Frequency Of First Mode Research Articles

Predictions of the design decisions for vehicle alloy wheel rims using neural network

The weight and modal performance of the vehicle wheels are two essential factors that affect the driving comfort of a vehicle. The main objective of this study is to present an efficient approach to reduce the weight and enhance the modal performance of the wheel by reducing the design time and computational cost. The alloy wheel rim is often used for lightweight wheel design. In this study, an approach is presented for the lightweight design of alloy wheel rims. An intelligent approach based on neural networks (NNs) is introduced to predict the optimum design parameters of the wheel rim during the wheel design phase and to improve the wheel optimization process. The Latin hypercube and Hammersley designs of the experimental methods were used to obtain a training dataset with finite element analysis. The NN and multiple linear regression (MLR) models were trained to predict the weight, first-mode frequency, and displacement values. A multi-objective genetic algorithm was employed to optimize the design decisions based on the predicted values. It was used to compute the optimum results with both the NN and MLR models for a better prediction accuracy of the wheel rim design parameters. The proposed approach allows designers to optimize design decisions and evaluate design modifications during the early stages of the wheel development phase. The surrogate-based optimization method plays an important role in the wheel rim optimization process, particularly when the optimization model is established based on computationally expensive finite element simulations, testing, and prototypes. The results show the effectiveness of the NN-combined genetic optimization approach in predicting the responses and optimizing the design decisions for the alloy wheel rim design by reducing engineering time and computational cost.

Experimental study on seismic vibration control of an offshore wind turbine with TMD considering soil liquefaction effect

Wind energy is clean and sustainable. Taiwan is establishing offshore wind farms using wind turbines in the Taiwan Strait. However, these are located in an earthquake-prone area with sandy seabed conditions. To ensure their safety and reliability, the turbines’ support structure must be protected against wind, waves, and seismic loads. Tuned mass dampers (TMDs) are commonly employed to reduce structural vibrations. A TMD is more simply incorporated into turbine structures than are other energy dissipation devices. In this study, a 1:25-scale test model with a TMD was constructed and subjected to shaking table tests to experimentally simulate the dynamic behavior of a typical 5-MW wind turbine with a jacket-type support structure and pile foundation. The scaled-down wind turbine model has a nacelle without rotating blades; therefore, the aerodynamic and rotational effects due to the rotating blades were ignored in this study. A large laminar shear box filled with saturated sandy ground was used to simulate the typical seabed conditions of Taiwanese offshore wind farms. The TMD system was designed to be tuned the first-mode frequency of the test model. Two ground accelerations, selected by considering wind farm site condition and near-fault characteristics, were used for excitation in the test. The responses of the test model with and without the TMD system were compared, and the influence of soil liquefaction on the effectiveness of TMD vibration control was addressed.

Frequency domain analysis-based optimal configurations and energy dissipation performance of combined damped outrigger systems

This paper investigates optimal configurations of combined damped outrigger systems (CDOs) using the newly proposed frequency domain analysis-based simplified models. The CDOs are constructed by the viscous-damper outrigger and the buckling-restrained-brace outrigger arranged vertically in different heights. This paper includes two types, CDO_11 (buckling-restrained-brace outrigger above viscous-damper outrigger), and CDO_22 (viscous-damper outrigger above buckling-restrained-brace outrigger). First, the paper proposes a simplified analytical model of a general outrigger system to derive a theoretical solution for the dynamic response of the structure in the time domain. Then, the solution in the time domain is transformed to the frequency domain via the Laplace transformation. The first-mode frequency response function is used to obtain the optimal locations for different types of outrigger systems. Finally, this paper compares the vibration characteristics of the outrigger systems in terms of the amplitude, phase, and variance of the response.

