External Excitation Frequency Research Articles

Vibration Analysis of Nonlinear Isolator’s Characteristics by ADAMS

A nonlinear spring-mass model is established to study the dynamic characteristics of nonlinear vibration isolator. By use of ADAMS software, the influence of stiffness, foundation displacement excitation and frequency of external excitation on the nonlinear vibration isolation systems are analyzed. Results indicate that the linear vibration system needs 4s to achieve stability, but the nonlinear vibration system only needs 0.1s. The response value increases with the increase of excitation frequency, the response pick value increases by 61.58% and 102.35% and each corresponding stable value increases by 159.35% and 309.87%.

Numerical Simulation of Sloshing Phenomena in Cubic Tank with Multiple Baffles

A two‐phase fluid flow model solving Navier‐Stokes equations was employed in this paper to investigate liquid sloshing phenomena in cubic tank with horizontal baffle, perforated vertical baffle, and their combinatorial configurations under the harmonic motion excitation. Laboratory experiment of liquid sloshing in cubic tank with perforated vertical baffle was carried out to validate the present numerical model. Fairly good agreements were obtained from the comparisons between the present numerical results and the present experimental data, available numerical data. Liquid sloshing in cubic tank with multiple baffles was investigated numerically in detail under different external excitation frequencies. Power spectrum of the time series of free surface elevation was presented with the aid of fast Fourier transform technique. The dynamic impact pressures acting on the normal and parallel sidewalls were discussed in detail.

Theoretical Research of the Active-Type Dynamic Vibration Absorbers

Active-type dynamic vibration absorbers (ADVA) is a kind of damping system, installed an actuators in the dynamic vibration absorbers (DVA). According to the actual needs, vibration energy of the structure is transferred to vibration absorbers actively in the process of structural vibration for the effect of external excitation. Therefore, the energy is decayed or transferred quickly and the structural vibration is controlled. If the nature frequency of additional system is the same as external excitation frequency of the original system, actuators doesn’t start and the whole system behaves the property of DVA (passive damping) .Otherwise, actuators starts, which makes the energy of original structure transfer to the vibration absorbers actively, achieving the purpose of energy consumed and vibration reduced. In this paper the concept of ADVA is proposed, and the working principle of ADVA is theoretically analyzed, furthermore the expressions of the system vibration response and active control coefficient are deduced. The curves of active control force and structure amplitude against incentive frequency are plotted respectively by examples.

Nonlinear dynamics of a three-beam structure with attached mass and three-mode interactions

Nonlinear dynamics of elastic structures with two-mode interactions have been extensively studied in the literature. In this work, nonlinear forced response of elastic structures with essential inertial nonlinearities undergoing three-mode interactions is studied. More specifically, a three-beam structural system with attached mass is considered, and its multidegree-of-freedom discretized model for the structure undergoing planar motions is carefully studied. Linear modal characteristics of the structure with uniform beams depend on the length ratios of the three beams, the mass of the particle relative to that of the structure, and the location of the mass particle along the beams. The discretized model is studied for both external and parametric resonances for parameter combinations resulting in three-mode interactions. For the external excitation case, focus is on the system with 1:2:3 internal resonances with the external excitation frequency near the middle natural frequency. For the case of the structure with 1:2:5 internal resonances, the problem involving simultaneous principal parametric resonance of the middle mode and a combination resonance between the lowest and the highest modal frequencies is investigated. This case requires a higher-order approximation in the method of multiple time scales. For both cases, equilibrium and bifurcating solutions of the slow-flow equations are studied in detail. Many pitchfork, saddle-node, and Hopf bifurcations appear in the amplitude response of the three-beam structure, thus resulting in complex multimode responses in different parameter regions.

Non-linear dynamics of the sandwich double circular plate system

Multi-frequency vibrations of a system of two isotropic circular plates interconnected by a visco-elastic layer that has non-linear characteristics are considered. The considered physical system should be of interest to many researches from mechanical and civil engineering. The first asymptotic approximation of the solutions describing stationary and no stationary behavior, in the regions around the two coupled resonances, is the principal result of the authors. A series of the amplitude–frequency and phase–frequency curves of the two frequency like vibration regimes are presented. That curves present the evolution of the first asymptotic approximation of solutions for different non-linear harmonics obtained by changing external excitation frequencies through discrete as well as continuous values. System of the partial differential equations of the transversal oscillations of the sandwich double circular plate system with visco-non-linear elastic layer, excited by external, distributed, along plate surfaces, excitation are derived and approximately solved for various initial conditions and external excitation properties. System of differential equations of the first order with respect to the amplitudes and the corresponding number of the phases in the first asymptotic averaged approximation are derived for different corresponding multi-frequency non-linear vibration regimes. These equations are analytically and numerically considered in the light of the stationary and no stationary resonant regimes, as well as the multi-non-linear free and forced mode mutual interactions, number of the resonant jumps.

