External Excitation Frequency Research Articles

Transverse vibration analysis of wire rope in deep mining hoisting system

In this paper, the transverse vibration displacement, velocity and acceleration of the wire rope of deep mining hoisting system is acquired by establishing a mathematical model and solving it by Galerkin discrete method. The results show that: for the deep mining hoisting system with hoisting depth of 1000m and hoisting load of 25 t, when there is an excitation with amplitude of 0.002 m and frequency of 10 Hz at one end, the transverse vibration displacement of the wire rope at 200 m is between -0.015 m and 0.015 m, the transverse vibration velocity is between –0.05 m/s and 0.05 m/s, and the transverse vibration acceleration is between –0.5 m/s2 to 0.5 m/s2. Meanwhile, it can be found that different loads, accelerations and mass of wire rope per unit length have little influence on the transverse vibration displacement of the wire rope, but different external excitation frequency have an impact on the transverse vibration displacement of the wire rope. Then the vibration energy and natural frequencies are analyzed. And the maximum vibration energy and 30 natural frequencies are obtained. Finally, the mathematical model is verified through the experiment and the validity of the mathematical model is proved.

Experimental and Numerical Study of Stratified Sloshing in a Tank under Horizontal Excitation

The density-stratified liquids horizontal sloshing was tested on a vibration table, and a series of laboratory experiments have been performed to analyze the influence of the excitation frequency on density-stratified liquids sloshing in a partially filled rectangular tank. The MultiphaseInterFOAM solver in OpenFOAM was employed to simulate two-layer fluids sloshing problems. The numerical results of dynamic pressure were validated against the experimental data, showing that the employed model can accurately simulate the stratified liquids sloshing phenomenon. Effects of two-layer fluids liquid depth ratio and total liquid depth on stratified sloshing characteristics were discussed in detail. The response law of the maximum interfacial wave elevation to external excitation frequency was presented in this study. The evolution of the velocity field of density-stratified liquids sloshing is also studied.

Electrode and electrolyte configurations for low frequency motion energy harvesting based on reverse electrowetting

Increasing demand for self-powered wearable sensors has spurred an urgent need to develop energy harvesting systems that can reliably and sufficiently power these devices. Within the last decade, reverse electrowetting-on-dielectric (REWOD)-based mechanical motion energy harvesting has been developed, where an electrolyte is modulated (repeatedly squeezed) between two dissimilar electrodes under an externally applied mechanical force to generate an AC current. In this work, we explored various combinations of electrolyte concentrations, dielectrics, and dielectric thicknesses to generate maximum output power employing REWOD energy harvester. With the objective of implementing a fully self-powered wearable sensor, a “zero applied-bias-voltage” approach was adopted. Three different concentrations of sodium chloride aqueous solutions (NaCl-0.1 M, NaCl-0.5 M, and NaCl-1.0 M) were used as electrolytes. Likewise, electrodes were fabricated with three different dielectric thicknesses (100 nm, 150 nm, and 200 nm) of Al2O3 and SiO2 with an additional layer of CYTOP for surface hydrophobicity. The REWOD energy harvester and its electrode–electrolyte layers were modeled using lumped components that include a resistor, a capacitor, and a current source representing the harvester. Without using any external bias voltage, AC current generation with a power density of 53.3 nW/cm2 was demonstrated at an external excitation frequency of 3 Hz with an optimal external load. The experimental results were analytically verified using the derived theoretical model. Superior performance of the harvester in terms of the figure-of-merit comparing previously reported works is demonstrated. The novelty of this work lies in the combination of an analytical modeling method and experimental validation that together can be used to increase the REWOD harvested power extensively without requiring any external bias voltage.

Numerical simulation of two-layered liquid sloshing in tanks under horizontal excitations

A numerical model NEWTANK has been developed to study two-layered liquid sloshing under horizontal external excitations. The model solves spatially averaged NSEs on a non-inertial coordinate for external excitations. The two-step projection method is employed in numerical solutions, and the Poisson equation for pressure field is solved by Bi-CGSTAB technique. A multi-layered volume-of-fluid method is proposed to track both free surface and interface between layered liquids simultaneously. In order to validate the accuracy of the model, the simulated results of sloshing responses are compared with linear analytical solutions and experimental data. Good agreements are obtained when response amplitude is within linear regime. However, when nonlinearity becomes strong, deviation from analytical solution will be large due to nonlinear energy transfer from the primary mode to higher modes. Further investigation reveals that for two-layered liquid sloshing, there exist two natural frequencies with the smaller one related to response of lower layer liquid and the larger one upper layer. Therefore, different external excitation frequencies may induce upper-layer resonance, lower-layer resonance or resonances of both layers, each of which exhibits very different patterns of energy transport between modes and layers. Finally, a violent 3-D sloshing with broken free surface and interface is simulated and discussed.

Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations

The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov’s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller’s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.

Asymptotic analysis of self-excited and forced vibrations of a self-regulating pressure control valve

Pressure vibrations in hydraulic systems are a widespread problem and can be caused by external excitation or self-exciting mechanisms. Although vibrations cannot be completely avoided in most cases, at least their frequencies must be known in order to prevent resonant excitation of adjacent components. While external excitation frequencies are known in most cases, the estimation of self-excited vibration amplitudes and frequencies is often difficult. Usually, numerical studies have to be executed in order to elaborate parameter influences, which is computationally expensive. The same holds true for the prediction of forced oscillation amplitudes. This contribution proposes asymptotic approximations of forced and self-excited oscillations in a simple hydraulic circuit consisting of a pump, an ideal consumer and a pressure control valve. Two excitation mechanisms of practical interest, namely pump pulsations (forced vibrations) and valve instability (self-excited vibrations), are analyzed. The system dynamics are described by a singularly perturbed third-order differential equation. By separating slow and fast variables in the system without external excitation, a first-order approximation of the slow manifold is computed. The flow on the slow manifold is approximated by an averaging procedure, whose piecewise defined zero-order solution maps the valve’s switching property. A modification of the procedure allows for the asymptotic approximation of the system’s forced response to an external excitation. The approximate solutions are validated within a realistic parameter range by comparison with numerical solutions of the full system equations.

Nonlinear transverse vibration of a hyperelastic beam under harmonic axial loading in the subcritical buckling regime

Equations of motion of a hyperelastic beam under time-varying axial loading are derived via the extended Hamilton’s principle in this work, where the transverse vibration is coupled with the longitudinal vibration, and nonlinear vibrations of the beam in the subcritical buckling regime are investigated. Complex nonlinear boundary conditions of the beam are determined under some geometric constraints. The critical buckling load is first determined through linear bifurcation analysis. Effects of material and geometric parameters on the forced longitudinal vibration of the beam are numerically investigated. Steady harmonic shapes of the beam at different times under harmonic axial loading are determined. The beam is in the barreling deformation state even when the axial load is not in excess of the critical buckling load. The governing equation for the nonlinear transverse vibration of the beam is obtained by decoupling its equations of motion. Natural frequencies of the free linearized transverse vibration of the beam are studied. By applying the eigenfunction expansion method, the governing equation for the nonlinear transverse vibration of the beam transforms to a series of strongly nonlinear ordinary differential equations (ODEs). Two-to-one internal resonance of the beam is studied by the numerical integration method and its phase-plane portraits are obtained. The harmonic balance method and pseudo arc-length method are used to determine steady-state periodic solutions of the beam from the strongly nonlinear ODEs, and amplitude-frequency responses of the beam are determined. Effects of the external mean axial load, excitation amplitude, and damping coefficient on the amplitude-frequency response of the beam are numerically investigated. Combined effects of the external excitation amplitude and frequency on response amplitudes are also investigated.

Effects of noise and harmonic excitation on the growth of Bacillus subtilis biofilm

We study the dynamic growth behaviors of Bacillus subtilis biofilms by using a stochastic delay differential equation similar to the Mackey-Glass equation. We observe a wealth of dynamic behavior from a mathematical perspective. Firstly, the change of the time delay (i.e. the time that the growth state of the periphery to affect the stress of the interior cells needs and the time required for the stress signal coming from the interior to reach the peripheral cells) and the external excitation (i.e. the change in temperature) frequency will influence the size of Bacillus subtilis biofilm and the collective growth of the cell community. We also found the resonance phenomena in mathematics, which is of great help in understanding the behavior of stress levels in the biofilm periphery. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold reduction. Numerical simulations are carried out to ensure theoretical results. Finally, the effects of noise on stress levels in the biofilm periphery are analyzed and reveal more complex dynamics of the system.