Proposal of lateral forces for capacity design of controlled rocking steel cores considering higher mode effects

Controlled rocking steel cores (CRSCs) may suffer progressive collapse because of inadequate structural design and loss of re-centering action. While the CRSCs displace in the first-mode frequency, the demands of their members are strongly affected by higher modes. Conventional lateral load distributions, such as the uniform and inverted triangular, cannot predicate the design forces of CRSCs. This paper proposes new lateral loads for the design of CRSCs. Continuum cantilever beam analogy is utilized to formulate the higher-mode contribution. The application of the lateral loads is validated through illustrative examples of low- and mid-rise CRSCs. Results supported by nonlinear time response analyses demonstrate the effectiveness of proposed formulae for reliable estimation of seismic demands. The proposed lateral forces are readily applicable in commercial software without gap modeling at the base boundary conditions of CRSCs.

Mode switching and standing-travelling waves in slug flow-induced vibration of catenary riser

An experiment in a small-scale air-water test loop is performed to investigate the flow-induced vibration behaviors of a flexible catenary riser conveying slug flow over a wide range of the gas-to-liquid flow rate ratios from 1.0 to 4.5. The clamped-clamped riser model has an inner diameter of 4 mm and an aspect ratio with the length over the inner diameter of about 360. The non-intrusive high-speed cameras are employed to simultaneously capture the catenary riser dynamics and the internal unsteady slug flow characteristics. The space-time varying features of the slug flow-induced vibration are presented and discussed in terms of the response amplitudes, frequencies, modal components, and associated flow-induced forces. Slug flow properties including the translational velocities, lengths, fluctuation frequencies and pressure changes are reported. When increasing the ratio of the gas-to-liquid flow rates, experimental results highlight how a variation of the slug length and frequency contributes to a mode-switching phenomenon over time. This switching from the dominant first-mode frequency to the second-mode frequency leads to the associated transition from the standing wave to the travelling wave of the catenary riser response. The response amplitudes are amplified by the increased translational velocity and slug length, entailing the increased flow-induced momentum and gravitational forces, as the gas-to-liquid flow rate ratio is increased. Consequently, higher vibration modes participate into the riser dynamics exhibiting a strong multi-mode competition.

Natural oscillations of a sessile drop on flat surfaces with mobile contact lines

Oscillation of sessile drops is important to many applications. In the present study, the natural oscillation of a sessile drop on flat surfaces with free contact lines (FCL) is investigated through numerical and theoretical analysis. The FCL condition represents a limit of contact line mobility, i.e. the contact angle remains constant when the contact line moves. In the numerical simulation, the interfaces are captured by the volume-of-fluid method and the contact angle at the boundary is specified using the height-function method. The oscillation frequencies for sessile drops with FCL are mainly controlled by the contact angle and the Bond number and a parametric study is carried out to characterize their effects on the frequencies for the first and high-order modes. Particular attention is paid to the frequency of the first mode, since it is usually the dominant mode. An inviscid theoretical model for the first mode is developed. The model yields an explicit expression for the first-mode frequency as a function of the contact angle and the Bond number, with all parameters involved fully determined by the equilibrium drop theory and the simulation. The predicted frequencies for a wide range of contact angles agree very well with the simulation results for small Bond numbers. The frequencies for both the first and high-order modes decrease with the contact angle and increase with the Bond number. For the high-order modes, the frequencies for different modes generally scale with the Rayleigh frequencies. The scaling relation performs better for small Bond numbers and large contact angles. A simple model is proposed to predict the frequencies of high-order modes for large contact angles and a good agreement with the simulation results is observed.

Estimation of nighttime ionospheric D-region parameters using tweek atmospherics observed for the first time in the North African region

Dispersive wave modes called tweek atmospherics produced by lightning strokes were observed using Stanford University designed AWESOME VLF receiver system installed at the University of Tunis El Manar, Tunisia (Geog. lat. 36.50° N; lon. 10.08° E). About 84 tweek atmospherics were analyzed during geomagnetically quiet days to provide important clues for estimating the effective ionospheric reflection height and electron density using the cut-off frequency of first modes. Variations of nighttime Wait ionospheric parameters (h′ and β) have been studied using tweeks observed for the first time at the low latitude station in the North African region. The distance of the lightning located in a range of 500–5000 km and the accuracy obtained by single-site technique had been estimated by a comparison with independent data from the World-Wide Lightning Location Network (WWLLN).

