Nonlinear Vibration Phenomenon Research Articles

Analysis of Bifurcation Vibrations of an Industrial Robot Arm System with Joints Compliance

This paper deals with the analysis of nonlinear vibration phenomena in the arm system of an industrial robot. The presented mathematical model of the robot takes into account the flexibility of the joints, which results in low-frequency vibrations in the arm. The study of vibration phenomena has been carried out using analytical, numerical and experimental methods. Special attention has been paid to bifurcation phenomena. The influence of two bifurcation parameters on the behaviour of the robot arm was studied. It was shown that the amplitude and frequency of the harmonic excitation create a nonlinear effect on the vibration amplitudes of the links. In bifurcation regions, the vibration amplitudes can even differ several times depending on the direction of changes in the bifurcation parameter. In general, the results indicate that, contrary to common practice, it is worth paying attention to nonlinear phenomena when analysing robot vibrations.

Open NASA Blade Models for Nonlinear Dynamics Simulations

Abstract This contribution presents a catalogue of open turbomachinery blade models dedicated to nonlinear dynamics simulations. Based on a specifically developed in-house computer code, three-dimensional computer-aided design (CAD) models and finite element (FE) models of multiple-circular-arc (MCA) NASA airfoils are generated. Both the in-house code and the models are made freely accessible online. To cover a wide range of geometries, 39 blades are considered from different stages and with different aspect ratios. It is expected that this blade catalogue will provide an opportunity for the direct comparison of recently developed methodologies relative to nonlinear vibration phenomena in turbomachines, including rubbing events and blade-tip/casing contacts. To this end, the paper also contains original results for some of the most emblematic NASA blades, with an emphasis on nonlinear interaction maps and a detailed presentation of redesign operations to mitigate high amplitude of vibrations when blade-tip/casing contacts occur.

Nonlinear vibration phenomena in hydrodynamically supported rotor systems

It is a well-known fact, that hydrodynamically supported systems are prone to nonlinear vibrations. Their exact simulative prediction with respect to frequency and amplitude is complicated by the fact that different system properties interact. The paper at hand outlines an approach that takes all relevant influences like rigid body motions, elastic deformations, nonlinear relation between fluid film pressure and bearing kinematics as well as temperature increase due to power loss or adjacent heat sources into account as detailed as necessary. Both journal and thrust bearings are considered as they contribute to the system's stiffness and damping capabilities. The approach is applied to self-excited pad vibrations of tilting pad thrust bearings as well as the run-up simulation of a turbocharger rotor under different axial loads. Both models are validated against measurements.

Nonlinear vibration modeling and analysis of bolted thin plate based on non-uniformly distributed complex spring elements

Due to the existence of bolt influence zone, the interface pressure of bolted joint presents a non-uniform distribution. The nonlinear mechanical behaviors of variable stiffness and variable damping will also occur in bolted joints under varying degrees of forced vibration. In this paper, a nonlinear finite element analysis model of bolted thin plate is established by introducing displacement-dependent nonlinear complex spring elements with non-uniformly distributed parameters. Sinusoidal, parabolic and linearly distributed complex spring elements are used to simulate the non-uniform pressure distribution in the bolt influence zone, respectively. The stiffness and damping displacement-dependent parameters of the complex spring elements are described by higher-order polynomials, and a method to obtain the above parameters by inverse identification is proposed. In the case study, the non-linear finite element model created is used to calculate the resonance frequency and frequency domain response of bolted thin plate under five excitation levels. The maximum differences between the results and the measured values are 2.7% and 0.66%, respectively. The simulation results also reproduce the soft nonlinear vibration phenomenon of the bolted thin plate. Furthermore, by comparing the vibration analysis results of the linear model and nonlinear model for bolted thin plate, the reason for the soft nonlinear phenomenon produced is explained.