Vibration analysis of a multi-layer beam containing magnetorheological fluid

Magnetorheological (MR) materials exhibit rapid variations in their rheological propertieswhen subjected to varying magnetic field and thus offer superior potential for applicationsin smart structures requiring high bandwidth. MR sandwich structures can applydistributed control force to yield variations in stiffness and damping properties of thestructure in response to the intensity of the applied magnetic field and could thus providevibration suppression over a broad range of external excitation frequencies. This studyinvestigates the properties of a multi-layered beam with MR fluid as a sandwichlayer between the two layers of the continuous elastic structure. The governingequations of a multi-layer MR beam are formulated in the finite element form andusing the Ritz method. A free oscillation experiment is performed to estimate therelationship between the magnetic field and the complex shear modulus of the MRmaterials in the pre-yield regime. The validity of the finite element and Ritzformulations developed is examined by comparing the results from the two models withthose from the experimental investigation. Various parametric studies have beenperformed in terms of variations of the natural frequencies and loss factor asfunctions of the applied magnetic field and thickness of the MR fluid layer for variousboundary conditions. The forced vibration responses of the MR sandwich beam arealso evaluated under harmonic force excitation. The results illustrate that thenatural frequencies could be increased by increasing the magnetic field whilethe magnitudes of the peak deflections could be considerably decreased, whichdemonstrates the vibration suppression capability of the MR sandwich beam.

A Concept for the Characterization and Analysis of the Permeability of Soft Magnetic Thin-Films

A simple approach for accomplishing soft thin film magnetic measurements is evaluated. A modular system based on a pair of HELMHOLTZ coils taken from an existing magnetometer was designed. To characterize it, a quantitative comparison between analytic calculations, Finite Element Methode (FEM) simulation and measurements was conducted. The field uniformity over the measured area of 10 cm along the x-axis was found to be within1.6% of toleration; a sampling rate of 50 kSPS and 50 Hz external magnetic field excitation frequency were used. The system setup and analysis methods were analyzed. The system shows high correlations to other magnetometers, that allows easy calibration with commercial HALL sensors and other magnetometers. The measurement of electroplated NiFe samples fabricated in thin-film technology at the imt demonstrated the validity of the approach.

Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading

This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin’s method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger’s method. An approximate solution technique—the method of multiple scales—is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

Nonlinear Transverse Vibrations and 3:1 Internal Resonances of a Beam With Multiple Supports

In this study, nonlinear transverse vibrations of an Euler–Bernoulli beam with multiple supports are considered. The beam is supported with immovable ends. The immovable end conditions cause stretching of neutral axis and introduce cubic nonlinear terms to the equations of motion. Forcing and damping effects are included in the problem. The general arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated. The method of multiple scales is directly applied to the partial differential equations. Natural frequencies and mode shapes for the linear problem are found. The correction terms are obtained from the last order of expansion. Nonlinear frequencies are calculated and then amplitude and phase modulation figures are presented for different forcing and damping cases. The 3:1 internal resonances are investigated. External excitation frequency is applied to the first mode and responses are calculated for the first or second mode. Frequency-response and force-response curves are drawn.