Influence of glow discharge on evolution of disturbance in a hypersonic boundary layer: The effect of first mode

The evolution of the first- and second-mode instabilities in a hypersonic flat plate boundary layer is investigated. Experiments are conducted in a Mach 6.5 quiet wind tunnel using particle image velocimetry, Rayleigh-scattering flow visualization, and schlieren methods. Glow discharge is introduced as an artificial disturbance. The results show that an artificially introduced disturbance in the first-mode frequency range can excite a specific second-mode wave that is one of the high-order harmonics of the added disturbance. For the first time, we find a clear harmonic relationship between the first- and second-mode waves, as well as the phase lock phenomenon between them.

Effect of glow discharge on hypersonic flat plate boundary layer

Glow discharge is introduced as an artificial disturbance to investigate the evolution of first- and second-mode instabilities in a hypersonic flat plate boundary layer. Experiments are conducted in a Mach 6.5 quiet wind tunnel using Rayleigh scattering visualization and particle image velocimetry (PIV). Detailed analysis of the experimental observations is provided. It is found that the artificially introduced 17 kHz disturbance, which belongs to the first-mode frequency band, can effectively enhance first-mode waves. Moreover, it can enhance second-mode waves even more intensely. Possible mechanisms to explain this phenomenon are discussed.

NATURAL FREQUENCY ANALYSIS OF LAYERED FUNCTIONALLY GRADED BEAMS

In this numerical study, natural frequency analysis of layered functionally graded beams in the thickness direction under clamped-free boundary condition was investigated using finite element program ANSYS. The layer arrangements were performed according to Taguchi L9 (3*3) orthogonal array. Mechanical properties of the layers made of different volume fractions of Ti-6Al-4V and ZrO2 materials was assumed as control factors. In order to determine the optimum layers and their levels, signal-to-noise (S/N) analysis is used. Significant layers and their percent contributions on the natural frequency are carried out using Analysis of Variance (ANOVA). In addition, the effects of the boundary conditions (B.C.) such as clamped-free (C-F) and clamped-clamped (C-C) and positions of the optimum layers were evaluated. According to results evaluated, maximum natural frequency for first mode were found to be top and bottom layers with metal-rich and middle layer with ceramic-rich. The most effective layers on the responses was obtained as Layer1 with 48.45%, Layer2 with 16.16% and Layer3 with 34.98%. Layer arrangements play important role on the natural first mode frequency.

Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth-order Runge–Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender pipes.

Three-dimensional dynamics of supported pipes conveying fluid

This paper deals with the three-dimensional dynamics and postbuckling behavior of flexible supported pipes conveying fluid, considering flow velocities lower and higher than the critical value at which the buckling instability occurs. In the case of low flow velocity, the pipe is stable with a straight equilibrium position and the dynamics of the system can be examined using linear theory. When the flow velocity is beyond the critical value, any motions of the pipe could be around the postbuckling configuration (non-zero equilibrium position) rather than the straight equilibrium position, so nonlinear theory is required. The nonlinear equations of perturbed motions around the postbuckling configuration are derived and solved with the aid of Galerkin discretization. It is found, for a given flow velocity, that the first-mode frequency for in-plane motions is quite different from that for out-of-plane motions. However, the second- or third-mode frequencies for in-plane motions are approximately equal to their counterparts for out-of-plane motions, keeping almost constant values with increasing flow velocity. Moreover, the orientation angle of the postbuckling configuration plane for a buckled pipe can be significantly affected by initial conditions, displaying new features which have not been observed in the same pipe system factitiously supposed to deform in a single plane.

An experimental and theoretical investigation into multimode machine tool vibration with surface generation in flycutting

Relative vibration between the cutting tool and the workpiece plays an important role in the surface generation in ultra-precision diamond machining. High-frequency vibration of the cutting tool has important influence on the surface roughness error, while the low-frequency vibration of machine tool structure affects the figure error. The previous related researches mainly focus on the first-mode frequency vibration of the machine tool. However, its multimode frequency vibration is rarely discussed. In this article, the multimode frequency vibration of the machine tool and its influences on the surface generation in flycutting are studied. The experimental results have been found to agree well with the simulation results.

