Nonlinear Coupling Vibration Research Articles

An improved model for the nonlinear simulation of the high‐speed vehicle‐track‐bridge coupling system under seismic shaking

AbstractWith the continuous development of high‐speed railway (HSR) construction technology, many HSR bridges are close to near‐fault earthquake zones. Due to the short warning time for earthquakes occurring in these areas, the scene of trains running on the HSR bridges under earthquakes will become more and more common. In order to effectively evaluate the train running safety performance on the HSR bridge under earthquakes, an improved model for the nonlinear simulation of the high‐speed vehicle‐track‐bridge (VTB) coupling system under seismic shaking is proposed. The commercial finite element software was utilized for the general modeling of track‐bridge structure, and nonlinear hysteric behaviors of key components were realized by using the local nonlinearity correction method. By adopting the unconditional stable explicit dynamic integration algorithm and an efficient wheel–rail contact model, an explicit dynamic solution framework is established. It can efficiently solve the nonlinear coupled vibration of the VTB system under earthquakes. Finally, based on the improved model developed in this paper, the influence of hysteretic behaviors of bridge bearings on the nonlinear coupling vibration of the VTB system under near‐fault earthquakes is discussed.

Coupled Vibration Analysis of Multi-Span Continuous Cable Structure Considering Frictional Slip

As important load-bearing structures, suspension cables have been widely used in suspension bridges, engineering ropeways, cable suspension systems and other special equipment. Their dynamic problems have always been a research hotspot. Especially for complex cable systems such as engineering ropeways and cable lifting equipment, there will be moving loads acting on multi-span continuous friction-slip cable structures, resulting in nonlinear coupled vibration. Therefore, few scholars have studied how to calculate the nonlinear coupling vibration effect between such moving loads and multi-span continuous cables considering friction slip. Therefore, this paper proposes the use of the combination of the direct stiffness method and the Newmark-β integration method to solve the nonlinear system of equations of motion, which can be derived from the coupled vibration response between the moving load and the main cable. The corresponding calculation program is prepared. Combined with the dynamic load test and simulation results of engineering cases, the correctness and reasonableness of the coupled vibration equations and the program can be verified through comparative analysis. The results show that the calculation results of the self-programmed program are in good agreement with the dynamic load test results, in which the maximum error of the vertical displacement in the span is −4.40% and 0.86%, and the error of the static calculation reaches −13.90%. The impact effect is more obvious when hoisting the weight out of the pulling cable, in which the impact coefficient of the main cable can be up to 2.0. The impact coefficient of the deviation of the cable tower is 4.0. During the traveling process of the moving load, the vertical downward deflection of the main cable at the action point is the largest, and the upward deflection is in the region of 0.2~0.8L from the action point.

Nonlinear Coupled Vibration Behavior of BFRP Cables on Long-Span Cable-Stayed Bridges under Parametric Excitation

Based on the cable-stayed beam model, this paper studies the nonlinear coupled vibration behavior of basalt fiber-reinforced polymer (BFRP) cables on long-span cable-stayed bridges under parametric excitation. Considering the sag, damping of BFRP cables, and the coupled interactions between stayed cables and the main girder, the nonlinear coupling vibration model of the BFRP cable–beam composite structure has been established. Taking the longest cable of Sutong Bridge as a case study, the nonlinear coupled vibration behavior of BFRP cables under parametric excitation has been numerically analyzed using the finite difference method. The analysis results indicate that (1) under parametric excitation, the large amplitude nonlinear vibration of the BFRP cable will be induced with an evident “beat” phenomenon. (2) Under the same parametric excitation, the nonlinear coupling vibration response and the beta frequency of the BFRP cable were both smaller than that of the traditional steel cable. (3) The nonlinear coupling vibration response of the BFRP cable increased with an increment in excitation amplitude and a decrement in cable force. With the increase in the excitation frequency, weight per unit length, and axial stiffness, the nonlinear vibration response of the BFRP cable increased first and then decreased. Meanwhile, the damping ratio of the BFRP cable had no significant influence on the nonlinear coupling vibration.