Resonance analysis of a single-walled carbon nanotube

Abstract To improve the reliability of carbon nanotube sensors is one of the key problems when they are applied to engineering practice. Thus, it is of great theoretical significance and practical engineering application value to study the influence of structural parameters and working environment of micro-nanosensor on the dynamic stability and complex behavior of nonlinear system involved in nanotube devices. In this paper, resonance behaviors of a single wall carbon nanotubes (SWCNT) with parametric excitation and external excitation is investigated under quasi-periodic perturbation. The global dynamics of the unperturbed system is explored, then the 1:2 subharmonic resonance and 2:1 superharmonic resonance are analyzed by using the second averaging method with the assumption that the parametric excitation frequency and external excitation frequency are irrational. Subsequently, the global dynamics of the unperturbed averaged systems are investigated by using Poincare compactification theories. The criteria for the existence of homoclinic Smale chaos of the approximate system with periodic perturbation is obtained by using the homoclinic Melnikov method. Finally, the numerical simulations including the bifurcation diagrams, Lyapunov exponent spectrums, various orbits (period-1, period-2, chaotic) and Poincare sections are presented to verify the theoretic results.

Homogenous asymptotic analysis on vibration energy dissipation characteristics of periodical honeycomb reinforced composite laminate filled with viscoelastic damping material

In this paper, free transverse vibration energy dissipation properties of honeycomb reinforced composite laminated structures are studied. By applying the homogenous asymptotic method (HAM) and representative unit cell (RUC) approach, considering the frequency- and temperature-dependent properties of the viscoelastic damping material (VDM), the constitutive equations of the laminated composite structure is obtained. Based on the transverse wave energy propagation and transmission theory in solid structures, the structural loss factor (SLF) of the composite structure can be ultimately determined, which is a frequency- and temperature-dependent variable according to the same properties of VDM’s physical parameters that were applied. Several geometry factors including the thickness of the VDM layer, the width and the inner angle of the honeycomb reinforcements, influence on the vibration energy dissipation characteristics of the composite structure are investigated qualitatively and quantitatively. The results are validated by the Galerkin method based asymptotic approach, which shows consistency with each other, especially when the external excitation frequency larger than 500 Hz in the considered frequency ranges.

Nonlinear dynamic responses of beamlike truss based on the equivalent nonlinear beam model

The main goal of this paper is to develop an equivalent nonlinear beam model (ENBM) for forced vibration analysis of the nonlinear beamlike truss (NBT) and its numerical implementation for describing the nonlinear behaviors of the periodic NBT. For the equivalent dynamic modeling method based on the energy equivalence principle of the truss structures, most of the existing approaches focus on studying the linear characteristic which cannot satisfy the nonlinear dynamic analytical requirement. Here, we extend the equivalent dynamic modeling to nonlinear forced vibration responses of the large NBT civil engineering structure with two pinned ends. We introduce the geometric nonlinearity into the equivalent dynamic model using the von Karman nonlinear strain-displacement relationship to imitate the nonlinear behaviors of the beamlike truss. On the basis of the Hamilton principle, the fourth-order governing partial differential equations of motion of the ENBM are obtained and solved utilizing the Galerkin method. It is shown that the ENBM accurately captures the nonlinear dynamic response of the beamlike truss subjected to external load by using the first four order modes. In order to showcase the efficiency and accuracy of the ENBM, time histories, phase maps and fast Fourier transform frequency spectra are investigated for the NBT and the ENBM under different external excitation magnitudes and frequencies. Comparisons between results of the ENBM and those obtained from the finite element simulations of the NBT show good agreements and identify the periodic motions of them. Furthermore, the effect of the external loading and damping parameters on the frequency-response and force-response curves is discussed. In addition, computing time of the proposed ENBM are compared with that of the full-scale finite element model in ANSYS so as to highlight the significant less computational cost of the equivalent nonlinear dynamic modeling. Particularly, the proposed ENBM can achieve the nonlinear mechanism of the NBT in analytical method and design the low-order control law conveniently.

Stability analysis and optimization of a hybrid rotating machinery support combining journal bearings with viscoelastic supports

Hybrid oil-bearing-viscoelastic-support systems are promising mechanical devices aiming to provide stability and vibration control in rotating systems. This paper proposes a mathematical model that combines analytical calculation of oil-film coefficients, fractional derivative approach for the viscoelastic materials dynamics and generalized equivalent parameters for dynamically modelling multi-DOF supports as stiffness coefficients. This general model accounts double frequency dependence of the hybrid system, i.e., spin speed and external excitation frequency, and temperature dependence of the viscoelastic material. The generalized equivalent parameter approach is fundamental for determining natural frequencies and ordaining the eigenvalues and eigenvectors of a rotating system that combines viscous and viscoelastic behaviors. The simulations show that viscoelastic supports improve the rotating system stability when compared to the system using oil bearings. Furthermore, the optimization can be applied to the hybrid system, improving the vibration suppression characteristics of the device.

