VRLM) with simple structure, good robustness, and high dynamic performance, is one of the potential candidates for linear direct-drive wave energy conversion (WEC) application replacing PM-excited linear machine. To ameliorate the fault-tolerance performance of VRLM, the researchers have come up with modular or segmented design, denoted as modular variable reluctance linear machines (MVRLM) However, suffering from large thrust ripple, the design of MVRLM still needs to be improved. To relieve the force ripple of MVRLM, a novel H-shaped modular variable-flux linear reluctance machine (HMVF-LRM) is proposed in this paper. The principle of force ripple suppression by using parallel-complementary structure is analyzed deeply. In this paper, the analytical calculation of induced voltage is developed quantitively with equivalent magnetic circuit method (EMC) and harmonics analysis. Then the design mechanism of HMVF-LRM is illustrated. Further, the performance and fault-tolerant capability of the proposed machine are simulated and evaluated by finite element analysis (FEA), and the prototype is tested to verify the effectiveness of the machine design.

Multiple Sets of M-Phase Winding Composition Principle of Permanent-Magnet Machine for MMF Harmonic Analysis

This paper presents the composition factor of the fractional-slot permanent-magnet (PM) machine equipped with multiple sets of m-phase windings. Besides, the intrinsic relationship between magnet-motive force (MMF) harmonics and the phase shift angle is revealed. Firstly, the structural characteristics and phase shift regulations of multiple sets of <i>m</i>-phase windings are analyzed. Based on a single set of <i>m</i>-phase windings, the MMF composition factors of the odd and even sets of <i>m</i>-phase windings are derived, respectively. Secondly, four PM machines with different slot-pole combinations and winding configurations were designed. Their MMF harmonics are analyzed by the finite-element method to verify the analytical results. Moreover, the performances and MMF harmonics of a 48-slots 22-poles (48s22p) PM machine with dual three-phase windings are analyzed. Finally, the 48s22p machine is prototyped, and experimental results are validated.

Structural, harmonic force field and vibrational studies of cholinesterase inhibitor tacrine used for treatment of Alzheimer's disease

Different structures of free base (FB), two cationic forms (CA) and three hydrochloride forms (HCl) of cholinesterase inhibitor tacrine used for treatment of Alzheimer ’s disease was evaluated using hybrid B3LYP calculations in order to perform their complete vibrational assignments using the scaled harmonic force fields. Structures of anhydrous form of tacrine have been optimized in gas phase and in aqueous solution. The structure of form III HCl is in agreement with the experimental determined by X-ray diffraction while the predicted IR, Raman, 1H– 13C NMR and UV spectra show good correlations with the corresponding experimental ones. Energy values show that the three forms of HCl can exist in both media because these energetic values decrease from 35.15 kJ/mol in gas phase to 5.51 kJ/mol in solution. For the most stable species of tacrine, the following stability order using natural bond orbital (NBO) studies was found: form I HCl > form III HCl > form I CA > FB. CA presents the higher solvation energy value, as reported for hydrochloride species of alkaloids and antihypertensive agents. The structural parameters of form III of HCl present better concordance and corresponds to that experimental observed in the solid phase. Higher topological properties of form III together with the strong N2–H26⋯Cl31 interaction could justify the presence of this form in the solid phase and in solution and the higher stabilities in both media. The gap values support the higher reactivity of form III while FB is the less reactive species in both media. Complete vibrational assignments for FB, CA and HCl species together with the corresponding scaled force constants are reported.

Tangential Force Noise Reduction of Vehicular PMSM Based on Reference Harmonic Current Analytical Computation

The harmonic current injection can remarkably reduce the noise of the vehicular electric drive system. However, the optimal reference harmonic current is difficult to obtain because of the vehicular motor’s non-linear electromagnetic characteristics. The existing methods are always time-consuming and cannot satisfy the real-time requirement of the vehicular application. This article proposed an analytical computation method of the reference harmonic current for tangential force noise reduction. Specifically, by combining two-dimensional Fourier series decomposition and polynomial fitting, a data-based non-linear model is constructed to accurately describe the tangential force harmonic under arbitrary current excitation. Then, considering the dominant effect of fundamental current, a simplified tangential force model is obtained by local linearization at each fundamental current working point. Meanwhile, by representing the stator current amplitude with a Fourier series combination, the suppression of tangential force harmonics is transferred to solving linear equations concerning each harmonic current vector. Finally, simulation and bench test experiments have been done to verify the effectiveness of the proposed method. The results demonstrate that the reference harmonic current at different speeds/torque can be computed in real-time, and the corresponding tangential noise can be reduced remarkably.

