An approximate approach is proposed in this paper for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces due to tip-rub. The dynamical equation of motion for a rotational cantilever blade in a centrifugal force field is established. Flow-induced distributed periodic forces and the internal material damping in the blade are accounted for in the governing equation of motion. The Galerkin method is employed to obtain a three-degree-of-freedom oscillator with friction damping due to tip-rub. The combined motion of impact and friction due to tip-rub produced a piecewise linear vibration which is actually nonlinear. Thus, a complete vibration cycle is divided into successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined using analytical solution forms. Numerical simulation shows that the parameters such as gap of the tip and the rotational speed of the blades have significant effects on the dynamical responses of the system. Finally, the nonlinear vibration characteristics of the blade are investigated in terms of the Poincare graph, and the frequency spectrum of the responses and the amplitude-frequency curves.

Dengqing Cao

Xiaochun Gong

Dong Wei

Shiming Chu

Ligang Wang

Nonlinear Vibration Characteristics of a Flexible Blade with Friction Damping due to Tip-Rub

In this paper, the dynamics of Duffing-van der Pol oscillators under linear-plus-nonlinear position feedback control with two time delays is studied analytically and numerically. By the averaging method, together with truncation of Taylor expansions for those terms with time delay, the slow-flow equations are obtained from which the trivial and nontrivial solutions can be found. It is shown that the trivial solution can be stabilized by appropriate gain and time delay in linear feedback although it loses its stability via Hopf bifurcation and results in periodic solution for uncontrolled systems. And the stability of the trivial solution is independent of nonlinear feedback. Different from the case of the trivial solution, the stability of nontrivial solutions is also associated with nonlinear feedback besides linear feedback. Non-trivial solutions may lose their stability via saddle-node or Hopf bifurcation and the resulting response of the system may be quasi-periodic or chaotic. The feedback gains and time delays have great effects on the amplitude of the periodic solutions and their bifurcation control. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.

Xinye Li

Huabiao Zhang

Lijuan Zhang

Response of the Duffing-Van der Pol Oscillator under Position Feedback Control with Two Time Delays

FEM/BEM is adopted to model the interaction between the fluid and structures. In the modeling, modal truncation and inertial coupling are applied to sufficiently reduce the coupled model order. This approach is adopted for the purpose of constructing a modal model in the time domain. Active vibration control is realized with piezoelectric actuators and an adaptive method. In the control, the summation of vibration responses is used as the control error since the integral of acceleration on the plate surface is approximately proportional to the far field sound pressure. A rigidly baffled plate connected with a mass through one piezoelectric actuator is simulated at first. In the experiment, the plate is excited by a rotating eccentric mass and controlled with four piezoelectric actuators. The results have shown that active vibration control with the piezoelectric actuators can lead to a noticeable attenuation in sound pressure.

Zhiyi Zhang

Yong Chen

Hongguang Li

Hongxing Hua

Simulation and Experimental Study on Vibration and Sound Radiation Control with Piezoelectric Actuators

We investigate synchronization of two asymmetric exciters in a vibrating system. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the two exciters (NDDETE). By using the condition of existence for the zero solutions of the NDDETE, the condition of implementing synchronization is deduced: the torque of frequency capture is equal to or greater than the difference in the output electromagnetic torque between the two motors. Using the Routh-Hurwitz criterion, we deduce the condition of stability of synchronization that the inertia coupling matrix of the two exciters is positive definite. A numeric result shows that the structural parameters can meet the need of synchronization stability.

Zhaohui Ren

Qinghua Zhao

Chunyu Zhao

Bangchun Wen

Synchronization of Two Asymmetric Exciters in a Vibrating System

An approach to a wide-band frequency passive vibration attenuation is introduced in this paper. This aims to suppress noise and vibration of extended multimode objects like plates, panels and shells. The absorber is arranged in the form of a single-layer assembly of small inertial bodies (balls) being distributed and moulded within the light visco-elastic media (e.g. silicone resin). The absorber as a whole is embedded into object face covering the critical patches of the system surface. For the purpose of characterization, the authors introduced the complex frequency response function relating the volume velocity produced by the vibrating object surface (response) stimulated by a point-wise force (stimulus) applied to a particular point. The simulation and optimization of the main frequency characteristics has been performed using a full scale 3-dimensional Finite Element model. These revealed some new dynamic features of absorber's structures, which can contribute to vibration attenuation. A full-scale physical experimentation with synthesised absorber's structures confirmed the main results of simulation and has shown significant noise reduction over a staggering 0&#x2013;20 kHz frequency band. This was achieved with a negligible weight and volume penalty due to the addition of the absorber. The results can find multiple applications in noise and vibration control of different structures. Some examples of such applications are presented.