A study of the vibration isolation performance of a limited phononic crystal vibration isolator based on local resonance theory

In this study, a limited phononic crystal vibration isolation (LPCVI) model is constructed based on a vibration isolator used in the field of rail transit, and analyses of the characteristics of the bandgap, the vibration isolation effect, and the vibrational energy transfer of the model are presented. In this paper, the Boltzmann integration theory and the Bloch theorem are used to establish a mathematical model that analyzes the band structure based on the viscoelastic damping of the system. Additionally, by comparing the practical finite periodic structure model and the conventional mass-spring-damping vibration isolation model, explicit forms of the vibration isolation coefficients of the models are derived. It is found that when the external excitation frequency is within the forbidden band range, the vibration isolation coefficient of the LPCVI system with a harmonic oscillator is much smaller than that of the vibration isolation system with a general mass-spring. Furthermore, the Newmark-β integration method is adopted to solve the vibration equation of the LPCVI model. The energy input, distribution, and output of the system are obtained when the energy is under excitation in the forbidden band and bandpass frequencies. It is found that the external excitation does both positive and negative works on the vibration isolation system within a certain period under the action of the central frequency excitation of the forbidden band; therefore, the energy cannot be input into the isolation system. This makes it possible to achieve effective vibration isolation at lower frequencies.

Dynamic mechanical properties of architectural coated fabrics under different temperature and excitation frequency

AbstractThe dynamic thermo‐mechanical analysis test is performed on the architectural coating fabric based on the dynamic thermo‐mechanical analyzer (DMA). The effects of excitation frequency, constant temperature, and dynamic temperature on the dynamic mechanical properties of architectural membrane materials are discussed. Through analysis and discussion, the various rules of damping loss factor, loss modulus, and storage modulus of architectural membrane materials in the application temperature and frequency range are obtained. As the frequency of the external excitation force increases, the storage modulus, loss modulus, and loss factor all increase, while the influence of temperature is non‐linear. Under the action of dynamic temperature and constant temperature, the difference between storage modulus and loss modulus is obvious, but the difference of loss factor is small. Due to the anisotropy of the polyester fiber substrate, the damping characteristics of the membrane material in the warp and weft yarns are different regardless of the effect of external excitation frequency or temperature. The discussion in this article provides a theoretical basis for further research on the damping characteristics of membrane materials and the vibration response of membrane structures.

Excitation of the collective states of qubits in a three-qubit system

In the present paper, we have proposed the experimentally achievable method for the characterization of the collective states of qubits in a linear chain. We study a temporal dynamics of absorption of a single-photon pulse by three interacting qubits embedded in a one-dimensional open waveguide. Numerical simulations were performed for a Gaussian-shaped pulse with different frequency detunings and interaction parameters between qubits. The dynamic behavior of the excitation probability for each qubit is investigated. It was shown that the maximum probability amplitudes of excitation of qubits are reached when the frequency of external excitation coincides with the frequency of excitation of the corresponding eigenstate of the system. In this case, the magnitude of the probability amplitude of each qubit in the chain unambiguously correlates with the contribution of this qubit to the corresponding collective state of the system, and the decay of these amplitudes is determined by the resonance width arising from the interaction of the qubit with the photon field of the waveguide. Therefore, we show that the pulsed harmonic probe can be used for the characterization of the energies, widths, and the wave functions of the collective states in a one dimensional qubit chain.

Nonlinear vibration of axially moving simply-supported circular cylindrical shell

This paper investigates the nonlinear free and forced vibration of axially moving simply-supported thin circular cylindrical shells in the sub-harmonic region, considering the effect of viscous structure damping. Motion equations of axially moving circular cylindrical shells in cylindrical coordinates are derived with the aid of the Hamilton principle and employing the Donnell–Mushtari nonlinear shells’ theory. Three nonhomogeneous nonlinear partial differential equilibrium equations concerning displacements across the three directions of cylindrical coordinate are reduced to two equations as a result of using the definition of the airy function. The particular and private solution of airy stress function is obtained utilizing the assumption of the form of the displacement in the radial direction based on the simply-supported boundary conditions and combination of axisymmetric and asymmetric driven and companion modes. By gaining the airy function, the third motion equation is discretized using the Galerkin method into the set of coupled nonlinear nonhomogeneous ordinary differential equations. The perturbation method and Runge–Kutta 4th order are employed as a semi-analytical and a numerical solution method, which in practice leads to the prediction of the nonlinear frequencies and amplitudes of various modes of vibration at different velocities and external excitation fluctuation domain and frequency. The bifurcation analysis of the velocity and external excitation parameters in sub-harmonic regions shows the changes in the instability condition of the system. It causes the appearance of the pitchfork bifurcation and the Neimark–Sacker bifurcation points. The accuracy of both, the direct normal form and numerical method results are compared against each other and validated in the particular case in the absence of the velocity with available data. The system would be more stable at a higher speed near 1:1 external resonance due to the activation of more asymmetric vibration modes and the growth of the nonlinear softening characteristic in the absence of companion vibration modes.