Interaction of two cylinders immersed in a viscous fluid. On the effect of moderate Keulegan–Carpenter numbers on the fluid forces

This work deals with the hydrodynamic interaction of two parallel circular cylinders, with identical radii, immersed in a viscous fluid initially at rest. One cylinder is stationary while the other one is imposed a harmonic motion with a moderate amplitude of vibration. The direction of motion is parallel to the line joining the centers of the two cylinders. The two dimensional fluid–structure problem is numerically solved by the Arbitrary Lagrangian–Eulerian method implemented in the open-source CFD code TrioCFD. First, we show that the fluid forces on the two cylinders are aligned with the direction of the imposed motion. Second, we show that the moderate oscillations of the moving cylinder create nonlinear effects in the fluid that strongly affect the characteristics (Fourier harmonics) of the hydrodynamic force acting on the stationary cylinder. The fluid force on the moving cylinder is shown to be poorly affected by the nonlinear effects, which makes it possible to extend the linear concept of self-added mass and damping coefficients. First, we show that the self-added coefficients decrease as Sk−1/2, with Sk the Stokes number (dimensionless number constructed from the imposed vibration frequency). Second, we show that the self-added mass (resp. damping) decreases (resp. increases) as −KC3 (resp. +KC3), with KC the Keulegan–Carpenter number (ratio between the imposed amplitude vibration and the separation distance between the cylinders). These variations are included in new power laws derived from nonlinear regressions of the numerical results. These new power laws for the self-added coefficients combine the effect of both Sk and KC, covering the viscous (Sk≥500) and weakly nonlinear (KC≤0.3) regimes.

Теоретическое исследование стабилизатора вибрации с обратной связью по интегралу смещения для энергетического оборудования

Reducing the vessel hull vibration caused by the power equipment is usually obtained by the effective vibration-isolating fastening. Vibration impact on the mechanisms and automation tools greatly reduces their reliability, affects the health of passengers and crew members. Despite the modern vibration-insulating materials and compensators, the problems of eliminating the variable forces transmitted from the vibration source have not been fully solved. Increasing the operational requirements for the vibration safety of water transport requires the scientifically based and technical solutions, improving the designs of vibration isolation supports for mounting the marine power plants. Vibration reduction problems must be solved both at the design stage and at the stage of construction, repair and modernization. The conducted studies of vibrations under the influence of the harmonic force, step load and gradually increasing load have shown high efficiency of the support in all cases of load application under different simulation modes. At stabilization of the position the support was controlled by the integral of the displacement. The results of the studies conducted on the test model for the vibration protection of marine power equipment showed the effectiveness of the stabilizer. There is presented a theoretical study of a stabilizer with feedback on the displacement integral in the MathCAD software package. The numerical experiment is based on the Newton equation. The parameters of the stabilizer are determined, on the basis of which it is possible to design the actuator. It can be an electric motor, the direction of rotation of which depends on the direction of displacement of the protected object. The motor rotates a screw pair that compresses the spring. The spring acts on the clutch, the torque changes and maintains the vibration source. The simulation results helped to infer that it is necessary to stabilize the position of the unit for all load application modes.