Michel Azoulay

Alexander Veprik

Vladimir Babitsky

Neil Halliwell

Distributed Absorber for Noise and Vibration Control

Nonlinear torsional models are used to analyze automotive transmission rattle problems and find solutions to reduce noise, vibration and dynamic loads. The torsional stiffness and inertial distribution of such systems show that the underlying mathematical problem is numerically stiff. In addition, the clearance nonlinearities in the gear meshes introduce discontinuous functions. Both factors affect the efficacy of time domain integration and smoothening functions are widely used to overcome computational difficulties and improve the simulation. In this paper, alternate smoothening functions are studied for their influence on the numerical solutions and their impact on global convergence and computation times. In particular, four smoothening functions (arctan, hyperbolic-cosine, hyperbolic-tan and quintic-spline) are applied to a five-degree-of-freedom generic torsional system with two backlash (clearance) elements. Each function is assessed via a global convergence metric across an excitation map (a design of experiment). Regions of the excitation map, along with multiple solutions, are studied and the implications to assessing convergence are critically examined. It is observed that smoothening functions do not lead to better convergence in many cases. The smoothening parameter needs to be carefully selected, or over-smoothened solutions may be found. The system studied is representative of a typical automotive rattle problem and it was found that benefits were limited from applying such smoothening functions.

Zhiwei Zhang

Rajendra Singh

Ashley R. Crowther

Limitations of Smoothening Functions for Automotive Vibro-Impact Problems

The process of ultrasonically-assisted turning (UAT) is a superposition of vibration of a cutting tool on its standard movement in conventional turning (CT). The former technique has several advantages compared with the latter, one of the main being a significant decrease in the level of cutting forces. In this paper the effects observed in UAT are analysed employing ideas of dynamic fracture mechanics. The active stage of loading duration depends heavily on ultrasonic frequency and the cutting speed; he application of the fracture criterion based on the notion of incubation time makes it possible to calculate a dependence of this duration on its threshold amplitude. An estimation of energy, necessary to create a threshold pulse in the material, is made by solving the contact Hertz problem. The obtained time dependence of energy has a marked minimum. Thus, the existence of energy-efficient loading duration is demonstrated. This explains the decrease in the cutting force resulting from superimposed ultrasonic vibration. The obtained results are in agreement with experiments on ultrasonic assisted machining of aluminium and Inconel 718 alloy.

G.A. Volkov

V.A. Bratov

A.A. Gruzdkov

V.I. Babitsky

Y.V. Petrov

V.V. Silberschmidt

Energy-Based Analysis of Ultrasonically Assisted Turning

The nonlinear dynamics theory is increasingly applied in the dynamics analysis of tilting pad journal bearing-rotor system. However, extensive work on system dynamics done previously neglects the influence caused by the moment of inertia of the pad. In this paper, a comparison is made between the responses of the rotor in the bearings with and without pad inertia effect. Taking the Jeffcott rotor system as an example, the characteristics of bearing-rotor system, such as bifurcation diagram, cycle response, frequency spectrum, phase trajectories, and Poincar&#xe9; maps, were attained within a certain rotation rate range. The pivotal oil-film force of tilting pad journal bearing was calculated by database method. The results directly demonstrate that considering the influence of the pad moment of inertia, system dynamics characteristics are found more complicated when rotor-bearing system works around natural frequency and system bifurcation is observed forward when rotor-bearing system works on high-speed range.

Jiayang Ying

Yinghou Jiao

Zhaobo Chen

Nonlinear Dynamics Analysis of Tilting Pad Journal Bearing-Rotor System

The dynamic parameters of a car body in white (BIW) are important during a new car developing. Based on the finite element method, the model of a BIW is developed in which the welding points are treated specially as a new element type and the vibration modes of it are calculated. In modal testing, a fixed sine-sweeping exciter is used to conduct a single-point input force for the structure, whereas the output responses are picked up at different points to identify modes. The obtained modes are coincided both with the FE results and the practical testing.

Ying Yang

Guangyao Zhao

Dongbo Ma

Xiaobin Xu

Mode Calculation and Testing of a Car Body in White

This paper presents a finite element model of a rotor system with pedestal looseness stemming from a loosened bolt and analyzes the effects of the looseness parameters on its dynamic characteristics. When the displacement of the pedestal is less than or equal to the looseness clearance, the motion of the rotor varies from period-one through period-two and period-three to period-five with the decreasing of stiffness of the non-loosened bolts. The similar bifurcation phenomenon can be also observed during the increasing process of the rotational speed. But the rotor motion is from period-six through period-three to period-four with the decreasing of the foundation stiffness. When the stiffness of the foundation is small and the displacement of pedestal is greater than the looseness clearance, the response of the rotor exhibits period-one and high order harmonic components with the decreasing of looseness clearance, such as 2X, 3X etc. However, when the stiffness of the foundation is great, the spectrum of the response of the rotor will be from combined frequency components to the continuous spectrum with the decreasing of the looseness clearance.

Hui Ma

Xueyan Zhao

Yunnan Teng

Analysis of Dynamic Characteristics for a Rotor System with Pedestal Looseness

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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