Accepted Manuscripts

Ahmad Mohammadpanah and Stanley Hutton
J. Vib. Acoust   doi: 10.1115/1.4039421
It can be predicted by Rayleigh’s interlacing eigenvalue theorem that structural modifications of a spinning disk can shift the 1st critical speed of the system up to a known limit. In order to corroborate this theorem, it is shown numerically, and verified experimentally that laterally constraining of a free spinning flexible thin disk with tilting and translational degree of freedom, the first critical speed of the disk cannot increase more than the second critical speed of the original system (the disk with no constraint). The governing linear equations of transverse motion of a spinning disk with rigid body translational and tilting degrees of freedom are used in the analysis of eigenvalues of the disk. The numerical solution of these equations is used to investigate the effect of the constraints on the critical speeds of the spinning disk. Experimental tests were conducted to verify the results.
TOPICS: Theorems (Mathematics), Eigenvalues, Rotating Disks, Disks, Degrees of freedom, Spinning (Textile), Spin (Aerodynamics)
Tiejun Yang, Di Huang, Xinhui Li, Michael J. Brennan, liubin Zhou, Minggang Zhu and Zhigang Liu
J. Vib. Acoust   doi: 10.1115/1.4039407
This paper describes an experimental investigation into the vibration control of multiple electrical machines installed on a large-scale floating raft system. Vibration transmission to a flexible hull-like structure that supports the floating raft, is controlled by adjusting the phases of the electrical power supply to the machines - a technique known as synchrophasing. Each machine is driven by a phase asynchronous motor and has two counter rotating shafts with adjustable eccentric masses, which allows the dynamic force generated by each machine to be set independently. Up to four rotating machines are considered. A genetic algorithm is used in the search for the optimum relative phases between each machine, because it is impractical to carry out an exhaustive search of the huge number of possible phase combinations. It is demonstrated that vibration control using syncrophasing is feasible in a marine environment, and can achieve significant vibration reduction, by simply adding some sensors and a control system. Reductions in the total transmitted vibration, as measured by the sum of the squared accelerations from 22 error sensors on the hull-like structure, was found to be up to 13 dB, and vibration reduction at higher harmonic frequencies was found to be up to 51 dB.
TOPICS: Machinery, Vibration control, Vibration, Sensors, Hull, Electricity (Physics), Control systems, Engines, Motors, Errors, Genetic algorithms
Xinlei Zhu, Ming Yang, Yaqiong Zhang, Na Ta and Zhushi Rao
J. Vib. Acoust   doi: 10.1115/1.4039401
Precisions of localization are a function of the size of an array. A kind of parasitoid fly, Ormia ochracea, performs an extraordinary directional hearing ability despite of its tiny-scaled auditory organ. In this paper, vibration modes and transfer functions of the Ormia ochracea’s ear model were calculated, and the phase difference amplification in responses are analyzed to investigate the directional hearing mechanism. A novel three-element bionic model is proposed for spatial sound source localization for small distance-wavelength ratios. The amplification of the phase difference of this model is verified. In order to realize the bionic localization model, based on electric-mechanic analogy method, a system that consists of a triangular acoustic array and a bionic coupling circuit is designed and tested. Frequency responses of the circuit output, as a means of transfer function of the system are taken into estimation of the source directions. The result has shown that this circuit design has better performance in estimating the direction of sound sources compared to the uncoupled array with same size.