Parameters optimization of a nonlinear dynamic absorber for a nonlinear system

One of the important methods to prevent the intensification of the main vibration system is using a dynamic vibration absorber (DVA). A DVA is a mechanical subsystem used to reduce Vibration amplitude and prevent the main vibration system from resonance. This paper aims to use a nonlinear dynamic absorber as a cantilever beam with a concentrated mass at its end to reduce the amplitude of the intensified oscillator vibration. The primary vibration system consists of mass, nonlinear spring, and viscous damping, and a harmonic excitation force is applied to it, resonance the system. In this case, using a nonlinear dynamic absorber reduces the vibration amplitude. For this purpose, first, the kinetic energy and the potential energy of the vibration system are calculated, and then, using Lagrange equations, the governing equations are extracted. Due to the nonlinearity of the equations of motion, the multiple scales method is used to solve the governing equations. In the results, the effect of nonlinear DVA on reducing the amplitude of intensified oscillator vibration is well visible. The effect of the main parameters of nonlinear dynamic absorbers on the vibration amplitude of the initial system is also investigated. Finally, the vibration amplitude of the system is optimized as a target function by the genetic algorithm method, and the optimal parameters of the nonlinear dynamic absorber and the optimal vibration amplitude are studied. Considering the main resonant vibration system as a structure under earthquake, the results of this research in reducing the vibration amplitude can be widely used in earthquake engineering.

Dissociation Rate Calculation via Constant-Force Steered Molecular Dynamics Simulation.

Steered molecular dynamics (SMD) simulations are used to study molecular dissociation events by applying a harmonic force to the molecules and pulling them at a constant velocity. Instead of constant-velocity pulling, we use a constant force: the constant-force SMD (CF-SMD) simulation. The CF-SMD simulation employs a constant force to reduce the activation barrier of molecular dissociation, thereby enhancing the dissociation event. Here, we present the capability of the CF-SMD simulation to estimate the dissociation time at equilibrium. We performed all-atom CF-SMD simulations for NaCl and protein-ligand systems, producing dissociation time at various forces. We extrapolated these values to the dissociation rate without a constant force using Bell's model or the Dudko-Hummer-Szabo model. We demonstrate that the CF-SMD simulations with the models predicted the dissociation time in equilibrium. A CF-SMD simulation is a powerful tool for estimating the dissociation rate in a direct and computationally efficient manner.

Estimation of magnetic bearing constant in active magnetic bearings

Active magnetic bearings (AMB) provide non-contact support to rotors and require closed-loop control systems as they are inherently unstable. The methodology to obtain parameters of the force model of an AMB from closed-loop control signals and air gap signals using a successive integration-based algebraic technique is presented in this work. This transient data-based approach does not require additional load cells or differentiation of control and gap sensor signals which lead to noise amplification. This estimation methodology is shown to apply to AMB with unequal bias currents in both current control and voltage control modes. This methodology is also shown to be robust in the presence of noise in sensor signals. Also, it can estimate the force model parameters in the presence of harmonic force disturbances on the AMB. This estimation approach is developed using linear and nonlinear AMB simulation models and then applied to initial transient data from the AMB test rig. The estimated magnetic bearing constant (Km) is compared to Km values obtained from the experimental measurements on the AMB actuators. This direct force measurement is further supported with steady-state closed-loop control signal data from the AMB test rig for a range of levitated positions within the air gap.

Optimization of methanol synthesis under forced periodic operation in isothermal fixed-bed reactors

Methanol is usually produced in large amounts in fixed-bed reactors under steady-state conditions using Cu/ZnO/Al2O3-catalyst. In this paper, possible improvements through forced periodic operation compared to optimal steady-state solution are investigated. The numerical study is done with a simplified model which describes a hypothetical 7-meter-long isothermal and isobaric fixed-bed reactor. The forced periodic operation is implemented using harmonic forcing and square-waves. Multi-objective optimization is performed for different operating conditions quantifying the achievable molar flow rate of methanol at the reactor outlet and the yield of methanol based on total carbon. The resulting PDE-constrained optimization problems are solved using a simultaneous approach, with orthogonal collocation as discretization. The results show most significant improvements through forced periodic operation with square-waves. The periodic operation can provide theoretical improvements of up to 50% for the methanol mean outlet molar flow rate and improvements of up to 10% for the yield based on total carbon.

Acoustic Radiation of a Beam Subjected to Transverse Load

In this paper, the dynamic response of a Euler–Bernoulli beam subjected to transverse harmonic forces is calculated. The method of separation of variables combined with the mode shape superposition method, which includes the determination of eigenvalues, is used to define the velocity field of the beam surface. The Rayleigh integral was used to calculate the sound radiation and the beam was placed in an infinite baffle. Additional actuators are introduced in order to minimize the sound radiation, or, more specifically, the total sound power level of the vibrating beam, and their optimal position and force amplitude are determined; the conclusions were drawn from the optimization results. This paper proposes a method for faster determination of the optimal actuator parameters in order to achieve the minimum total sound power level. The validity of the obtained results is demonstrated with examples, whose solutions are compared to the results in the published literature.

