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research-article  
Osamu Nishihara
J. Vib. Acoust   doi: 10.1115/1.4040575
In this study, the maximum amplitude magnification factor for a linear system equipped with a three-element dynamic vibration absorber (DVA) is exactly minimized for a given mass ratio using a numerical approach. The frequency response curve is assumed to have two resonance peaks, and the parameters for the two springs and one viscous damper in the DVA are optimized by minimizing the resonance amplitudes. The three-element model is known to represent the dynamic characteristics of air-damped DVAs. A generalized optimality criteria approach is developed and adopted for the derivation of the simultaneous equations for this design problem. The solution of the simultaneous equations precisely equalizes the heights of the two peaks in the resonance curve and achieves a minimum amplitude magnification factor. The simultaneous equations are solvable using the standard built-in functions of numerical computing software. The performance improvement of the three-element DVA compared to the standard Voigt type is evaluated based on the equivalent mass ratios. This performance evaluation is highly accurate and reliable because of the precise formulation of the optimization problem. Thus, the advantages of the three-element type DVA have been made clearer.
TOPICS: Optimization, Vibration absorbers, Magnification, Resonance, Dampers, Design, Computer software, Frequency response, Linear systems, Performance evaluation, Springs
research-article  
Anup Pydah and Dr. Romesh Batra
J. Vib. Acoust   doi: 10.1115/1.4040576
We present a novel beam-based vibration energy harvester that uses a structural tailoring concept to tune its resonance frequencies. Using a solution of the beam theory equations, verified with finite element (FE) simulations using a shell theory, we show that introducing folds or creases along the span of a slender beam, varying the the fold angle at a crease, and changing the crease location helps tune the beam natural frequencies to match an external excitation frequency and maximize the energy harvested. For a beam clamped at both ends, the first frequency can be increased by 232% with a single fold, while selective frequencies can be tuned, leaving others unchanged, with two folds. The fold location, the number of folds and the fold angle act as tuning parameters which provide high sensitivity and controllability of the frequency response of the harvester. The analytical model can be used to quickly optimize designs with multiple folds for anticipated external frequencies.
TOPICS: Vibration, Energy harvesting, Frequency response, Shells, Euler-Bernoulli beam theory, Excitation, Resonance, Simulation, Engineering simulation, Finite element analysis
research-article  
Zhongming Xu, Kai Tian, Yansong He, Zhifei Zhang and Shu Li
J. Vib. Acoust   doi: 10.1115/1.4040521
Conventional frequency domain beamforming (FDBF) relies on the measured cross-spectral matrix (CSM). However, in wind tunnel tests, the CSM diagonal is contaminated by the interference of incoherent noise after long-time averaging which leads the source map to poor resolution. Diagonal removal can suppress the noise in beamforming results via the deletion of CSM diagonal; but this method leads to the underestimation of source levels and some negative powers in source maps. Some advanced methods, such as background subtraction, make use of background noise reference to counteract the effects of contamination; however, the results usually become unreliable, because the background noise is difficult to keep constant in the different measurements. Diagonal denoising beamforming is a recent approach to suppress the contamination effects; but it attenuates the noise suppression performance. To overcome the limitations of the above methods, a new method called denoising weighting beamforming (DWB) is proposed in this study on basis of CSM diagonal denoising and an iterative regularization method is applied to solve the acoustical inverse problem. Besides, in order to correct the phase mismatch caused by the influence of flow on sound propagation, the shear flow correction is added before using DWB. Experiments on sound source reconstruction are conducted in the environment with the flow. Acoustics data obtained via this method show the successful removal of incoherent noise and the corrected phase mismatch. Furthermore, the sound source localization results are promising and the proposed method is simple to implement.
