Vibration energy harvesting for low frequency using auto-tuning parametric rolling pendulum under exogenous multi-frequency excitations

An electromagnetic parametrically excited rolling pendulum energy harvester with self-tuning mechanisms subject to multi-frequency excitation is proposed and investigated in this paper.The system consists of two uncoupled rolling pendulum.The resonance frequency of each the rolling pendulum can be automatically tuned by adjusting its geometric parameters to access parametric resonance.This harvester can be used to harvest the energy at low frequency.A prototype is developed and evaluated.Its mathematical model is derived.A cam with rolling follower mechanism is employed to generate multi-frequency excitation.An experimental study is conducted to validate the proposed concept.The experimental results are confirmed by the numerical results.The harvester is successfully tuned when the angular velocity of the cam is changed from 1.149 to 1.236 Hz.

Parametric Vibration of Submerged Floating Tunnel Tether Under Random Excitation

For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.

Parametric Vibration Analysis of Submerged Floating Tunnel Tension Legs

According to the characteristics of submerged floating tunnel anchored by tension legs,simplifying the tube as point mass and assuming that the tension leg is a nonlinear beam model hinged at both ends,the nonlinear vibration equation of the tension leg is derived.The equation is solved by the Galerkin method and Runge Kutta method.Subsequently,numerical analysis of typical submerged floating tunnel tension leg is carried out.It is shown that,the parametric vibration response of the submerged floating tunnel tension leg is related to the amplitude and frequency of the end excitation.Without considering axial resonance and transverse resonance,it is reasonable that higher order modes are abandoned and only the first three modes are considered.The axial resonance amplitude of the second or third order mode is equivalent to the first order mode axial resonance amplitude,which should not be ignored.

Parametric vibrations in offset printing units

Vibrations of offset printing presses are serious problem, which cause many difficulties while printing and impair quality of the prints. The biggest problem lies in construction of printing unit. It mainly consists of three cylinders, but two of them are in a direct contact generate undesired vibrations. Construction of the cylinders makes that stiffness of the unit varies periodically while printing. In this paper model of offset printing unit is presented. The model is described by the system of two parametric differential equations. Computer simulations of the behaviour of the printing unit have been performed. Conditions in which parametric resonance appears are also appointed here.

Semiactive variable stiffness control for parametric vibration of cables

In this paper, a semiactive variable stiffness （SVS） device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented. The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect. From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.

Investigation for parametric vibration of rolling mill

The vibration unsteady condition of rolling mill caused by flexural vibration of strip has been investigated. The parametric flexural vibration equation of rolled strip has been established. The parametric flexural vibration stability of rolled strip has been studied and the regions of stability and unstability have been determined based on Floquet theory and perturbation method. The flexural vibration of strip is unstable when the frequency of variable tension is two times as the natural frequency of flexural vibration strip. The characteristic of current in a temp driving motor’s main loop has been studied and tested, it has been proved that there are 6 harmonic component and 12 harmonic component in main loop of driving motor electricity. The vertical vibration of working roller has been tested, the test result approves that the running unsteady is caused by parametric vibration. It attaches importance to the parametric vibration of rolling mill.

Parametric vibration stability and active control of nonlinear beams

The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic aonlineax equation of motion with damping is established by employing Hamilton＇s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve axe analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

Parametric CAD Modelling of Aircraft Wings for FEA Vibration Analysis

Excessive vibration of aircraft wings during flight is harmful and may cause propagation of existing cracks in the material, leading to catastrophic failures as a result of material fatigue. This study investigates the variations of modal characteristics of aircraft wings with respect to changes in the structural configurations. We develop parametric Computer-Aided Design (CAD) models to capture new design intend on the aircraft wing architectures. Subsequent Finite Element Analysis (FEA) based vibration analysis is performed to study the effects of architecture changes on the wing’s natural frequencies and mode shapes. It is concluded that the spar placement and the number of ribs have significant influence on the wing’s natural vibration properties. Integrating CAD modelling and FEA vibration analysis enables designers to develop alternative wing architectures to implement design requirements in the preliminary design stage.