Hybrid Frame-Based Current Control Scheme for LC-Equipped PMSM With Non-Sinusoidal Back-EMF

Permanent-magnet synchronous machine (PMSM) drive with a sine wave <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filter has the features of low insulation stress and current harmonics. However, few studies consider the impact of back-electromotive force (EMF) harmonics on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -equipped PMSM drive system. The non-sinusoidal back-EMF can cause current harmonics, meanwhile, it also affects the stability analysis and high-frequency resonance suppression. In order to solve these two problems simultaneously, a hybrid frame-based current control scheme is proposed in this paper. The quantitative effect of back-EMF harmonics on control behaviors is analyzed first. A virtual triple three-phase system with auxiliary currents is developed to decompose the fundamental and harmonic contents, which not only contributes to independent current harmonic regulation in multiple synchronous reference frames, but also simplifies system stability analysis considering non-sinusoidal back-EMF. Then, an active damping method based on stator current feedback is implemented in the stationary frame to suppress the resonance, and no additional passive components or sensors are required. Finally, experimental results are provided to verify the effectiveness and superiority of the proposed method.

Linear response analysis of supersonic turbulent channel flows with a large parameter space

In this work, the linear responses of turbulent mean flow to both harmonic and stochastic forcing are investigated for supersonic channel flow. Well-established universal relations are utilized to obtain efficiently the mean profiles with a large parameter space, with the bulk Mach number up to 5 and the friction Reynolds number up to$10^4$, so a systematic parameter study is feasible. The most amplified structure takes the form of streamwise velocity and temperature streaks forced optimally by the streamwise vortices. The outer peak of the pre-multiplied energy amplification corresponds to the large-scale motion, whose spanwise wavelength ($\lambda _z^+$) is very insensitive to compressibility effects. In contrast, the classic inner peak representing small-scale near-wall motions disappears for the stochastic response with increasing Mach number. Meanwhile, the small-scale motions become much less coherent. A decomposition of the forcing identifies different effects of the incompressible counterpart and the thermodynamic components. Wall-cooling effects, arising with high Mach number, increase the spacing of the most amplified near-wall streaks; the spacing becomes nearly invariant with Mach number if expressed in semi-local units. Meanwhile, the coherence of stochastic response with$\lambda _z^+&gt;90$is enhanced, but on the other hand, with$\lambda _z^+&lt;90$it is decreased. The geometrical self-similarity of the response in the mid-$\lambda _z$range is still roughly satisfied, insensitive to Mach number. Finally, theoretical analyses of the perturbation equations are presented to help with understanding the scaling of energy amplification.

Vibration Suppression on the Composite Laminated Plates Subjected to Aerodynamic and Harmonic Excitations Based on the Nonlinear Piezoelectric Shunt Damping

This paper proposes a nonlinear piezoelectric shunt damping circuit to mitigate the vibration of the plate structures subjected to the aerodynamic and harmonic excitations. The nonlinear piezoelectric shunt damping circuit consisting of the piezoelectric patch, inductor, resistor, negative capacitor and nonlinear capacitor is considered. Firstly, the governing equations of the electro-mechanical coupling nonlinear system are formulated based on the energy method and modified Ritz method. Furthermore, the complexification-averaging method combined with pseudo arc-length continuation method is adopted to analyze the steady-state response of the coupled system with aerodynamic and harmonic forces. A considerable number of numerical cases are performed to validate the proposed model and the time domain and frequency domain dynamic responses of the plate structures with and without control are further compared to validate the effectiveness of the proposed control strategy. Meanwhile, the energy transfer analysis between the plate structure and external piezoelectric shunt damping circuit is investigated. Finally, the effects of key parameters of the nonlinear piezoelectric shunt damping circuit including the negative capacitance and nonlinear capacitance on the vibration suppression performance of the piezoelectric shunt damping are discussed.