Coupled vibration characteristics of marine shafting with complex change of inclination under ice loads

With the intensifying exploitation of the resources and the waterway of the Arctic region in worldwide, the variable inclination propulsion system are gradually used in the ice-sailing ship, its design and strength study are of great engineering significance and application value. A variable inclination propulsion shafting with universal joint is introduced and its mechanical model is established in this paper. By combine torsional stress and inclination angle calculation, a decoupling algorithm based on Newmark is designed, and then the analysis of ice loads response in both frequency domain and time domain are completed. The results show that due to the complex triangle function relation among the various components of the shafting, there is an interaction between the propeller and the transmission shafting. In particular, when considering the dynamic change of inclination, nonlinear bending-torsional coupling vibration may occur and further lead to the enhancement effect of torsional vibration. Among the three working conditions defined by DNV, the bending-torsional coupling effect vary with rotation speed and inclination angle, and is mainly concentrated in high frequency bands. In the ice loads condition 2, with the largest time domain excitation amplitude and the smallest high order component, it’s vibration response is the strongest, and the change law of dangerous phase angle is similar to the bending moment. With the increase of initial inclination angle, the amplitude of low frequency vibration decreases, yet the amplitude of high frequency vibration increase. This trend is more obvious with the increase of rotation speed, and more high frequency resonance points appear in the condition 1 and condition 3.

Nonlinear coupling vibration analyses of large-scale wind turbine system

With the development of wind energy, the unit capacity of wind turbine is becoming larger and the height of the support tower is getting higher. Limited by the transport conditions, the diameter of the tubular steel tower cannot further increase with the increase of the tower height, which results in the lower natural frequencies of the tower. The higher and more slender wind turbine towers are more sensitive to the external excitation and many tower collapses have occurred in recent years because of the interplay with the longer rotor blades. A 2 MW wind turbine system with a 120 m full steel tubular tower is taken as an example in this study to research the nonlinear coupling vibration mechanism under the normal operation case and the emergency shut-down case. An integrated model of large-scale wind turbine system including the tower, blades, hub, and nacelle is established by the open-source software FAST to study its nonlinear interaction vibration mechanism. Under the normal operation load case, the acceleration response of the steel wind turbine tower is greatly affected by the rotational frequency of the rotor. The maximum accelerations in the fore-aft and side-side directions both appear around the middle-upper height of the tower. Under the emergency shut-down load case, the maximum fore-aft acceleration response appears at the top of the tower, but the maximum side-side response still appears around the middle-upper height of the tower. The first-order vibration mode plays a dominant role in the top fore-aft acceleration and the second-order vibration mode has great contribution to the side-side acceleration under the emergency shut-down load case. The numerical results of this study can provide insight into the vibration control mechanism of the full steel tower.

Three-dimensional nonlinear coupling vibration of drill string in deepwater riserless drilling and its influence on wellbore pressure field

Three-dimensional nonlinear coupling vibration of drill string in deepwater riserless drilling and its influence on wellbore pressure field

Study on coupling vibration sorting parameters of waste plastic film and experimental verification

The waste plastic film is seriously polluted and needs to be sorted and recycled. Vibration sorting of waste plastic film is a highly efficient sorting method at present. A new method for sorting waste plastic film was proposed: coupling vibration sorting. The dynamic interaction of thin film, bed surface and vibrating bed was researched. The nonlinear coupling vibration differential equation of thin film-bed surface-vibrating bed was established. It was found that the sorting distance between the two kinds of films under coupling vibration was 50% higher than that under uncoupling vibration, the validity of the model was verified. The influence of vibration frequency, eccentric block angle, longitudinal inclination angle and transverse inclination angle of the bed surface on the sorting effect in the coupling vibration sorting system were studied, and the vibration sorting trajectories of polyethylene film and polypropylene film under different parameters were obtained. The correctness of the theoretical model was verified by the adjustable vibration sorting experimental prototype. The experimental results show that the thin film-bed surface-vibrating bed coupling vibration sorting model can accurately simulate the thin film sorting law in the coupling vibration process, and the sorting effect of plastic film is improved. It lays a foundation for effectively improving the accuracy of waste plastic film vibration sorting and the optimization of sorting equipment.