Slosh Suppression for Infinite Modes in a Moving Liquid Container

Control of a moving liquid container is challenging because of unwanted transient and residual slosh. Although significant progress has been achieved at eliminating the fundamental sloshing mode, less success has been achieved with designing a controller to suppress slosh for an infinite number of modes. This study presented two methods to reduce an infinite number of sloshing modes in a moving liquid container. The first method is command smoothing to eliminate slosh by using the first-mode frequency. The second one is a combined input-shaping and command-smoothing architecture. The input shaper reduces slosh for the first mode, while the command smoother suppresses slosh for the third and higher modes. Both the command smoothing and the combined control scheme eliminate the transient and residual slosh to a very low level. However, the rise time of the combined controller is shorter than that of the command smoother. Simulations of a large range of motions are used to analyze liquid sloshing dynamics by using the proposed methods. Experimental results obtained from a moving container validate the simulated dynamic behavior and the effectiveness of the methods.

発電式動吸振器による標識柱の振動低減

The authors propose an absorber that generates electrical power in order to not only suppress vibration but also get electrical energy when many traffic signal poles are oscillated by wind, traffic turbulence. The absorber consists of a displacement magnifying mechanism by using levers, solenoid coils and rare-earth magnets. It is useful for small deformation between a beam and a column of the traffic pole. Vibration modes of the pole are analyzed by using FEM, and then a small scale model of the traffic pole is built up. The small scale model has 2.7 m high, consists of a steel column and a cantilever beam due to rescale about 1/3 times of a real scale model, and the natural frequency of first mode is arranged to 3.5 Hz. Trial absorber is manufactured and a damping force, which is caused by the coils crossing magnetic field, is adjusted. Dynamic characteristics of the trial absorber are measured by a shaking actuator. In order to confirm vibration reduction and energy conversion, harmonic vibration test of small scale model when the trial absorber is installed is carried out by using a shaking table. The experimental results of the harmonic responses are compared with the calculated results which are derived by FEM. Effect of vibration suppression and efficiency of generating electrical power are evaluated experimentally and numerically.

Eigenvalues and modes of distributed-mass symmetric multispan bridges with restrained ends for seismic response analysis

Closed-form solutions are developed for the elastic response of symmetric bridges, continuous over two, three or four spans, for unidirectional earthquake perpendicular to the deck, i.e., in the transverse or the vertical direction. The ends of the deck are restrained along the earthquake component, but free to rotate within the plane of bending. The mass and flexural rigidity of the deck are uniform along its length and modelled as continuous. The piers may support the deck through flexible bearings or are rigidly connected to it, in which case a lumped mass is considered at the connection. For each bridge geometry a nonlinear transcendental equation is derived for the modal circular frequency and solved numerically. Closed formulas are given for participation factors, participating masses, the curvature and end slope of the deck and the end reactions. The frequency and cumulative participating mass of the important modes are plotted as a function of the dimensionless total stiffness of the piers. Parametric analyses are presented for the mass of the piers, the location of the intermediate piers and their relative stiffness. They suggest that the eigenvalues are close to those of a simply supported beam with uniformized transverse restraint and mass, except for relatively high pier stiffness and for a single pier of medium stiffness. Even if this approximation is made, modal shapes and elastic forces or deformations of the deck may differ significantly from those of a simply supported beam with uniformized parameters and should be calculated with the closed-form expressions presented. The analytical first-mode frequency and the one from the single-mode method of the AASHTO code in general agree very well, but the first mode participating masses from the two methods may differ.