TOPICS: Bionics, Acoustics, Circuits, Transfer functions, Ear, Vibration, Circuit design, Frequency response, Wavelength
Mennatullah M. Abdel Hafeez and Ayman A. El-Badawy
J. Vib. Acoust   doi: 10.1115/1.4039402
This work presents a new aeroelastic model that governs the extensional, chordwise, flapwise and torsional vibrations of an isolated horizontal axis wind turbine blade. The model accounts for the sectional offsets between the shear, aerodynamic and mass centers. The centrifugal stiffening effects are also accounted for by including nonlinear strains based on an ordering scheme that retains terms up to second order. Aerodynamic loading is derived based on a modified Theodorsen’s theory adapted to account for the blade rotational motion. A set of four coupled nonlinear partial differential equations are derived using the Hamiltonian approach that are then linearized about the steady state extensional position. The FEM (Finite Element Method) is then employed to spatially discretize the resulting equations with the aim of obtaining an approximate solution to the blade’s dynamic response, utilizing state space techniques and complex modal analysis. Investigation of the blade’s flutter stability limit is carried out. Effects of parameters such as wind speed and blade sectional offsets on the flutter limit and dynamic response are also investigated.
TOPICS: Blades, Flutter (Aerodynamics), Horizontal axis wind turbines, Finite element methods, Dynamic response, Partial differential equations, Steady state, Rotation, Stability, Wind velocity, Shear (Mechanics), Modal analysis, Vibration
Xiongtao Cao, Wang MingSheng and Shi Lei
J. Vib. Acoust   doi: 10.1115/1.4039403
Sound radiation from stationary and rotating point acoustic sources with shield of rigid prolate spheroidal baffles is explored in the prolate spheroidal coordinate system. The formulae of far-field sound pressure and acoustic power are derived and acoustic power spectral density (PSD) in terms of circumferential and azimuthal wavenumber is manifested from the low frequency range to high frequency range. Acoustic wave propagation features in the spherical coordinate system as a particular case of the prolate spheroidal coordinate system are presented. Rotating sound sources cause the frequency veering phenomenon and change the patterns of PSD. Some spheroidal harmonic waves with lower and higher wavenumber for the large prolate spheroids can't contribute to far-field sound radiation in the high frequency range when sound sources are close to the axes of the spheroids. Sound pressure directivity and acoustic power of stationary point sound sources are also analyzed with the variation of source location.
TOPICS: Acoustics, Sound, Sound pressure, Spectral energy distribution, Waves, Wave propagation
Rajiv Kumar Vashisht and Qingjin Peng
J. Vib. Acoust   doi: 10.1115/1.4039404
It is confirmed experimentally that in case of a rotor with crack, multiple harmonics are generated when the rotor revolves at a particular frequency. Only few modeling techniques successfully predict this particular behavior of the cracked rotor. It is observed in this research that modeling cracked rotors using conventional finite element methods cannot predict this particular behavior successfully. A nonlinear dynamic model of the flexible rotor with ball bearings is developed using discrete mass spring damper elements combined with an existing model of the crack to truly predict this confirmed experimental behavior. Certain crack detection techniques based on the steady state response work well on this basic concept of the multi-harmonics generation due to nonlinearities caused by cracks in the rotor. The presence of ball bearings, rotor-coupling misalignment, rotor-stator rub and rotor bow can also cause significant nonlinearities in the overall system. These additional nonlinearities render these crack detection techniques to lose their effectiveness. Our work justifies the model through simulations that the Jeffcott rotors are the over simplified version of real life rotor bearing systems. Hence, these crack detection techniques cannot be efficiently applied for condition monitoring of real rotor bearing systems. The proposed model also helps to understand that the presence of flexible bearing supports affects the dynamics of the system considerably and negatively affects the effectiveness of these crack detection techniques.
TOPICS: Rotors, Ball bearings, Dynamic modeling, Damage, Crack detection, Fracture (Materials), Bearings, Modeling, Springs, Stators, Steady state, Dynamic models, Dampers, Engineering simulation, Condition monitoring, Dynamics (Mechanics), Simulation, Finite element methods
Haitao Liao and Wenwang Wu
J. Vib. Acoust   doi: 10.1115/1.4039405
A hybrid approach is proposed to evaluate the probability of unacceptable performance with respect to the uncertain parameters. The evaluation of the structural reliability and the solution of maximum vibration response is performed simultaneously. A constrained optimization problem is deduced for which several techniques have been developed to obtain the reliability index. The nonlinear equality constraints of the optimization problem are constructed based on the harmonic balance equations, the optimality condition of the maximum vibration response with respect to the vibration frequency and the limit state failure function. With the nonlinear equality constraints imposed on the harmonic balance equations and the derivative of the maximum vibration response with respect to the vibration frequency, the inner loop for solving the maximum vibration response is avoided. The sensitivity gradients are derived by virtue of the adjoint method. The original optimization formulation is then solved by means of the Sequential Quadratic Programming method(SQP) method. Finally, the developed approach has been verified by comparison with reference values from Monte Carlo simulation. Numerical results reveal that the proposed method is capable of predicting the failure probability of nonlinear structures with random uncertainty.