A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners

Manufacturing new Magnetic Resonance Imaging (MRI) scanners represents a computational challenge to industry, due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of user-friendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where high-dimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time. This paper presents a novel Proper Generalised Decomposition (PGD) based metamodel for the analysis of electro-magneto-mechanical interactions in the context of MRI scanner design, with three distinct novelties. First, the paper derives, from scratch, a five-dimensional parametrised offline solution process, expressed in terms of (axisymmetric) cylindrical coordinates, external excitation frequency, electrical conductivity of the embedded shields and strength of the static magnetic field. Second, by exploiting the staggered nature of the coupled problem at hand, an efficient sequential PGD algorithm is derived and compared against a previously published monolithic PGD algorithm. As a third novelty, the paper draws some interesting comparisons against an alternative tailor-made ROM technique, where the electromagnetic equations are solved using a Proper Orthogonal Decomposition model. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and potential of the considered approach, especially in terms of cost reduction.

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

http://mts.hindawi.com/update/) in our Manuscript Tracking System and after you have logged in click on the ORCID link at the top of the page. This link will take you to the ORCID website where you will be able to create an account for yourself. Once you have done so, your new ORCID will be saved in our Manuscript Tracking System automatically."?>In this paper, the parametric dynamics of bidirectional functionally graded (BDFG) beams subjected to a time-dependent axial force are studied. The material properties of beam which vary along both thickness and axial directions follow the power law, and four different distribution patterns are considered. The coupled nonlinear partial differential equations describing the longitudinal-transverse displacements and the shear deformation are derived using Hamilton’s principle based on Timoshenko beam theory. The Galerkin scheme is employed to discrete the continuous model resulting in a multiple degree-of-freedom system, namely, the reduced order model. The nonlinear parametric response of the beam is obtained by solving the discrete system numerically, and the frequency- and force-response curves are constructed by tracing the period motion using the pseudoarclength continuation technique. Numerical results are presented to examine the effects of system parameters, e.g., gradient parameters, magnitude and frequency of external excitation, and damping coefficients. Cyclic-fold bifurcation and branch points of the period motion are spotted in parametric resonance of the BDFG beam. Results show that the asymmetrical material distribution in thickness direction of beam leads to the asymmetry of dynamic responses. Moreover, the gradient of material in axial direction has more significant effect on the dynamic features of BDFG beam than that in the thickness direction.

Bursting oscillations with boundary homoclinic bifurcations in a Filippov-type Chua’s circuit

A modified version of the typical Chua’s circuit, which possesses a periodic external excitation and a piecewise nonlinear resistor, is considered to investigate the possible bursting oscillations and the dynamical mechanism in the Filippov system. Two new symmetric periodic bursting oscillations are observed when the frequency of external excitation is far less than the natural one. Besides the conventional Hopf bifurcation, two non-smooth bifurcations, i.e., boundary homoclinic bifurcation and non-smooth fold limit cycle bifurcation, are discussed when the whole excitation term is regarded as a bifurcation parameter. The sliding solution of the Filippov system and pseudo-equilibrium bifurcation of the sliding vector field on the switching manifold are analysed theoretically. Based on the analysis of the bifurcations and the sliding solution, the dynamical mechanism of the bursting oscillations is revealed. The external excitation plays an important role in generating bursting oscillations. That is, bursting oscillations may be formed only if the excitation term passes through the boundary homoclinic bifurcation. Otherwise, they do not occur. In addition, the time intervals between two symmetric adjacent spikes of the bursting oscillations and the duration of the system staying at the stable pseudonode are dependent on the excitation frequency.

Numerical researches of three-dimensional nonlinear sloshing in shallow-water rectangular tank

The Boussinesq-type equations in terms of velocity potential are adopted for the solutions of three-dimensional nonlinear sloshing motions in a shallow-water rectangular tank. The total velocity potential is divided into two parts: a particular solution and the rest which is calculated by the Boussinesq-type equations. Particular solutions of six degrees of freedom motions are constructed. The fully nonlinear free surface boundary conditions are satisfied and finite difference scheme is adopted for the spatial derivatives. The free surface profiles in tank with external excitation frequencies close to the first natural frequency are presented. Numerical results demonstrate that the Boussinesq-type equations with particular solutions can accurately model nonlinear sloshing waves in shallow-water rectangular tank.