Nonlinear Dynamics of an Euler-Bernoulli Beam with Parametric and Internal Resonances

The nonlinear transverse vibration of a simply-supported travelling Euler-Bernoulli beam subjected to principal parametric resonance in presence of internal resonance is investigated. The variable velocity of beam is assumed to be comprised of a harmonically varying component superimposed over a mean value. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times the natural frequency of first mode for a range of mean velocity of the beam, resulting in a three-to-one internal resonance. The method of multiple scales (MMS) is directly applied to the governing nonlinear integral-partial-differential equations and the associated boundary conditions. This results in a set of first order ordinary differential equations governing the modulation of amplitude and phase of the first two modes, which are analyzed numerically for principal parametric resonance of first mode. The nonlinear steady state response along with the stability and bifurcation of the beam are investigated. The dynamical behaviour of the system is observed in terms of periodic, quasiperiodic and chaotic responses, showing the influence of internal resonance.

Structure design and mechanical measurement of inflatable antenna

This paper deals with the initial shape analysis, cutting-pattern analysis, surface accuracy measurement and modal testing of high-precision inflatable antennas reflectors that are intended for spaceflight applications. The initial shape analysis method, formulated on the basis of membrane theory and elastic mechanics, determines the required as-manufactured shape of the reflective surface of the antenna reflector. On the other hand, the cutting-pattern analysis method, with its formulation based on spring-mass representations, numerically calculates the required cutting pattern of the planar membrane gores that are to be assembled to form the 3-dimensional reflective surface. To validate the effectiveness of the proposed analysis methods, a 3.2-m antenna reflector model was designed, manufactured, and assembled for ground demonstration and testing. The reflective surface accuracy of this demonstration reflector model was measured by a photogrammetric measuring system. Shape adjustments of the reflective surface were performed by systematically adjusting the tension in the cables that were used to mount the reflector to its support structure. It was found that the reflective surface accuracy of the reflector model, as defined by its RMS error from a best-fit parabolic shape, was less than 1mm. In addition, dynamic and RF tests were also performed on the demonstration reflector model. The test results indicated that the first-mode frequency of the reflector model agreed well with the corresponding analytical prediction, and its radiation pattern was also well focused.

Experimental measurement of the surface velocity field in an externally induced sloshing tank

In this work, the unsteady free-surface velocities during the surge motion of a liquid tank are determined through experimental investigation. A new experimental approach has been discussed for capturing the free surface of the liquid during tank excitation. In order to avoid violent motion in the tank, the tank is excited with a low frequency (up to 47 per cent of the first-mode frequency) which leads to low-steepness waves in the container. When a container oscillates at a low excitation frequency, the wave amplitude A is usually small. Since the wave steepness E is directly proportional to the wave amplitude, the wave steepness is also small during the motion. The planar two-dimensional particle image velocimetry technique is used to calculate the U and V velocities of the free surface, while the interface location technique is used to determine the vertical velocity W of the interface. The velocities are measured for various liquid fill levels and excitation frequencies. The average line velocity Vw near the tank wall and the average line velocity Vc near the velocity tank centre with respect to time are estimated and compared with the tank velocity. The observed flow patterns indicate the presence of complicated flows during the sloshing experiment.

Two-to-one internal resonance in microscanners

To realize large scanning angles, torsional microscanners are normally excited at their natural frequencies. Usually, a bias DC voltage is also applied to scan around a desired nonzero tilt angle. As a result, a deep understanding of the mirror’s response to a DC-shifted primary resonance excitation is imperative. Along these lines, we use the method of multiple scales to obtain a second-order nonlinear approximate analytical solution of the mirror steady-state response. We show that the response of the mirror exhibits a softening-type behavior that increases as the magnitude of the DC component increases. For a given mirror, we can also identify a DC voltage range wherein the mirror exhibits a two-to-one internal resonance between the first two modes; that is, ω 2≈2ω 1. To analyze the mirror behavior within that range, we first treat the case where the excitation frequency is near the first-mode frequency; that is, Ω≈ω 1. Then we treat the case where the excitation frequency is near the second-mode frequency; that is, Ω≈ω 2. We analyze the stability of the response and compare the analytical results to numerical solutions obtained via long-time integration of the equations of motion. We show that, due to the internal resonance, the mirror exhibits complex dynamic behavior characterized by aperiodic responses to primary resonance excitations. This behavior results in undesirable oscillations that are detrimental to the mirror performance, namely bringing the target point in and out of focus and resulting in distorted images.