Parametric Vibration and Vibration Reduction of Cables in Cable-stayed Space Latticed Structure

Mechanical model and vibration equation of a cable in cable-stayed space latticed structure (CSLS) under external axial excitation were founded.Determination of the mass lumps and natural frequencies sup- plied by the space latticed structure (SLS) was analyzed.Multiple scales method (MSM) was introduced to analyze the characteristics of cable's parametric vibration,and the precise time-integration method (PTIM) was used to solve vibration equation.The vibration behavior of a cable is closely relative to the frequency ratio of the cable and SLS.The cable's parametric vibration caused by the external axial excitation easily occurs if the frequency ratio of the cable and SLS is in a certain range,and the cable's vibration amplitude varies greatly even if the initial disturbance supplied by SLS changes a little.Furthermore,the mechanical model and vibration equation of the composite cable system consisting of main cables and assistant cables were studied. The parametric analysis such as the pre-tension level and arrangement of the assistant cables was carried out. Due to the assistant cables,the single-cable vibration mode can be transferred to the global vibration mode, and the stiffness and damping of the cable system are enhanced.The natural frequencies of the composite cable system with the curve line arrangement of assistant cables are higher than those with the straight-line arrangement and the former is more effective than the latter on the cable's vibration suppression.

In-plane Auto-Parametric Vibration of Inclined Cables under Random Transverse Excitation

In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.

Instability Assessment of Deep-Sea Risers Under Parametric Excitation

This study deals with the nonlinear dynamic response of deep-sea risers subjected to parametric excitation at the top of a platform. As offshore oil and gas exploration is pushed into deep waters, difficulties encountered in deep-sea riser design may be attributed to the existence of parametric instability regarding platform heave motions. Parametric resonance in risers can cause serious damage which might bring disastrous accidents such as environment pollution, property losses and even fatalities. Therefore, the paranletric instability analysis should attract more attention during the design process of deep-sea risers. In this work, an equation of motion for a deep-sea riser is derived firstly. The motion equation is analyzed by the Floquet theory which allows the determination of both system response and stability properties. The unstable regions in which parametric resonance easily occurs can be determined. The effects of damping on parametric instability are also investigated, and the stability maps are presented. The results demonstrate that the available damping is vital in suppressing the instability regions. The suggestions for reduction of instability regions are proposed in deep-sea riser design.

Transversal vibrations of double-plate systems

This paper presents an analytical and numerical analysis of free and forced transversal vibrations of an elastically connected double-plate system. Analytical solutions of a system of coupled partial differential equations, which describe corresponding dynamical free and forced processes, are obtained using Bernoulli＇s particular integral and Lagrange＇s method of variation constants. It is shown that one-mode vibrations correspond to two-frequency regime for free vibrations induced by initial conditions and to three-frequency regime for forced vibrations induced by one-frequency external excitation and corresponding initial conditions. The analytical solutions show that the elastic connec- tion between plates leads to the appearance of twofrequency regime of time function, which corresponds to one eigenamplitude function of one mode, and also that the time functions of different vibration modes are uncoupled, for each shape of vibrations. It has been proven that for both elastically connected plates, for every pair of m and n, two possibilities for appearance of the resonance dynamical states, as well as for appearance of the dynamical absorption, are present. Using the MathCad program, the corresponding visualizations of the characteristic forms of the plate middle surfaces through time are presented.

Pendulum systems for harvesting vibration energy from railroad tracks and sleepers during the passage of a high-speed train: A feasibility evaluation

We evaluate the feasibility of recovering energy from the vibrations of track and sleepers,during passage of a high-speed train,by means of a pendulum harvester.A simple mathematical model of the parametric pendulum is employed to obtain numerical predictions,while measured data of vibration tests during the passage of a Thalys high-speed train are considered as input forcing.Since a sustained rotation is the most energetic motion of a pendulum,the possibility of achieving such state is evaluated,taking into account the influence of initial conditions,damping and other factors.Numerical simulations show that rotating pendulum harvesters with sufficiently low viscous damping could be able to generate a usable average power on the order of 5–6 W per unit.Considering a modular arrangement of devices,such energy is enough to feed variety of rail-side equipment,as wireless sensors or warning light systems.However,a suitable choice of initial conditions could be a difficult task,leading to the need of a control action.