Axial-transverse coupled vortex-induced vibration characteristics of composite riser under gas-liquid two-phase internal flow

In this paper, the dynamic behavior of axial (AX) and transverse coupled vortex-induced vibration (VIV) of composite riser under gas-liquid two-phase internal flow is studied. Firstly, based on Hamilton's principle, considering the structural characteristics of composite materials, gas-liquid two-phase internal flow, AX and transverse nonlinear coupling vibration and nonlinear external excitation, a more realistic VIV prediction model of composite riser is proposed. Compared with the existing experimental results, the validity of the model in this paper is verified, and it is found that the VIV prediction of the riser is more accurate when considering the AX and transverse coupling effects. Then, the effects of current velocity, liquid phase velocity, gas volume fraction and fiber orientation angle on the coupled VIV characteristics of gas-liquid mixed transport composite riser are studied. The results show that with the increase of current velocity, gas volume fraction and liquid phase velocity, the in-line (IL) vibration of the riser changes modally before the cross-flow (CF), but the fiber orientation angle has the opposite effect on this phenomenon. At the same time, when the two directions are in two different vibration modes, the vibration frequency in IL direction is obviously larger than that in CF direction. In addition, the riser AX vibration is almost unaffected by the parameters, but its vibration frequency is much larger than the other two directions, and the vibration center has shifted. We also find that the specific liquid phase velocity value will cause the chaotic vibration of the riser in the CF and IL directions, and the vibration displacements of the composite riser are almost equal in both directions.

Mechanical Rectifier for Broadband Piezoelectric Vibration Energy Harvesting and Self-Adapting Synchronous Electric Charge Extraction

The synchronized switch interface circuit is believed to boost the piezoelectric power generation. The threshold voltage of electronic components causes rectification loss and delay of peak detection. This work reports a novel design of a mechanical rectification piezoelectric vibration energy harvester (MR-PVEH). Compact and low loss mechanical rectification is achieved by double switch with 5 electrodes contact at the cantilever tip. The switch as a mechanical stopper also contributes to broadband performance. The saturation voltage and response frequency range can be adjusted in modeling and simulation of nonlinear electromechanical coupling vibration. Self-adapting Mechanical rectification optimized synchronous electric charge extraction (M-OSECE) circuit is also proposed with less electronic components in this paper and shows an extra 60% increase in generated power than the traditional standard energy harvesting circuit (SEH) in test. This novel design gives a promising solution for self-adapting synchronous switching in broadband piezoelectric vibration energy harvesting.

Veering of frequency loci and nonlinear coupling vibration analysis between traveling waves of rotational hard-coated cylindrical shells

The studies on the veering of frequency loci and coupling forced vibration between traveling waves of rotational hard-coated cylindrical shells have been rarely found in previous papers, especially in the presence of the strain-dependent property of coatings. This paper establishes the semi-analytical model of rotational hard-coated cylindrical shells by utilizing Sanders’ shell theory and the Lagrange equation. The non-uniform arc constraint is presented to characterize the boundary of bolted shells through reforming the traditional uniform and continuous constraint. A unified method based on the region division approach is developed to introduce the strain-dependent property of coatings in the rotational state. Moreover, a general and effective algorithm for solving the nonlinear equation with strain-dependent property is developed. The convergence of the region division approach is evaluated. Combined with the FEA, published papers, modal test, and nonlinear response test, the accuracy of the present model in calculating the natural characteristics and nonlinear response with the strain-dependent property is validated. Further, the mechanism of nonlinear traveling-wave vibration is analyzed. The essence of veering for frequency loci and vital rules of nonlinear traveling-wave coupling vibration are revealed.

Investigation on axial-lateral-torsion nonlinear coupling vibration model and stick-slip characteristics of drilling string in ultra-HPHT curved wells

In view of the vibration failure of drilling string system in ultra-high temperature and high pressure (ultra-HPHT) curved wells, an axial-lateral-torsion coupling (ALTC) nonlinear vibration model of drilling string system was established using energy method and Hamiltonian principle, in which, the influence of wellbore trajectory change, wellbore constraint, interaction between bit and rock and ultra-HPHT of wellbore on elastic modulus and viscosity of drilling fluid were taken into account. The finite element method (FEM) is used to realize the numerical solution of the nonlinear vibration model. The correctness and validity of the ALTC nonlinear vibration model was verified by comparing the measured data of four ultra-HPHT wells with the theoretical calculation results of the proposed model.Based on this, according to the parameters of M directional well in Ledong ultra-HPHT block, South China Sea, the influences of ground rotation speed, drilling string length, weight on bit (WOB), torsional impact tools and drill collar length on stick slip vibration characteristics were investigated, and the method of increasing drilling speed in ultra-HPHT curved wells was put forward. The results obtained demonstrate that, firstly, when other requirements were met, the rotary speed should be increased as much as possible, which can effectively improve the drilling efficiency. Secondly, with the increase of drilling depth on-site, the drilling efficiency will be reduced, the whirl phenomenon of drill string system will be intensified, and the service life of bottom hole assembly (BHA) will be reduced. Thirdly, the optimized parameters of WOB and the torsional impact tool depended on the well structure, downhole tool size, etc. and can be determined using the proposed analysis method. The research results provide a theoretically sound guidance for designing and practically sound approach for effectively improving rate of penetration (ROP) and the service life of drilling string in ultra-HPHT curved wells.