인공 감정 모델의 설계

인간의 감정을 모방하여 다양한 외부 자극에 대해 인위적으로 감정을 생성하는 인공 감정에 관한 연구가 최근에 시작되어 이루어지고 있다. 그러나 기존의 인공 감정 연구에서는 외부 감정 자극에 대한 감정 상태를 선형적, 지수적으로 변화시킴으로써 감정 상태가 급격하게 변하는 단점을 갖고 있다. 본 논문에서는 외부 감정 자극의 강도와 빈도뿐만 아니라 자극의 반복 주기를 감정 상태에 반영하고, 시간에 따른 감정의 변화를 시그모이드 곡선 형태로 표현하는 인공 감정 생성 모델을 제안한다. 그리고 기존의 감정 자극에 대한 회상을 통해 외부 감정 자극이 없는 상황에서도 감정을 생성할 수 있는 인공감정 시스템을 제안하고 컴퓨터 모의실험 결과를 통해 그 효용성을 보인다. Researches on artificial emotion which generates emotion artificially from various external excitations imitating human emotion has been initiated in recent years. But the conventional studies in which the emotion state is changed exponentially or linearly by external emotion excitation have a drawback that the variation of emotion state is changed rapidly and abruptly. In this paper, we propose an artificial emotion generation model which reflects not only strength and frequency of external emotion excitations but also period of it in the emotion state and represents the emotion state with a sigmoid curve w.r.t. time. And we propose an artificial emotion system which generates emotion at the situation of no external emotional excitations through recollection of past emotional excitations, and show its effectiveness through computer simulation results.

Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps

A frequent goal of the design of vibrating structures is to avoid resonance of the structure in a given interval for external excitation frequencies. This can be achieved by, e.g., maximizing the fundamental eigenfrequency, an eigenfrequency of higher order, or the gap between two consecutive eigenfrequencies of given order. This problem is often complicated by the fact that the eigenfrequencies in question may be multiple, and this is particularly the case in topology optimization. In the present paper, different approaches are considered and discussed for topology optimization involving simple and multiple eigenfrequencies of linearly elastic structures without damping. The mathematical formulations of these topology optimization problems and several illustrative results are presented.

Drift of Levitated/Suspended Body in High-$T_{c}$ Superconducting Levitation Systems Under Vibration—Part II: Drift Velocity for Gap Varying With Time

To study levitation drift further, i.e., the gap between a superconductor and a permanent magnet varying with time in high-Tc superconducting levitation systems, drift velocity is introduced. Based on the numerical simulations of the dynamic response of a levitated body, and according to the essential reasons for drift, the drift velocity is first divided into two regimes: Vff [related to flux flow (FF)] and Vtc [related to flux creep (FC)]. The drift velocity is shown to be mainly dependent upon properties of superconductivity (such as the critical current density of superconductors), initial disturbances, and applied excitations (such as the amplitude and the frequency of external excitations). Furthermore, the corresponding influences of the drift velocities Vff and Vfc have been investigated quantitatively in this paper.

In vivo characterization of attachment safety between cardiac pacing lead and canine heart muscle

ABSTRACT In vivo experiments of screwing the electrode of canine hearts and assigning external excitation on the lead-myocardium interface was carried out to evaluate the lead/myocardium adherence safety. The electrode is specially designed to host a measurement unit of strain gauges. We obtained the lead/heart interactions data from12 dogs under natural heart beating and beating with external excitations. The data recorded from the acute phase and the chronic phase of pulling out pacing leads were compared with each other. The electrode/heart interaction is caused by the heart beat and influenced by the lung breath. This process induced tolerable damage to the lead or myocardium. The interaction decreases as the frequency of external excitations increases. The lead is more likely to be detached from myocardium under higher excitation frequency. At the same implanting sites, safer pacing lead/myocardium attachment can be realized in the chronic tests than in the acute tests.

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.

Experimental and numerical study on tuned liquid dampers for controlling earthquake response of jacket offshore platform

Earthquake loading has to be considered when the offshore platform is constructed in active fault zone. Tuned liquid dampers (TLD) have been proposed to control the dynamic response of structures. Liquid sloshing experiments on cylinder tank show the sloshing happens more seriously when the frequency of external excitation is close to the fundamental sloshing frequency of liquid. Lumped mass method is employed to numerically analyze the controlling earthquake effect on TLD. Based on TLDs the feasibility to control earthquake response of jacket platform is studied and applied to CB32A oil tank platform. Using extra TLDs in CB32A to control the seismic response of the platform is researched by the model test and numerical simulation. Lumped mass method can simulate the behavior of TLD during earthquake very well and gives close numerical results compared with those from model experiments. It has been found that the ratio of the fundamental sloshing frequency of liquid to the natural frequency of platform is the key factor to control earthquake response. The larger ratio of water-mass to platform-mass is also useful to reduce vibration as well.