Ince-Strutt Stability Charts for Ship Parametric Roll Resonance in Irregular Waves

Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.

Parametric Stability Analysis of Marine Risers with Multiphase Internal Flows Considering Hydrate Phase Transitions

This study investigates the effects of multiphase internal flows that consider hydrate phase transitions on the parametric stability of marine risers.A numerical model of the multiphase internal flow that considers a hydrate phase transition is established.The model first solves the flow parameters and subsequently obtains the natural frequencies of risers with different gas intake ratios.The stability charts of marine risers with different gas intake ratios are plotted by applying Floquet theory,and the effects of the gas intake ratio on the instability and vibration response of the risers are identified.The natural frequency increases with an increase in the gas intake ratio;thus,instability zones move to higher frequency ranges in the stability charts.As the increasing gas intake ratio reduces the damping effect of the Coriolis force,the critical amplitude of the heave in the unstable region decreases,especially when hydrodynamic damping is not considered.As a result,higher-order unstable regions are excited.When in an unstable region,the vibration response curve of a riser with a high gas intake ratio excited by parametric resonance diverges quickly due to parametric resonance.

Parametrically excited oscillation of stay cable and its control in cable-stayed bridges＂

This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the stay cable are considered in the model, based on which, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation. It is noted that parametrically excited oscillation of a stay cable with certain sag, inclination angle and initial static tension force may occur in cable-stayed bridges due to deck vibration under the condition that the natural frequency of a cable approaches to about half of the first model frequency of the bridge deck system. A new vibration control system installed on the cable anchorage is proposed as a possible damping system to suppress the cable parametric oscillation. The numerical calculation results showed that with the use of this damping system, the cable oscillation due to the vibration of the deck and/or towers will be considerably reduced.

PARAMETRIC MATCHING SELECTION OF MULTI-MEDIUM COUPLING SHOCK ABSORBER

To achieve the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety of protection for precision equipment such as MEMS packaging system, a theo- retical mathematical model of multi-medium coupling shock absorber is presented. The coupling of quadratic damping, linear damping, Coulomb damping and nonlinear spring are considered in the model. The approximate theoretical calculating formulae are deduced by introducing transformation-tactics. The contrasts between the analytical results and numerical integration results are developed. The resisting impact characteristics of the model are also analyzed in progress. In the meantime, the optimum model of the parameters matching selection for design of the shock absorber is built. The example design is illustrated to confirm the validity of the modeling method and the theoretical solution.

Study on Vibration Characteristics of Stay Cable-Nonlinear Viscous Damper System

Tension cables are easily prone to generating varied vibrations under the action of external loads, which adversely affects the safety of bridges. Therefore, it is necessary to take effective measures to suppress the vibrations of tension cables. Cable end dampers are widely used in vibration reduction for cable-stayed bridges due to their convenient installation and low costs. However, the previous studies on the tension cable-viscous damper systems mostly adopt the linear method, and the weakening effect of the flexibility of mounting brackets on the damper vibration reduction is not sufficiently taken into account. Therefore, this paper adopts the improved Kelvin model to conduct the derivation, solution, and parametric analysis of vibration equations for the stay cable-nonlinear viscous damper systems. The results of parametric analysis show that the maximum modal damping ratio that can be obtained by cables and the corresponding optimal damping coefficient of dampers are correlated with the damping nonlinear coefficient α, stiffness nonlinear coefficient β, vibration order n, installation position a/L, and stiffness coefficient μ, etc.;among them, n damping nonlinear coefficient α and stiffness nonlinear coefficient β are the key parameters that affect the parameter design of dampers, where damping nonlinear coefficient α mainly controls the optimal damping coefficient and stiffness nonlinear coefficient β mainly controls the maximum damping ratio. Based on the parametric analysis, the design principles of dampers and value requirements of key parameters under different vibration suppression objectives are presented.