Sine Mode Research Articles

Research on Active Disturbance Rejection Control with Parameter Autotuning for a Moving Mirror Control System Based on Improved Snake Optimization

In order to improve the control of a moving mirror control system and enhance the anti-interference ability of the system, active disturbance rejection control (ADRC) with parameter autotuning is proposed and applied to control a rotary voice coil motor (RVCM). Improved snake optimization (I-SO) was applied to tune and optimize ADRC’s key parameters. To obtain excellent parameters efficiently, in the population initialization phase of SO, the quality and diversity of initial solutions were improved through a chaotic elite opposition learning algorithm. In the local search phase, a sine and cosine (SC) search mode was introduced to enhance the local search ability of SO. The simulation results show that I-SO can effectively find the ideal parameters. I-SO has excellent search capability and stability. The experimental control system of a moving mirror was established, and the effectiveness of the parameters optimized by I-SO was verified. ADRC with parameter autotuning showed excellent control in the moving mirror control system, and the stability of the optical path scanning speed reached 99.2%.

1/2 and 1/3 Subharmonic Resonance Behaviors of a Rotating FG-CNTRC Beam with Geometric Imperfections

This paper aims at investigating 1/2 and 1/3 subharmonic resonances of a rotating functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam in the presence of geometric imperfections. A general function is introduced to denote three types of imperfections containing sine, global, and local modes. At first, based on the von-Kármán geometric nonlinearity assumption, the forced vibration equation is set up. Then, the Galerkin method and multiple scale method are utilized to study subharmonic resonance behaviors. Finally, coupled effects of FG-CNTRCs, rotating motion, and geometric imperfections on subharmonic resonance responses are investigated. It is found that a specific range of the excitation amplitude and frequency motivates the subharmonic resonance behavior. The coupling of geometric imperfections and geometric nonlinearities generates the 1/2 resonance phenomena, and geometric nonlinearities result in the 1/3 resonance behavior. Both the imperfection mode and amplitude can affect the resonance response and resonance regions. Moreover, in contrast with the 1/3 subharmonic resonance, geometric imperfections produce greater influence on the 1/2 subharmonic resonance.

Identification of load cells parameters under applying creep and dynamic force for dynamic force calibrations

Many mechanical systems in industry need dynamic force calibration for accurate measurements. This is due to the sensitivity of load cells changed greatly after their natural frequencies. Load cell parameters are used in predicting sensitivity and the frequency range where this cell can be used. These parameters values are constants depending on the load cell’s material and structural design. Consequently, they can be obtained under exerting static, or dynamic force. The aim of this paper is to demonstrate a new study for measuring the load cell parameters accurately under applying long-term creep test. Then, these parameters are compared to those measured while exerting dynamic force of sine mode. A clear difference has been observed between the two measurement methods. Rocking modes, and adapters in the dynamic measurement method affect the parameters accuracy. Generally, static measurement methods are well defined than dynamic in force application and deflection measurement, and less complex.

MHD mode tracking using high-speed cameras and deep learning

We present a new algorithm to track the amplitude and phase of rotating magnetohydrodynamic (MHD) modes in tokamak plasmas using high speed imaging cameras and deep learning. This algorithm uses a convolutional neural network (CNN) to predict the amplitudes of the n = 1 sine and cosine mode components using solely optical measurements from one or more cameras. The model was trained and tested on an experimental dataset consisting of camera frame images and magnetic-based mode measurements from the High Beta Tokamak - Extended Pulse (HBT-EP) device, and it outperformed other, more conventional, algorithms using identical image inputs. The effect of different input data streams on the accuracy of the model’s predictions is also explored, including using a temporal frame stack or images from two cameras viewing different toroidal regions.

Underwater acoustic spiral wave navigation system

A spiral wave navigation beacon is described that creates an outgoing signal with a wavefront that is a diverging spiral cylindrical wave followed by a reference signal of circular wavefront as previously described by Dzikowicz and Hefner in JASA. In this demonstration, the signals are created by driving a cylindrical transducer’s orthogonal sine and cosine modes of vibration in phase quadrature as previously described by Brown and Bachand in JASA. The two dipolar radiation patterns combine to create a helically diverging spiral wavefront that may be used for navigation and communication. The electronic system design and transducer characterization will be presented and are the subject a senior-capstone design project in the College of Engineering at UMass Dartmouth for four of the authors (I.D.B., C.G., K.C., Z.F.). [The project provided a multidisciplinary opportunity in acoustical engineering, instrumentation, calibration, and signal processing and was sponsored by industry (BTech).]