Modeling, chaotic behavior, and control of dissipation properties of hysteretic systems

In the present work, hysteresis is simulated by means of internal variables. Analytical models of different types of hysteresis loops enable reproduction of major and minor loops and provide good agreement with experimental data. Using an effective algorithm based on the analysis of wandering trajectories, an evolution of chaotic behavior regions of oscillators with hysteresis is presented in various parametric planes. A substantial influence of a hysteretic dissipation value on the form and location of these regions and also restraining and generating effects of the hysteretic dissipation on chaos occurrence are shown. It was demonstrated that for fixed parameters, which govern the shape of a hysteresis loop, the extent of pinch of this loop could be controlled by means of the amplitude and frequency of external periodic excitation.

Influence of Flux Creep on Dynamic Behavior of Magnetic Levitation Systems With a High-<tex>$T_c$</tex>Superconductor

Significant flux creep may be generated in some high-T/sub c/ superconductors with weak pinning, which could yield an influence on the dynamic behavior of a high-T/sub c/ superconductor-magnet levitation system. To investigate this influence, this article presents a numerical analysis of dynamic features of the levitation generated by an interaction between a high-T/sub c/ superconductor (HTSC) and a permanent magnet (PM) after the flux creep in the superconductor is taken into account in a macro-model of superconductivity. The influence is comprehensively displayed by comparing the predictions of dynamic responses of such systems in which the flux creep in the superconductor is and is not taken into account. The obtained results show that whether or not the flux creep results in a noticeable influence to the levitation of superconductor-magnet systems is mainly dependent upon properties of superconductivity and applied excitation, e.g., critical current density of superconductors, and amplitude and frequency of external excitations. When the critical current density is less than 4.5/spl times/10/sup 8/ A/m/sup 2/, and the system is subjected to a periodic excitation, the influence of flux creep should be taken into account in the theoretical analysis.

Fermi-Like Behavior of Weakly Vibrated Granular Matter

Vertical movement of zirconia-yttria stabilized 2 mm balls is measured by a laser facility at the surface of a vibrated 3D granular matter under gravity. Realizations z(t) are measured from the top of the container by tuning the fluidized gap with a 1D measurement window in the direction of the gravity. The statistics obeys a Fermi-like configurational approach which is tested by the relation between the dispersions in amplitude and velocity. We introduce a generalized equipartition law to characterize the ensemble of particles which cannot be described in terms of a Brownian motion. The relation between global granular temperature and the external excitation frequency is established.

Effect of External Excitations on a Nonlinear System with Time Delay

The trivial equilibrium of a two-degree-of-freedom autonomous system may become unstable via a Hopf bifurcation of multiplicity two and give rise to oscillatory bifurcating solutions, due to presence of a time delay in the linear and nonlinear terms. The effect of external excitations on the dynamic behaviour of the corresponding non-autonomous system, after the Hopf bifurcation, is investigated based on the behaviour of solutions to the four-dimensional system of ordinary differential equations. The interaction between the Hopf bifurcating solutions and the high level excitations may induce a non-resonant or secondary resonance response, depending on the ratio of the frequency of bifurcating periodic motion to the frequency of external excitation. The first-order approximate periodic solutions for the non-resonant and super-harmonic resonance response are found to be in good agreement with those obtained by direct numerical integration of the delay differential equation. It is found that the non-resonant response may be either periodic or quasi-periodic. It is shown that the super-harmonic resonance response may exhibit periodic and quasi-periodic motions as well as a co-existence of two or three stable motions.

Some specific features of chaotization of the pulsating barotropic flow over elliptic and axisymmetric sea-mounts

A comparison of the chaotic advection in the barotropic inviscid unidirectional pulsating flow over a sea-mount of axisymmetric and elliptic form is presented. The process of passive markers’ transport from vortical region into the flow-through region is studied. In particular the evolution of the corresponding Poincaré sections with the change of frequency and amplitude of oscillations is presented. An approach to study the mechanism and parameters of chaotic advection in the open systems with finite lifetime trajectories is presented, which is based on the study of the distribution of time necessary to carry markers into the flow-through region. The optimal for chaotic mixing frequency of external excitation is calculated. The results show that in the case of elliptic sea-mount chaotic transport of markers can be more efficient than in the axisymmetric case, and the corresponding phase portraits have significantly different structures.