Stick-Slip Vibrations of Layered Structures Undergoing Large Deflection and Dry Friction at the Interface

The present study focuses on the nonlinear analysis of the dynamical behavior of layered structures, including interfacial friction in the presence of the stick-slip phenomenon and large deformation. To achieve a proper outlook for the two-layer structure's behavior, it is essential to precisely realize the mechanisms of motion. Taking the dry friction into account, coupled equations of the transversal and longitudinal large vibration of two-layers are derived and nondimensionalized. Furthermore, the free and forced vibration of the aforementioned system is investigated. From the results of the numerical simulation, it is observed that there exist quasi-periodic and stick–slip chaotic motions in the system. The results demonstrate that the single mode method usually utilized may lead to incorrect conclusions and, instead, the higher order mode method should be employed. A comparative study with ANSYS is developed to verify the accuracy of the proposed approach.

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A Single and Double Mode Approach to Chaotic Vibrations of a Cylindrical Shell with Large Deflection

Shock and Vibration ◽

10.1155/2004/486249 ◽

2004 ◽

Vol 11 (5-6) ◽

pp. 533-546 ◽

Cited By ~ 1

Author(s):

Liming Dai ◽

Qiang Han ◽

Mingzhe Dong

Keyword(s):

Cylindrical Shell ◽

Large Deflection ◽

Single Mode ◽

Order Mode ◽

Governing Equations ◽

Chaotic Vibrations ◽

Nonlinear Dynamic Equations ◽

Different Types ◽

Mode Method ◽

Research Show

The chaotic vibrations of a cylindrical shell of large deflection subjected to two-dimensional exertions are studied in the present research. The dynamic nonlinear governing equations of the cylindrical shell are derived on the basis of single and double mode models established. Two different types of nonlinear dynamic equations are obtained with varying dimensions and loading parameters. The criteria for chaos are determined via Melnikov function for the single mode model. The chaotic motion of the cylindrical shell is investigated and the comparison between the single and double mode models is carried out. Results of the research show that the single mode method usually used may lead to incorrect conclusions under certain conditions. Double mode or higher order mode methods should be used in these cases.

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Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0355 ◽

1995 ◽

Author(s):

Wayne E. Whiteman ◽

Aldo A. Ferri

Keyword(s):

Dry Friction ◽

Damping Ratio ◽

Strong Dependence ◽

Time Integration ◽

Single Mode ◽

Stick Slip ◽

Friction Forces ◽

Equivalent Damping ◽

Damping Characteristics ◽

Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

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BIFURCATION AND CHAOTIC MOTION OF AN ELASTIC PLATE OF LARGE DEFLECTION UNDER PARAMETRIC EXCITATION

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405013666 ◽

2005 ◽

Vol 15 (09) ◽

pp. 2849-2863

Author(s):

Q. HAN ◽

L. DAI ◽

M. DONG

Keyword(s):

Large Deflection ◽

Single Mode ◽

Harmonic Excitation ◽

Governing Equations ◽

External Excitation ◽

Mode Method ◽

Elastic Rectangular Plate ◽

The Stability ◽

Nonlinear Elastic ◽

Bifurcation Behavior

The dynamic behavior of a nonlinear elastic rectangular plate of large deflection subjected to harmonic excitation is investigated. Using the Galerkin principle, a double mode model is established for the plate. The stability and bifurcation behavior of the plate is studied in detail for various loading conditions and system parameters. A set of autonomous equations is derived with the method of averaging. The bifurcation behavior is examined on the basis of the autonomous equations, and the results of theoretical bifurcation analysis are numerically verified. The chaotic response of the plate to the external excitation is also investigated. The governing equations of single as well as double modes are established and the comparison between the single and double mode models is carried out. The applicable conditions of the single mode method are provided. The results obtained show that the single mode approach usually used may lead to incorrect conclusions under certain conditions.

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Analytical prediction on stick-slip whirling oscillations induced by dry friction between a rotating imbalanced rotor and a flexibly supported stator

Journal of Sound and Vibration ◽

10.1016/j.jsv.2021.116333 ◽

2021 ◽

pp. 116333

Author(s):

Shunzeng Wang ◽

Ling Hong ◽

Jun Jiang

Keyword(s):

Dry Friction ◽

Analytical Prediction ◽

Stick Slip

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Bistable dynamics beyond rotating wave approximation

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863514500192 ◽

2014 ◽

Vol 23 (02) ◽

pp. 1450019 ◽

Cited By ~ 3

Author(s):

Y. A. Sharaby ◽

S. Lynch ◽

A. Joshi ◽

S. S. Hassan

Keyword(s):

Ring Cavity ◽

Dynamical Behavior ◽

Single Mode ◽

Unstable State ◽

Nonlinear Dynamical ◽

Rotating Wave Approximation ◽

Wave Approximation ◽

Atomic Medium ◽

Bistable Dynamics ◽

Rotating Wave

In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.

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Energy Balancing Method to Identify Nonlinear Damping of Bolted-Joint Interface

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.693.318 ◽

2016 ◽

Vol 693 ◽

pp. 318-323 ◽

Cited By ~ 2

Author(s):

Xin Liao ◽

Jian Run Zhang

Keyword(s):

Dry Friction ◽

Harmonic Excitation ◽

Joint Interface ◽

Damping Factor ◽

Viscous Damping ◽

Bolted Joint ◽

Energy Balancing ◽

Stick Slip ◽

Non Linear ◽

Linear Damping

The interface of bolted joint commonly focuses on the research of non-linear damping and stiffness, which affect structural response. In the article, the non-linear damping model of bolted-joint interface is built, consisting of viscous damping and Coulomb friction. Energy balancing method is developed to identify the dry-friction parameter and viscous damping factor. The corresponding estimation equations are acquired when the input is harmonic excitation. Then, the vibration experiments with different bolted preloads are conducted, from which amplitudes in various input levels are used to work out the interface parameters. Also, the fitting curves of dry-friction parameters are also obtained. Finally, the results illustrate that the most interface of bolted joint in lower excitation levels occurs stick-slip motion, and the feasibility of the identification approach is demonstrated.

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Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

Volume 8: 26th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2014-34282 ◽

2014 ◽

Author(s):

Ge Kai ◽

Wei Zhang

Keyword(s):

Nonlinear Dynamics ◽

Numerical Simulation ◽

Differential Equations ◽

Chaotic System ◽

Dynamical Behavior ◽

Three Dimensional ◽

Phase Portraits ◽

State Variables ◽

Chaotic Motions ◽

Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

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Second Order Averaging Study of an Autoparametric System

14th Biennial Conference on Mechanical Vibration and Noise: Nonlinear Vibrations ◽

10.1115/detc1993-0038 ◽

1993 ◽

Author(s):

Bappaditya Banerjee ◽

Anil K. Bajaj ◽

Patricia Davies

Keyword(s):

Dynamical Behavior ◽

Period Doubling ◽

Nonlinear Effects ◽

Single Mode ◽

Pitchfork Bifurcation ◽

Second Order ◽

System Response ◽

Response Curves ◽

Vibratory System ◽

First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

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