TOPICS: Nonlinear systems, Failure, Probability, Uncertainty, Vibration, Optimization, Reliability, Oscillating frequencies, Quadratic programming, Simulation
Ashu Sharma and Subhash C. Sinha
J. Vib. Acoust   doi: 10.1115/1.4039406
In most parametrically excited systems stability boundaries cross each other at several points to form closed unstable sub-regions commonly known as ‘Instability Pockets’. The first aspect of this study explores some general characteristics of these instability pockets and their structural modifications in the parametric space as damping is induced in the system. Secondly, the possible destabilization of undamped systems due to addition of damping in parametrically excited systems has been investigated. The study is restricted to SDF systems that can be modeled by Hill and Quasi-Periodic Hill equations. Three typical cases of Hill equation, e.g., Mathieu, Meissner and three-frequency Hill equations are analyzed. State transition matrices of these equations are computed symbolically/analytically over a wide range of system parameters and instability pockets are observed in the stability diagrams of Meissner, three-frequency Hill and Quasi-Periodic Hill equations. Locations of the intersections of stability boundaries (commonly known as coexistence points), are determined using the property that two linearly independent solutions coexist at these intersections. For Meissner equation, with a square wave coefficient, analytical expressions are constructed to compute the number and locations of the instability pockets. In the second part of the study, the symbolic/analytic forms of state transition matrices are used to compute the minimum values of damping coefficients required for instability pockets to vanish from the parametric space. The phenomenon of destabilization due to damping, previously observed in systems with two degrees-of-freedom or higher, is also demonstrated in systems with one degree-of-freedom.
TOPICS: Damping, Stability, Degrees of freedom, Waves
Meng-Hsuan Tien, Tianyi Hu and Kiran X. D'Souza
J. Vib. Acoust   doi: 10.1115/1.4039296
Analysis of the influence of cracks on the dynamics of bladed disks is critical for design, failure prognosis, and structural health monitoring. Predicting the dynamics of cracked bladed disks is computationally challenging for two reasons: (1) the model size is quite large, and (2) the piecewise-linear nonlinearity caused by contact eliminates the use of linear analysis tools. Recently, a technique referred to as the X-Xr approach was developed to efficiently reduce the model size of cracked bladed disks. The method employs relative coordinates to describe the motion of crack surfaces such that an effective model reduction can be achieved using single sector calculations. More recently, a method referred to as the generalized bilinear amplitude approximation (generalized BAA) was developed to approximate the amplitude and frequency of piecewise-linear nonlinear systems. This paper modifies the generalized BAA method and combines it with the X-Xr approach to efficiently predict the dynamics of cracked bladed disks. The combined method is able to construct the reduced-order model of full disks using single-sector models only and estimate the amplitude and frequency with a significantly reduced computational effort. The proposed approach is demonstrated on a three degrees-of-freedom spring-mass system and a cracked bladed disk.
