Flow induced vibration is an important factor affecting the performance of the rotor-seal system. From the point of view of flow induced vibration, the nonlinear models of the rotor-seal system are presented for the analysis of the fluid force, which is induced by the interaction between the unstable fluid flow in the seal and the vibrating rotor. The nonlinear characteristics of flow induced vibration in the rotor-seal system are analyzed, and the nonlinear phenomena in the unbalanced rotor-seal system are investigated using the nonlinear models. Various nonlinear phenomena of flow induced vibration in the rotor-seal system, such as synchronization phenomenon and amplitude mutation, are reproduced.

Nan Zhang

Ying Liu

Fulei Chu

Dynamic Characteristics of Flow Induced Vibration in a Rotor-Seal System

Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.

Zheng Ling

Xie Ronglu

Wang Yi

Adel El-Sabbagh

Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach

This paper proposes a new approach combining autoregressive (AR) model and fuzzy cluster analysis for bearing fault diagnosis and degradation assessment. AR model is an effective approach to extract the fault feature, and is generally applied to stationary signals. However, the fault vibration signals of a roller bearing are non-stationary and non-Gaussian. Aiming at this problem, the set of parameters of the AR model is estimated based on higher-order cumulants. Consequently, the AR parameters are taken as the feature vectors, and fuzzy cluster analysis is applied to perform classification and pattern recognition. Experiments analysis results show that the proposed method can be used to identify various types and severities of fault bearings. This study is significant for non-stationary and non-Gaussian signal analysis, fault diagnosis and degradation assessment.

Lingli Jiang

Yilun Liu

Xuejun Li

Anhua Chen

Degradation Assessment and Fault Diagnosis for Roller Bearing Based on AR Model and Fuzzy Cluster Analysis

The presence of a crack in a structure affects its dynamic behaviour under working conditions. Cracks introduce nonlinearities into the system; the use of such nonlinearities for damage detection should be investigated. A model of a one-dimensional cracked cantilever bar subjected to longitudinal harmonic excitation is used to analyse a vibro-impact response as a way to monitor structural health. The effect of contact nonlinearity due to crack's faces interaction is considered. This nonlinear information is obtained based on a combination of the analytical technique and the Matlab-Simulink computation. The procedure uses a numerical approximation for dynamic compliance operators and a nonlinear model of contact faces interaction implemented numerically as a nonlinear feedback. Nonlinear resonant phenomena due to vibro-impact interaction in the cracked bar are obtained and analysed. A distribution of the higher harmonics along the bar length, generated due to the nonlinear response of the crack, is revealed as a function of the distance from the crack. Recommendations on structural health monitoring of cracked bars due to contact nonlinearity are presented

Vikrant R. Hiwarkar

Vladimir I. Babitsky

Vadim V. Silberschmidt

Vibro-Impact Response of a Cracked Bar

The large-scale rotary machine with multi-supporting, such as rotary kiln and rope laying machine, is the key equipment in the architectural, chemistry, and agriculture industries. The body, rollers, wheels, and bearings constitute a chain multibody system. Axis line deflection is a vital parameter to determine mechanics state of rotary machine, thus body axial vibration needs to be studied for dynamic monitoring and adjusting of rotary machine. By using the Riccati transfer matrix method, the body system of rotary machine is divided into many subsystems composed of three elements, namely, rigid disk, elastic shaft, and linear spring. Multiple wheel-bearing structures are simplified as springs. The transfer matrices of the body system and overall transfer equation are developed, as well as the response overall motion equation. Taken a rotary kiln as an instance, natural frequencies, modal shape, and response vibration with certain exciting axis line deflection are obtained by numerical computing. The body vibration modal curves illustrate the cause of dynamical errors in the common axis line measurement methods. The displacement response can be used for further measurement dynamical error analysis and compensation. The response overall motion equation could be applied to predict the body motion under abnormal mechanics condition, and provide theory guidance for machine failure diagnosis.

Yiping Shen

Songlai Wang

Dynamic Modeling and Analysis of the Large-Scale Rotary Machine with Multi-Supporting

The variations of the supporting condition, which change the stiffness of tilting pad thrust bearing, may alter the dynamic behavior of the rotor system. The effects of supporting condition of thrust pad on the lateral vibration of a hydroelectric generating set are investigated in this paper. The action of a thrust bearing is described as moments acting on the thrust collar, and the tilting stiffness coefficients of thrust bearing are calculated. A model based on typical beam finite element method is established to calculate the dynamic response, and the effects of supporting conditions such as elastic oil tank support, different heights of the thrust pads with rigid support are discussed. The results reveal that the influence of thrust bearing is small when the elastic oil tanks work normally. When the supporting conditions turn to be rigid due to the oil leakage, the differences of thrust pad heights have evident influence on the load distribution of the thrust pads; while the effects on the tilting stiffness of the thrust bearing and the amplitude of the lateral shaft vibration is small when the maximum load on thrust pads is smaller than the allowable value.

Xiaohui Si

Wenxiu Lu

Lateral Vibration of Hydroelectric Generating Set with Different Supporting Condition of Thrust Pad

Adhesives are being increasingly used in structural applications, especially in aerospace, automotive and naval structures, making their structural integrity an important issue. In-service loading histories of such structures usually contain low-energy impacts, repetition of which can significantly affect their performance. This paper deals with the behaviour of the toughened epoxy adhesive FM73 under repeated impacts, known as impact fatigue. Izod impact fatigue tests were performed on FM73 specimens in order to study the evolution of damage and to characterise this via measurable parameters, such as the maximum force and the contact time. A finite element model was developed to simulate the impact tests and this was used to calculate the dynamic strain energy release rate, which was compared with that determined using a simple analytical method. A relationship between the maximum dynamic strain energy release rate and impact fatigue crack growth rate was established that was used as the basis of an impact fatigue crack growth law.

Ian A. Ashcroft

Benjamin Echard

Juan Pablo Casas Rodriguez

Crack Propagation in a Toughened Epoxy Adhesive under Repeated Impacts

The shaft crack is one of the main serious malfunctions that often occur in rotating machinery. However, it is difficult to locate the crack and determine the depth of the crack. In this paper, the acoustic emission (AE) signal and vibration response are used to diagnose the crack. The wavelet transform is applied to AE signal to decompose into a series of time-domain signals, each of which covers a specific octave frequency band. Then an improved union method based on threshold and cross-correlation method is applied to detect the location of the shaft crack. The finite element method is used to build the model of the cracked rotor, and the crack depth is identified by comparing the vibration response of experiment and simulation. The experimental results show that the AE signal is effective and convenient to locate the shaft crack, and the vibration signal is feasible to determine the depth of shaft crack.

Shaft Crack Identification Based on Vibration and AE Signals

Fractional-order derivative has been shown an adequate tool to the study of so-called &#x22;anomalous&#x22; social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots). The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.

Z.H. Wang

M. L. Du

Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

Qingkai Han

Xueyan Zhao

Xingxiu Li

Bangchun Wen

Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

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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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