Investigation on axial-lateral-torsion nonlinear coupling vibration characteristic of drilling string in ultra-HPHT curved wells

In view of the vibration failure of drilling string system in ultra-high temperature and high pressure (ultra-HPHT) curved wells, an axial-lateral-torsion coupling (ALTC) nonlinear vibration model of drilling string system was established using energy method and Hamiltonian principle, in which, the influence of wellbore trajectory change, wellbore constraint, interaction between bit and rock and ultra-HPHT of wellbore on elastic modulus and viscosity of drilling fluid were taken into account. The finite element method (FEM) is used to realize the numerical solution of the nonlinear vibration model. The correctness and validity of the ALTC nonlinear vibration model was verified by comparing the measured data of four ultra-HPHT wells with the theoretical calculation results of the proposed model. The research results provide a theoretically sound guidance for designing and practically sound approach for effectively improving rate of penetration (ROP) and the service life of drilling string in ultra-HPHT curved wells.

Nonlinear Coupled Vibration of Electrically Actuated Arch with Flexible Supports.

The nonlinear coupled vibration of an electrically actuated arch microbeam has attracted wide attention. In this paper, we studied the nonlinear dynamics of an electrically actuated arch microbeam with flexible supports. The two-to-one internal resonance between the first and second modes is considered. The multiple scales method is used to solve the governing equation. Four first-order ordinary differential equation describing the modulation of the amplitudes and phase angles were obtained. The equilibrium solution and its stability are determined. In the case of the primary resonance of the first mode, stable periodic motions and modulated motions are determined. The double-jumping phenomenon may occur. In the case of the primary resonance of the second mode, single-mode and two-mode solutions are possible. Moreover, double-jumping, hysteresis, and saturation phenomena were found. In addition, the approximate analytical results are supported by the numerical results.

Stability Analysis of a Nonlinear Coupled Vibration Model in a Tandem Cold Rolling Mill

Mill chatter in tandem cold rolling mill is a major rejection to the quality and production of the strips. In most mill vibration models, either the roll mass is usually limited to vibrate in vertical direction and vertical‐horizontal directions, or the multiple rolls system is simplified to a single mass system. However, the torsional chatter is also a typical type of mill chatter, and the presence of intermediate roll and backup roll will affect the overall vibration of the mill structure system. In this paper, a newly cold rolling mill vibration model coupled with the dynamic rolling processing model and nonlinear vibration model is proposed with the consideration of dynamic coupling and nonlinear characteristics of the rolling process, multiroll equilibrium, and roll movement in both vertical‐horizontal‐torsional directions. By using Hopf bifurcation theorem and Routh–Hurwitz determinant, the existence of the Hopf bifurcation point of the mill vibration system and bifurcation characteristics are analyzed. At last, the influence of different rolling conditions on the stability of the coupled mill system is investigated, and these results can also be used to design an optimum rolling schedule and determine the appearance of mill chatter under certain rolling conditions.

Semi-active bounded optimal control of uncertain nonlinear coupling vehicle system with rotatable inclined supports and MR damper under random road excitation

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

Nonlinear electro-mechanical coupling vibration of corrugated graphene/piezoelectric laminated structures

An analytical method is presented to investigate the nonlinear dynamic behavior of corrugated graphene/piezoelectric (CGP) laminated structures under electro-mechanical coupling loads, where the corrugated graphene is affixed on a piezoelectric film. An equivalent orthotropic plate method is used to obtain the stiffness coefficients of corrugated graphene sheet, and its accuracy is validated by the finite element method (FEM). The nonlinear dynamic governing equations of CGP laminated films are constructed based on von Kármán nonlinear geometric relations, then is solved by the Galerkin method and iterative homotopy harmonic balance method. Results show that the equivalent orthotropic plate method is reliable in analyzing the resonant frequency of corrugated film, and both geometry nonlinearity and external control voltage exerted on piezoelectric film have significant effects on the dynamic behaviors of CGP laminated films. Additionally, though corrugated graphene sheet exhibits smaller material stiffness, a significant effect on resonant frequency is observed by affixing corrugated graphene on piezoelectric plate. The meaningful results could serve as references for the applications of soft super-capacitors, stretchable electrode devices, nano-sensors, and etc.