TOPICS: Fracture (Materials), Modeling, Disks, Dynamics (Mechanics), Approximation, Failure, Springs, Structural health monitoring, Nonlinear systems, Degrees of freedom, Design
Jing Wei, Peixin Bai, Datong Qin, Teik C. Lim, Panwu Yang and Hong Zhang
J. Vib. Acoust   doi: 10.1115/1.4039246
Based on the requirements of the dynamic design of geared turbofan (GTF) engines, the vibration characteristic of the fan shaft is investigated. The effect of sudden imbalance caused by blade off, the time-varying meshing stiffness, and meshing errors on the vibration characteristics are fully considered in the dynamic model. The improved Euler-Bernoulli beam element considering the effects of shear deformation is employed and a coupled relationship between the gear-shaft-bearing-casing is established. Under windmilling condition with a single blade completely lost, the vibration characteristics of the fan shaft of the turbofan engine with and without a gearbox system are compared. The effect of the gear system on the vibration of the fan shaft under different rotating speeds is examined. The results show that the orbit of the fan shaft center in the turbofan engine with the gearbox system exhibits a multi-frequency whirling motion and has a stable limit cycle. Under windmilling condition, the meshing frequency and modal frequency have multiple intersection points. The critical speed is dense and the peak value of the transient vibration of the GTF engine gearbox shows a wave rise with an increase in speed. The results of this study could provide a reference for the parameter design and optimization of GTF engines.
TOPICS: Engines, Vibration, Blades, Turbofans, Mechanical drives, Design, Gears, Optimization, Limit cycles, Errors, Shear deformation, Stiffness, Whirls, Dynamic models, Waves, Transients (Dynamics), Bearings
Aman Kumar and Anirvan Dasgupta
J. Vib. Acoust   doi: 10.1115/1.4039239
A dynamic model for a shell-type amplified piezoelectric actuator (APA) is proposed. The dimensions of the shell of a typical shell-type actuator allows one to model it as a set of connected beams. The contribution of the geometric nonlinearity in the axial direction of the beams due to bending is accounted for in the formulation. Subsequent nonlinear analysis using both analytical and numerical approaches reveals the presence of second harmonics in the response spectrum. This occurrence is also seen experimentally. A frequency regime is also identified within which the effect of quadratic nonlinearity is minimal and the actuator exhibits maximum fidelity. Dependence of the response spectrum on the actuator geometry has been studied. For a given forcing frequency, a certain geometric configuration is shown to exist which maximizes the nonlinear effects. The effect of prestressing of the piezoelectric stack on the frequency spectrum is also studied. The obtained results are expected to lead to improved design of such actuators.
TOPICS: Dynamics (Mechanics), Piezoelectric actuators, Shells, Actuators, Design, Geometry, Dimensions, Dynamic models
David Griese, Joshua D. Summers and Lonny Thompson
J. Vib. Acoust   doi: 10.1115/1.4029043
This work defines a finite element model to study the sound transmission properties of aluminium honeycomb sandwich panels. Honeycomb cellular metamaterial structures offer many distinct advantages over homogenous materials because their effective material properties depend on both their constituent material properties and their geometric cell configuration. From this, a wide range of targeted effective material properties can be achieved thus supporting forward design by tailoring the honeycomb cellular materials for specific applications. One area that has not been fully explored is the set of acoustic properties of honeycomb materials and how these can offer increased acoustic design flexibility. Understanding these relations, the designer can effectively tune designs to perform better in specific acoustic applications. One such example is the insulation of target sound frequencies to prevent sound transmission through a panel. This work explores how certain geometric and effective structural properties of in-plane honeycomb cores in sandwich panels affect the sound pressure transmission loss properties of the panel. The two acoustic responses of interest in this work are the general level of sound transmission loss of the panel and the location of the resonance frequencies that exhibit high levels of sound transmission, or low sound pressure transmission loss. Constant mass honeycomb core models are studied with internal cell angles ranging from -45° to +45°. It is shown in this work that models with lower core internal cell angles, under constant mass constraints, have more resonances in the 1-1000 Hz range, but exhibit a higher sound pressure transmission loss between resonant frequencies.
TOPICS: Sound, Honeycomb structures, Geometry, Acoustics, Materials properties, Sound pressure, Resonance, Design, Finite element model, Insulation, Metamaterials, Aluminum, Mechanical properties, Acoustical properties

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