Investigation of Nonthermal Plasma Jet Excitation Mode and Optical Assessment of Its Electron Concentration

The results of a study of a plasma jet of atmospheric-pressure helium driven by a capacitive discharge using sine and pulsed modes of excitation are presented. The homogeneous discharge of a multi-channel plasma jet at gas temperature of 34 °C and helium flow rate of 0.5 L/min was achieved with short pulse excitation. A digital holography method is proposed to estimate a basic plasma parameter, i.e., its electron concentration. An automated digital holographic interferometry set-up for the observation and study of a nonthermal plasma jet in a pulse mode is developed and described. The synchronization features of recording devices with the generation of plasma pulses are considered. The electron concentration of the plasma jet is also estimated. The disadvantages of the proposed technique and its further application are discussed.

Dynamic stability analysis for rotating pre-twisted FG-CNTRC beams with geometric imperfections restrained by an elastic root in thermal environment

This paper deals with the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment. The imperfect beam contains different modes of geometric imperfections such as sine, global, and local modes, and it is restrained by an elastic root. Three types of CNTs distributions including FG-X, UD, and FG-O distributions are considered and the material is temperature-dependent. First, bending–bending coupled governing equations are established through the Hamilton’s principle based on the Euler–Bernoulli beam theory. By setting different parameters, the governing equations can solve the problems of free vibration, buckling, and dynamic stability of the beam. Then, the differential quadrature method (DQM) is employed to get the discrete equations and numerical solutions of the natural frequency, critical buckling load, and instability region. Finally, parametric studies are carried out to present the effects of hub radius, rotating speed, material properties, geometric imperfections, and rigidity of the elastic root on the natural frequencies, critical buckling load, and instability regions. Results show that the elastic root and imperfection mode have obvious influence on the instability regions.

Spatial distributions of the fields in guided normal modes of two coupled parallel optical nanofibers

We study the cross-sectional profiles and spatial distributions of the fields in guided normal modes of two coupled parallel optical nanofibers. We show that the distributions of the components of the field in a guided normal mode of two identical nanofibers are either symmetric or antisymmetric with respect to the radial principal axis and the tangential principal axis in the cross-sectional plane of the fibers. The symmetry of the magnetic field components with respect to the principal axes is opposite to that of the electric field components. We show that, in the case of even -cosine modes, the electric intensity distribution is dominant in the area between the fibers, with a saddle point at the two-fiber center. Meanwhile, in the case of odd -sine modes, the electric intensity distribution at the two-fiber center attains a local minimum of exactly zero. We find that the differences between the results of the coupled mode theory and the exact mode theory are large when the separation distance between the fibers is small and either the fiber radius is small or the wavelength of light is large. We show that a slight difference between the radii of the nanofibers leads to strong asymmetry of the intensity distributions of the guided normal modes.

New tools for theoretical comparison of rectangular and sine wave operation of ion traps, guides and mass filters.

The first completely digital quadrupole mass filter was recently introduced. There is now a need to understand and demonstrate the benefits of digital operation and compare them to the commercial standards. Our work to date has demonstrated that sine and square wave operation are very similar because of their similar stability diagrams and because they use a direct current (DC) potential between the electrode pairs to narrow and limit the mass range. In contrast, rectangular wave-operated digital mass filters and ion traps narrow and limit the stable mass range with the waveform duty cycle without the need for a DC potential. To understand and compare the differences between rectangular and sinusoidal modes of operation, our group has developed new spreadsheet tools that permit calculation of the m/z versus frequency space stability diagrams with the application of a DC potential between the electrode sets for rectangular and sine waveforms, and plots of the pseudopotential well depth against the entire range of stable m/zs for rectangular and sine waveforms. Our spreadsheets were used to make comparisons between fixed-frequency variable-voltage and fixed-voltage variable-frequency modes of operation. They provide a comprehensive companion tool for operating in the laboratory frame and are tunable to the instrument. This manuscript introduces these tools as it compares sine and rectangular wave modes of operation and provides a basis for understanding the advantages and disadvantages of digital operation relative to conventional technology.