Influence of Electromagnetic Shunt Damper on Nonlinear Vibration of HTS Maglev System

The levitation force in the high temperature superconducting (HTS) maglev system has obvious nonlinear characteristics. When the excitation frequency and amplitude meet certain conditions, nonlinear vibration phenomena such as period-doubling bifurcation would appear. Nonlinear vibration will bring difficulties to dynamic analysis and even affect the safety and comfort of driving. While an electromagnetic shunt damper (EMSD) can effectively reduce the vibration amplitude. This paper analyzes the influence of EMSD on the nonlinear vibration of HTS maglev systems from the perspective of experiments and simulations. Firstly, free vibration and forced vibrations in the resonance interval are tested. Secondly, based on numerical simulations, the vibration response under various excitation was analyzed. The results show that the EMSD can effectively suppress its nonlinear vibration. This research has reference value for the detailed understanding of the dynamic characteristics of the HTS maglev and further vehicle design.

Dynamics, stability and bifurcation analysis of rotors in air ring bearings

Classical air foil bearings consist of a top foil, which is usually supported by a bump or beam foil structure. For this bearing type, the air gap is a function of the top foil deformation. Here, an alternative air bearing design – called air ring bearing – is investigated, which may be regarded as a straightforward and very obvious modification of the classical air bearing design. The basic idea is to insert a rigid ring between the shaft and the foil structure. The ring may therefore be considered to be elastically mounted in the housing by means of a bump or beam-type structure. Alternatively, a viscoelastic supporting structure (elastomer) may be used to connect the ring with the housing. Hence, the air film is separated by a rigid ring from the supporting structure. As a consequence, the bearing gap for the fluid film has rigid walls, which simplifies the numerical calculation significantly.In this manuscript, a detailed numerical analysis of rotor systems supported in air ring bearings is presented. The basic nonlinear dynamical effects occurring in such rotor systems are investigated with a particular focus on the stability and bifurcation behavior. Therefore, a detailed co-simulation model of the rotor/bearing system is used. Different possible bifurcation scenarios are described and explained with the help of run-up simulations.Rotor systems with air ring bearings exhibit a completely different vibration and stability behavior than rotors in classical air foil bearings. Diverse interesting nonlinear vibration phenomena, not known in connection with classical air foil bearings, are discussed in detail and physically explained in a clear manner.

Nonlinear forced vibration analysis of the composite shaft-disk system combined the reduced-order model with the IHB method

In this paper, the internal resonance phenomena of a composite shaft-disk system with multi-degrees-of-freedom are analyzed. The force caused by the unbalanced mass of the disk is considered as an external excitation force. The shaft is simply supported. Shear deformation and gyroscopic effects are considered. The strain–displacement relationship of the shaft element is expressed using the Timoshenko beam theory. Each node has 5 degrees of freedom. SHBT (simplified homogenized beam theory) is applied to calculate the stiffness of the composite shaft. WQEM (weak form quadrature element method) is used to construct the element matrices, and the system matrices are established using the element matrix assembly rule of the FEM (finite element method). The reduced-order model is applied to reduce the calculation time. IHB (incremental harmonic balance) method is utilized to solve the nonlinear equations of motion of the composite shaft-disk system. The nonlinear vibration characteristics of the Jeffcott rotor are analyzed using the proposed method and compared with the results of previous researches, and the results are very similar. Based on these considerations, the nonlinear vibration phenomena of the composite shaft-disk system with multi-degrees-of-freedom are considered at the several resonance points.

Post flutter energy map for H-shaped bridge girder

In this study, with the help of the three-degree-of-freedom random forced vibration device developed independently by Tongji University, high-precision measurement of bridge aerodynamic force under large torsional amplitude was realized, and a potential energy spectrum was established in consideration of the energy evolution and amplitude effect that varies with reduced velocity. As a result, a new research strategy for nonlinear flutter of bridge girders is proposed. Taking the Old Tacoma Narrows Bridge as an example, the mechanism of nonlinear vibration phenomena at post-flutter state was analyzed, and the wind-induced instability path of the bridge and its potential development path were deduced. The results show that flutter response can be divided into two components according to the energy spectrum. One component is related to the aerodynamic effect, and the other component is related to the mechanical damping ratio effect, which is helpful for studying the relationships between the mechanical damping ratio and bifurcation phenomena of bridge flutter. At the collapse of the Old Tacoma Narrows Bridge, both the aerodynamic nonlinearity and variations of the mechanical damping ratio with vibration amplitude have important contributions to the post-flutter behavior of the bridge in terms of energy effects. Variations of the mechanical damping ratio in torsion with amplitude greatly improve the flutter performance of the bridge. Thus, the development path of the structural displacement response depends on the competitive relationships among the structural torsional damping ratio, structural rigidity, and oncoming wind velocity.