Synchronous control of two counter-rotating eccentric rotors in nonlinear coupling vibration system

Abstract In this paper, the problem of speed and phase synchronization control of two eccentric rotors (ERs) driven by asynchronous motors in a nonlinear vibration system (NVS) with nonlinear time-varying load torque is investigated. The electromechanical dynamic coupling model of NVS is established, in which the complex control of the electromechanical coupling model converts to speed and phase synchronization control of two ERs. A precise control method of speed and phase synchronization of ERs for NVS is proposed. Design the speed and phase synchronization controller by cross-coupling control (CCC) strategy and adaptive global sliding mode control (AGSMC) algorithm. The controller stability is verified by Lyapunov theorem and Barbalat lemma. The performance of the proposed control system is proved by simulation analysis and compared with the traditional self-synchronization method. The results show that the proposed control system considering the cross-coupling characteristics of ERs can effectively control the speed and phase synchronization of two ERs in NVS. The proposed control method can reduce the chattering clearly and improve the control precision. The influence of the nonlinear force of the material on the vibration system is analyzed. The influence of reference speed and parameter perturbation on the synchronization performance is discussed, and the proposed controller is proved with strong robustness. The proposed control system considering the cross-coupling characteristics of ERs can make the NVS implement stable linear vibration locus in the working direction.

Influence of Bearing Stiffness on the Nonlinear Dynamics of a Shaft-Final Drive System

The bearing stiffness has a considerable influence on the nonlinear coupling vibration characteristics of the shaft-final drive system. A 14-DOF nonlinear coupled vibration model was established by employing the lumped mass method so as to identify the coupling effects of the bearing stiffness to the vibration response of the shaft-final drive system. The engine’s torque ripple, the alternating load from the universal joint (U-joint), and the time-varying mesh parameters of hypoid gear of the shaft-final drive system were also considered for accurate quantitative analysis. The numerical analysis of the vibration response of the coupled system was performed and the experimental measurements were carried out for the validation test. Results show that, at the given driving speed, improving the bearing stiffness can reduce the vibration response of the given coupled system; however, when the bearing stiffness increases to a critical value, the effects of bearing stiffness on the vibration reduction become insignificant; when the driving speed changes, the resonance regions of the coupled system vary with the bearing stiffness. The results are helpful to determine the proper bearing stiffness and the optimum control strategy for the shaft-final drive system. It is hoped that the optimal shaft-final drive system can provide good vibration characteristics to achieve the energy saving and noise reduction for the vehicle application.

Research on a Model of Nonlinear Coupled-Vibration of Directional Well Drill String

Drill string vibrations are inevitable movement patterns during drilling process, the drill string vibrations form including longitudinal, lateral and torsional are recognized by most scholars. In the actual drilling process, the coupled vibration exhibits nonlinear features due to the impact of the eccentric rotation of the drill string and the influence of drilling fliud. Taking the whole drill string of directional well as the research object, a three-direction of longitudinal, transverse and torsional nonlinear coupled vibration model of drill string is established based on the nonlinear coupled deformations analysis in the longitudinal, transverse and torsional directions by using finite element analysis method. The nonlinear coupled vibration of drill string is studied by considering the effects of viscous forces of drilling fluid during the drilling process. The results show that the drill string resonance interval is relatively concentrated and the nonlinear coupled vibration frequency increase with the decrease of the length of the drill string.

852 水平基礎励振を受ける構造物と振り子型動吸振器の非線形連成振動(OS5-3 減衰・動吸振器・動的挙動,OS5 振動解析と制振)

852 水平基礎励振を受ける構造物と振り子型動吸振器の非線形連成振動(OS5-3 減衰・動吸振器・動的挙動,OS5 振動解析と制振)