Influence of Waveforms on Fatigue Crack Growth Characteristics of Tire Tread Rubber using Finite Element Analysis

ABSTRACT Rubber products are typically subjected to cyclic fatigue loading in service. During prolonged exposure to cyclic loading, damages initiate at intrinsic defect sites at microscopic levels and subsequently propagate, leading to catastrophic failure. Therefore, the material that offers better resistance to fatigue crack growth (FCG) is suitable for a durable product. FCG characteristics of rubber compounds depend on many factors, such as constituent material (rubber, filler, etc.), environment, and operational conditions (loading amplitude, loading pattern, etc.). To simulate the realistic service condition of a product, the choice of loading pattern is a key factor and has emerged as a very important research topic in recent times. The present work focuses on the effect of loading pattern on FCG characteristics of tire tread rubber compounds. In the present study, FCG characteristics of a 100% natural rubber (NR) compound were measured on a tear and fatigue analyzer (TFA, Coesfeld, Germany) using double edge notched pure shear specimen. Fatigue loading was applied using sinusoidal and pulse waveforms over a wide range of tearing energy levels. Pulse mode recorded a very high crack growth rate (∼2 times) compared to sine mode at equivalent peak energy levels. In order to understand the mechanics of the higher crack growth rate in pulse mode, finite element analysis (FEA) of a pure shear specimen was performed wherein FCG experimental conditions were used as boundary conditions. FE analyses were carried out using both linear and nonlinear viscoelastic material models. Nonlinear viscoelastic FEA results revealed that viscous energy dissipation at the crack tip is much lower in the case of pulse mode, which is in support of higher the FCG rate in pulse mode as observed in the experiments.

Initial conditions of the Universe: A sign of the sine mode

In the standard big bang model the universe starts in a radiation dominated era, where the gravitational perturbations are described by second order differential equations, which will generally have two orthogonal set of solutions. One is the so called {\it growing(cosine)} mode and the other is the {\it decaying(sine)} mode, where the nomenclature is derived from their behaviour on super-horizon(sub-horizon) scales. The decaying mode is qualitatively different to the growing mode of adiabatic perturbations as it evolves with time on \emph{super-horizon} scales. The time dependence of this mode on super-horizon scales is analysed in both the synchronous gauge and the Newtonian gauge to understand the true gauge invariant behaviour of these modes. We then explore constraints on the amplitude of this mode on scales between $k \sim 10^{-5}$ Mpc$^{-1}$ and $k \sim 10^{-1}$ Mpc$^{-1}$ using the temperature and polarization anisotropies from the cosmic microwave background, by computing the Fisher information. Binning the primordial power non-parametrically into 100 bins, we find that the decaying modes are constrained at comparable variance as the growing modes on scales smaller than the horizon today using temperature anisotropies. Adding polrisation data makes the decaying mode more constrained. The decaying mode amplitude is thus constrained by $\sim 1/l$ of the growing mode. On super-horizon scales, the growing mode is poorly constrained, while the decaying mode cannot substantially exceed the scale-invariant amplitude. This interpretation differs substantially from the past literature, where the constraints were quoted in gauge-dependent variables, and resulted in illusionary tight super-horizon decaying mode constraints. The results presented here can generally be used to non-parametrically constrain any model of the early universe.

Discovery of a New Song Mode in Drosophila Reveals Hidden Structure in the Sensory and Neural Drivers of Behavior

SUMMARYDeciphering how brains generate behavior depends critically on an accurate description of behavior. If distinct behaviors are lumped together, separate modes of brain activity can be wrongly attributed to the same behavior. Alternatively, if a single behavior is split into two, the same neural activity can appear to produce different behaviors. Here, we address this issue in the context of acoustic communication in Drosophila. During courtship, males vibrate their wings to generate time-varying songs, and females evaluate songs to inform mating decisions. For 50 years, Drosophila melanogaster song was thought to consist of only two modes, sine and pulse, but using unsupervised classification methods on large datasets of song recordings, we now establish the existence of at least three song modes: two distinct pulse types, along with a single sine mode. We show how this seemingly subtle distinction affects our interpretation of the mechanisms underlying song production and perception. Specifically, we show that visual feedback influences the probability of producing each song mode and that male song mode choice affects female responses and contributes to modulating his song amplitude with distance. At the neural level, we demonstrate how the activity of four separate neuron types within the fly’s song pathway differentially affects the probability of producing each song mode. Our results highlight the importance of carefully segmenting behavior to map the underlying sensory, neural, and genetic mechanisms.

Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

We study the stability of a pre-tensioned, heavy cable traveling vertically against gravity at a constant speed. The cable is modeled as a slender beam incorporating rotary inertia. Gravity modifies the tension along the traveling cable and introduces spatially varying coefficients in the equation of motion, thereby precluding an analytical solution. The onset of instability is determined by employing both the Galerkin method with sine modes and finite element (FE) analysis to compute the eigenvalues associated with the governing equation of motion. A spectral stability analysis is necessary for traveling cables where an energy stability analysis is not comprehensive, because of the presence of gyroscopic terms in the governing equation. Consistency of the solution is checked by direct time integration of the governing equation of motion with specified initial conditions. In the stable regime of operations, the rate of change of total energy of the system is found to oscillate with bounded amplitude indicating that the system, although stable, is nonconservative. A comprehensive stability analysis is carried out in the parameter space of traveling speed, pre-tension, bending rigidity, external damping, and the slenderness ratio of the cable. We conclude that pre-tension, bending rigidity, external damping, and slenderness ratio enhance the stability of the traveling cable while gravity destabilizes the cable.

Transient Analysis of a Flexible Pin-on-Disk System and Its Application to the Research Into Time-Varying Squeal

In this paper, a flexible pin-on-disk system is used to simulate how squeal noise can be generated in frictional contact. As the research object, the modeling process and transient simulation method of the flexible pin-on-disk system are introduced. By means of numerical simulation, the time-varying frictional squeal reappears by introducing periodic frictional coefficient generated from rotation. Afterward, the features of time-varying squeal are studied including time-domain features, frequency-domain features, transient deformation features of the disk and the pin on the occurrence of squeal, as well as energy features. Finally, the conception and mathematical expressions of modal contribution factor are defined, and the transient modal contribution factor features of every mode are studied to make clear the function of every mode. The relationship between mode contribution factors and the vibration is revealed. It reveals that modal contribution factors between squeal and not are quite different from each other. On no occurrence of squeal, the modal contribution factors of sine and cosine modes of the disk fluctuate in the way similar to harmonic wave, and the phase difference between the contribution factors of sine and cosine mode with the same nodal circle and the same nodal diameter is 90 deg. During squeal, the coupling mode may play the most important role but not all the time. At any time, the low-frequency modes play the leading role.

Viscoelastic and Orientational Relaxation of Linear and Ring Rouse Chains Undergoing Reversible End-Association and Dissociation

For dilute telechelic linear and ring Rouse chains undergoing reversible end-association and dissociation, the time (t) evolution equation was analytically formulated for the bond vector of the subchain (or segment), u[c](n,t) with n being the subchain index and the superscript c specifying the chain (c = L and R for the linear and ring chains). The end-association of the linear chain (i.e., ring formation) occurs only when the ends of the linear chain come into close proximity. Because of this constraint for the ring formation, the time evolution equation for u[L](n,t) of the linear chain was formulated with a conceptually new, two-step expansion method: u[L](n,t) was first expanded with respect to its sinusoidal Rouse eigenfunction, sin(pπn/N) with p = integer and N being the number of subchains per chain, and then the series of odd sine modes is re-expanded with respect to cosine eigenfunctions of the ring chain, cos(2απn/N) with α = integer, so as to account for that constraint. This formulation allow...

A soil-plate-oscillator apparatus for research projects and student demonstrations

In studying the complex vibration of compliant buried objects in soils, a simplified model apparatus called the “soil-plate-oscillator” (SPO) has been useful in understanding resonant behavior. The SPO is an open column of granular medium supported at the bottom by a thin circular clamped elastic plate. A rigid vertical circular sleeve (sidewall) keeps the soil in a circular column. Two 4.5 in. I.D. plastic PVC closet flanges are used to clamp a 1/8 in. thick acrylic plate. The elastic plate is driven from below by an AC coil located coaxially below a rare earth magnet (fastened to the plate’s underside at the center). An amplified swept sinusoidal chirp drives the coil. A small accelerometer, attached to the magnet, generates a charge amplified signal fed into a spectrum analyzer placed in the swept sine mode. Results for (a) dry sifted masonry sand and (b) 6 mm glass spheres are compared. In both experiments, the resonant frequency versus granular mass loading first decreases (reaching a minimum) and th...