Nonlinear forced vibration analysis of composite beam combined with DQFEM and IHB

In this paper, a forced vibration model of composite beams under the action of periodic excitation force considering geometric nonlinearity is proposed. For the strain–displacement relationship, Timoshenko beam theory is used, and the element and system matrices are developed using the differential quadrature finite element method. Each node has 3 degrees of freedom. The incremental harmonic balance method is used to solve the nonlinear forced vibration equation. In order to prove the validity of the proposed model, the solution of the Duffing equation is calculated using the analytical method and the proposed method. Next, linear forced vibration analysis of the beam made of isotropic material is performed and compared with the result of ABAQUS. The results are very close. Based on these comparisons, nonlinear vibration phenomena of composite beams are studied under the action of periodic forces.

Characterization test on nonlinear vibration of the fibre-reinforced composite thin plate

In this research, the characterization test on nonlinear vibration of a fibre-reinforced composite thin plate is studied. First, in order to improve the efficiency and precision of the test, a laser scanning vibration system is designed and developed. Then, test methods and procedures of the harmonic distortion and nonlinear time-varying damping of such thin plates are proposed from the time-domain perspective. Corresponding test methods and procedures of nonlinear vibration properties such as the hard/soft stiffness and amplitude-dependent damping are also presented from the frequency-domain perspective. Finally, the TC500 carbon fibre/resin composite plate is selected as an example for the research to carry out a case study. Potential nonlinear vibration phenomena of such plates are characterized by the proposed test methods. It has been proved that the related test system and techniques adopted in this paper can provide an important reference for the establishment of the nonlinear vibration test methodology of fibre-reinforced composite structures.

Research on the Coupled Axial-Transverse Nonlinear Vibration of Sucker Rod String in Deviated Wells

The coupled axial-transverse nonlinear vibration simulation model of sucker rod sting (SRS) in deviated wells is established. Based on the simulation results, the nonlinear vibration phenomenon of SRS is analyzed, and the influence of centralizer arrangement on the nonlinear vibration of SRS is discussed. The mechanical simulation model of the coupled axial-transverse vibration of SRS in deviated wells can be simplified to the coupled axial-transverse vibration model of longitudinal and transverse curved beam with initial bending under borehole constraints. In this paper, when establishing the simulation model of the coupled axial-transverse vibration of SRS, it is proposed that the bending borehole trajectory is a main excitation of the vibration of SRS. Based on the theory of elastic vibration, a nonlinear dynamic simulation model of the coupled axial-transverse vibration of SRS in deviated well is established. Then the fourth-order Runge–Kutta method is used to solve the simulation model. The nonlinear vibration phenomenon of the SRS is studied by example analysis. The simulation results show that: (1) the simulation curve of polished rod dynamometer card is in good agreement with the test curve, and the error value of polished rod maximum load and minimum load is within 5%, which shows that the coupled axial-transverse vibration simulation model of SRS established in this paper has high accuracy. (2) When the centralizer is not arranged, the chaotic motion of SRS mainly occurs in the compression section of SRS, which shows that the instability of SRS is the main reason for the chaotic motion of SRS. (3) The arrangement of centralizer can improve the bending rigidity of SRS, restrain or even eliminate the chaotic motion of SRS.

An experimental study on the nonlinear vibration phenomenon of a rotor system subjected to barrel roll flight and coupled rub-impact faults

This study focuses on the nonlinear vibration phenomenon of a rotor system subjected to aircraft barrel roll flight and coupled rub-impact faults. An experimental device is designed to imitate the rotor installed on an aircraft, which is rare because of the complex installation conditions of a rotor system. The transient nonlinear dynamic behavior of a rub-impact fault rotor and a coupled rub-impact fault rotor with misalignment are investigated for an aircraft in barrel roll flight. By combining a spectrum cascade, reassigned wavelet scalogram, and spectrogram, some novel nonlinear features of two types of rub-impact fault rotors are obtained, the most critical being the distinguishable transient harmonic components due to the time-varying influence of the aircraft barrel roll flight. This analysis contributes to a deep understanding of the complex nonlinear vibration phenomenon of coupled rub-impact fault rotors during flight maneuvers.

Aspects on the study of nonlinear vibration phenomenon in friction welding with rotating active element

The friction welding with rotating active element is a complex process including heating of the materials using friction and plastic deformation generated by a tool that has both rotation and translation motions. The paper is analysing the nonlinear vibrations that occurs during the friction welding with rotating active element process, mainly due to the motion of the rotating element. Using the dynamic systems theory, the nonlinear equation of the motion is deduced and the motion characteristics are presented using specific qualitative methods. The results are contributing to a more accurate understanding of the phenomena, in this case the nonlinear vibrations, generated in the friction welding with rotating active element process, and to better performances of welding process.

Nanoacoustofluidics: Unprecedented fluid manipulation via controlled MHz-order vibration at the nanoscale

Manipulation of fluids and colloids at the nanoscale is made exceptionally difficult by the dominance of surface and viscous forces. The use of MHz-order vibration has dramatically expanded in microfluidics, enabling fluid manipulation, atomization, and microscale particle/cell separation. We find even more powerful results at the nanoscale, with the key discovery of a new mechanism of acoustic wave-fluid motion interaction. We show that MHz-order surface acoustic waves (SAW) can manipulate fluids and fluid droplets within fully transparent, high-aspect ratio 5–150 nm tall, 10–100 μm wide, 5 mm long nanoslits fabricated via a direct, room temperature bonding method for lithium niobate (LN). The application of SAW causes fluid draining and pumping, developing ∼1 MPa pressure through the nanoslit structure. The mechanism of specific draining pattern is well explained by a detailed theoretical model based on the nonlinear acoustic vibration phenomenon in nanoscale channels. We also show how individual fluid droplets of only 1–10 fl are propelled by incident SAW in the nanoslit structure, entrapping them at locally widened regions along the nanoslit due to the capillary pressure difference. Our results indicate MHz-order SAW as a powerful tool for fluid manipulation in nanoscale.

Research on vibration performance of the nonlinear combined support-flexible rotor system

A finite element model of the cantilever combined support rotor included two discs established in this paper to predict and explain the nonlinear vibration phenomenon. The model considered local nonlinear support force generated by the combined support and the coupling effects of the rotor with the combined support. The nonlinear factors contained the clearance, the Hertz contact force and the vibration of the rolling bearing and the nonlinear force of the squeeze film damper. The combined support included bearing, squeeze film damper and squirrel cage elastic support. Finally, the high-dimensional partial differential equations with local nonlinearity were derived and solved by Newmark- $$\upbeta $$ combined with Runge–Kutta method. Based on the above theoretical results, the bifurcation phenomenon of vibration response at different positions was analysed and the dynamic response of the rotor system at different positions due to the rotational speed was compared.

Design and experiment of nonlinear absorber for equal-peak and de-nonlinearity

This paper generalizes and modifies the Equal-peak method for the design of nonlinear vibration absorber for use in the vibration suppression of nonlinear primary vibration system. For a vibration system with nonlinearity, the most relevant bandwidth is the resonance band, in which the undesirable nonlinear vibration phenomenon occurs because of the dramatically amplified of vibration amplitude. To generalize the Equal-peak method for a complex nonlinear primary system under force/base excitations, we utilize the nonlinear perturbation method and bifurcation theory to investigate the vibration performances and critical conditions for dynamical transition. In addition to the Equal-peak property, another novel advantage, called De-nonlinearity (introduced by coupling nonlinearity), is revealed for vibration control in addition to the known effect of nonlinearity on vibration suppression. It is discovered that by applying the nonlinear vibration absorber with appropriate design on the NL primary system, the Equal-peak property can be accurately realized, and unexpected nonlinear vibration performances can be effectively eliminated. A relevant experimental prototype is carried out to illustrate the Equal-peak and De-nonlinearity properties, which is composed of a primary vibration system with complex nonlinearity and a designed tunable nonlinear vibration absorber. The proposed modified design method for Equal-peak and De-nonlinearity properties has huge potential application in the vibration suppression for low-frequency and strong nonlinearity fields such as ships, aircrafts and ocean platform.