The effect of residual bending on coiled tubing buckling behavior in a horizontal well

This paper builds an analytical model to describe the comprehensive buckling behavior of CT (coiled tubing) with residual bending in a horizontal well. The new model is built on the basis of beam-column theory and solved by the Galerkin method of weighted residuals. The initial configuration of CT with residual bending are assumed to be in two typical trigonometric shapes, sine mode or cosine mode. By using the new buckling equations, critical buckling force and radial contact force are calculated accounting for the residual bending. Axial compressive displacement and maximum bending moment are also calculated. The calculation results show that a CT with residual bending behaves more easily to buckle than a straight CT, and the maximum contact force of CT with residual bending is larger than that of straight CT. As for the two initial trigonometric shapes, the sinusoidal critical buckling force of these two initial modes is almost the same, but CT with initial cosine mode tends to buckle easier than CT with initial sine mode in helical buckling. To verify the proposed model, the results of this paper are compared to Saliés's experimental results, which support the proposed solutions. The comparison between buckling solutions of CT with residual bending and CT without residual bending show that the effect of residual bending on CT cannot be ignored in buckling analysis.

Vibration Control of the Submerged Floating Tunnel under Combined effect of Internal Wave and Ocean Current

For investigating vibration control of the Submerged Floating Tunnel (abbreviated to ‘SFT’) under combined effect of internal wave and ocean current on the basis of inherent characteristics of structure itself and combined loads, the tunnel tube is modeled on a beam with a superposition of simple and rigid beams, that is, the vibration shape is approximated by the combination of a flexural sine mode and a rigid body mode. By establishing combined fluid field in stable stratified ocean, the free vibrations other than the forced vibrations of the SFT induced by combined loads are controlled to achieve the goal of vibration control. Finally, the verification of vibration control measure is conducted by the dynamic response of a proposed project of SFT. The results show that the measure presented in this paper is effective, and the optimal stiffness coefficient of tension leg for vibration control is determined by load period of combined effect of internal wave and ocean current, only several preceding odd multiples of environmental load period to half of vibration period of the SFT should be considered in analyzing the dynamic response because of smaller vibration amplitudes. The conclusions in this paper provide useful discussions for vibration control analysis of the SFT and meaningful references for the study of the complicated periodical ocean environment loads around the SFTs and even other ocean strait-crossing engineering structures.

Fabrication of TiO2 Nanotube Arrays by Rectified Alternating Current Anodization

Anodization is a popular method of preparing TiO2 nanotube array films (TiNTs) by using direct current (DC) power as the driving voltage. In this study, three driving voltage modes, namely, the sine alternating current (sine) mode, the full-wave rectification of sine waves via four diodes (sine-4D, where D means diode) mode, and the DC mode, were used to prepare TiNTs by anodization. At 20 V, TiNTs were formed under sine-4D mode but only irregular porous TiO2 films were formed under DC mode. At 50 V, TiNTs formed under both the sine-4D and DC modes. No TiNTs formed in the sine mode anodization at either 20 or 50 V. Compared with the DC mode, the sine-4D mode required a lower oxidation voltage for TiNT formation, which suggests that sine-4D is an economical, convenient, and efficient driving voltage for TiNT preparation by anodization. The morphologies and structures of TiNT samples anodized at 50 V in the sine-4D and DC modes at different oxidation time (1, 5, 10, 30, 60, and 120 min) were analyzed. TiNT growth processes were similar between the studied modes. However, the growth rate of the films was faster under the sine-4D mode than the DC mode during the first 30 min of anodization.

Modal density and modal distribution of bending wave vibration fields in ribbed plates

Plates reinforced by ribs or joists are common elements in lightweight building structures, as well as in other engineering structures such as vehicles, ships, and aircraft. These structures, however, are often not well suited for simple structural acoustic prediction models such as statistical energy analysis. One reason is that the modal density is not uniformly distributed due to the spatial periodicity introduced by the ribs. This phenomenon is investigated in the present paper, using a modal model of a ribbed plate. The modal model uses the Fourier sine modes, and the coupling between the plate and ribs is incorporated using Hamilton's principle. This model is then used to investigate the modal density of the considered spatially periodic structure, and a grouping of the modes in different dominating directions is proposed. Suggestions are also given regarding how to proceed towards a simplified prediction model for ribbed plates.