Nonlinear vibration phenomenon of maneuvering spacecraft with flexible jointed appendages

A nonlinear analytical model for a spacecraft with flexible jointed appendages is presented and subsequently used to investigate the nonlinear vibration phenomenon of the system caused by the joints nonlinearities during the spacecraft maneuvering. In this model, the joint transmitted characteristics which included linear and nonlinear stiffness, damping and friction are introduced into the system by applying the equilibrium conditions between the beams and the joints. Consequently, an explicit set of reduced-order nonlinear ordinary differential equations (ODEs) of motion for the flexible spacecraft with nonlinear joints are obtained based on the global mode method. Through the nonlinear ODEs obtained in this model, the dynamic responses of the system with various joint parameters are worked out numerically for the cases of attitude maneuver and orbit maneuver, respectively. For the case of attitude maneuver, the simulation results show that the damping and friction in the joints have a great influence on the vibration response of the system, especially the residual vibration. For the case of orbit maneuver, some nonlinear behaviors caused by the nonlinear joints are observed such as hardening, jump, sub-harmonic and super-harmonic resonance. More importantly, due to the cubic stiffness of the joint, modal coupling is exhibited, which result in the interaction between translation and rotation of the central rigid body.

Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates

This work investigates the porosity-dependent nonlinear forced vibrations of functionally graded piezoelectric material (FGPM) plates by using both analytical and numerical methods. The FGPM plates contain porosities owing to the technical issues during the preparation of FGPMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. A modified power law model is adopted to describe the material properties of the porous FGPM plates. Using D’Alembert’s principle, the out-of-plane equation of motion is derived by taking into account the Kármán nonlinear geometrical relations. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by employing the harmonic balance method. The approximate analytical results are verified by using the adaptive step-size fourth-order Runge–Kutta method. By means of the perturbation technique, the stability of approximate analytical solutions is examined. An interesting nonlinear broadband vibration phenomenon is detected in the FGPM plates with porosities. Nonlinear frequency-response characteristics of the present smart structures are investigated for various system parameters including the porosity type, the porosity volume fraction, the electric potential, the external excitation, the damping and the constituent volume fraction. It is found that these parameters have significant effects on the nonlinear vibration characteristics of porous FGPM plates.

Nonlinear vibration behaviors of high-Tc superconducting bulks in an applied permanent magnetic array field

The nonlinear vibration of high temperature superconducting (HTS) bulks in an applied permanent magnetic array (Halbach array) field, as a precondition for commercial application to HTS maglev train and HTS bearing, is systematically investigated. This article reports the actual vibration rules of HTS bulks from three aspects. First, we propose a new numerical model to simplify the calculation of levitation force. This model could provide precise simulations, especially the estimation of eigenfrequency. Second, an approximate analytic solution of the vibration of the HTS bulks is obtained by using the method of harmonic balance. Finally, to verify the results mentioned above, we measure the vertical vibration acceleration signals of an HTS maglev model, consisting of eight YBaCuO bulks, oscillating freely above a Halbach array with large displacement excitation. Higher order harmonic components, which indicate the nonlinear vibration phenomenon, are detected in the responses. All the three results are compared and agreed well with each other. This study combines the experimental and theoretical analyses and provides a deep understanding of the physical phenomenon of the nonlinear vibration and is meaningful for the vibration control of the relevant applications.

Axial control for nonlinear resonances of electrostatically actuated nanobeam with graphene sensor

The nonlinear resonance response of an electrostatically actuated nanobeam is studied over the near-half natural frequency with an axial capacitor controller. A graphene sensor deformed by the vibrations of the nanobeam is used to produce the voltage signal. The voltage of the vibration graphene sensor is used as a control signal input to a closed-loop circuit to mitigate the nonlinear vibration of the nanobeam. An axial control force produced by the axial capacitor controller can transform the frequency-amplitude curves from nonlinear to linear. The necessary and sufficient conditions for guaranteeing the system stability and a saddle-node bifurcation are studied. The numerical simulations are conducted for uniform nanobeams. The nonlinear terms of the vibration system can be transformed into linear ones by applying the critical control voltage to the system. The nonlinear vibration phenomena can be avoided, and the vibration amplitude is mitigated evidently with the axial capacitor controller.