TOPICS: Flow (Dynamics), Acoustics, Air flow, Resolution (Optics), Shear flow, Contamination, Noise (Sound), Inverse problems, Microphone arrays, Wind tunnels
research-article  
Gizem Acar and Brian Feeny
J. Vib. Acoust   doi: 10.1115/1.4040522
General responses of multi-degree-of-freedom (MDOF) systems with parametric stiffness are studied. A Floquet-type solution, which is a product between an exponential part and a periodic part, is assumed, and applying harmonic balance, an eigenvalue problem (EVP) is found. Solving the EVP, frequency content of the solution, and response to random initial conditions are determined. Using the eigenvalues and the eigenvectors, the system response is written in terms of "Floquet modes", which are non-synchronous, contrary to linear modes. Studying the eigenvalues (i.e. characteristic exponents), stability of the solution is investigated. The approach is applied to MDOF systems, including an example of a three-blade wind turbine, where the equations of motion have parametric stiffness terms due to gravity. The analytical solutions are also compared to numerical simulations for verification.
TOPICS: Wind turbines, Eigenvalues, Stiffness, Stability, Gravity (Force), Computer simulation, Equations of motion, Blades
research-article  
Qing Li and Deqing Yang
J. Vib. Acoust   doi: 10.1115/1.4040514
Sandwich structures that are embedded with cellular materials show excellent performance in terms of mechanics, electromagnetics and acoustics. In this paper, sandwich panels with hybrid cellular cores of hexagonal, re-entrant hexagonal and rectangular configurations along the panel surface are designed. The spectral element method (SEM) is applied to accurately predict the dynamic performance of the sandwich panels with a reduced number of elements and the system scale within a wide frequency range. The mechanical and acoustic performance of the proposed structures is investigated and compared with conventional honeycomb panels with fixed cell geometries. It was found that the bending stiffness, fundamental frequencies and sound transmission loss (STL) of the presented sandwich panels can be effectively changed by adjusting their hybrid cellular core configurations. A shape optimization design for a hybrid cellular core for maximum STL is presented for specified tonal and frequency band cases. Besides, hybrid sandwich panels can increase sound insulation by 24.7%, 20.6%, and 109.6% for those cases, respectively, compared with conventional panels in this study. These results indicate the potential of sandwich structures with hybrid cellular cores in acoustic attenuation applications. Hybrid cellular cores can lead to inhomogeneous mechanical performance and constitute a broader platform for the optimum mechanical or acoustic design of sandwich structures.
TOPICS: Acoustics, Sandwich structures, Design, Electromagnetism, Stiffness, Shape optimization, Sound, Acoustical materials, Honeycomb structures, Equipment performance, Electromagnetic force, Electromagnetic spectrum
research-article  
Alborz Niknam and Kambiz Farhang
J. Vib. Acoust   doi: 10.1115/1.4040513
The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and pre-compression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.
TOPICS: Friction, Vibration, Compliant mechanisms, Springs, Belts, Damping, Steady state, Stability, Dampers, Equilibrium (Physics), Equations of motion, Trajectories (Physics), Hardening, Bifurcation, Compression, Eigenvalues
research-article  
Jonathan Salvi, Egidio Rizzi, Emiliano Rustighi and Neil Ferguson
J. Vib. Acoust   doi: 10.1115/1.4040475
Tuned Mass Dampers (TMDs) are typically introduced and calibrated as natural passive control devices for the vibration mitigation of the steady-state response of primary structures subjected to persistent excitations. Otherwise, this work investigates the optimum tuning of TMDs towards minimising the transient structural response. Specifically, a single-degree-of-freedom system is considered as a primary structure, with added TMD, subjected to pulse-like excitations. First, the system is analytically analysed, within the time domain, for unit impulse base displacement, through Laplace transform. Then, the tuning process is numerically explored by an optimisation procedure focused on an average response index, to extract the optimum condition towards best TMD calibration. The efficiency of the proposed control device is then assessed and demonstrated through further post-tuning numerical tests, by considering as dynamic loadings: first, a time unit impulse base displacement, coherent with the source description above; second, different pulse-like excitations, to detect the effectiveness of the so-conceived TMD for generic ideal shock actions; third, a set of non-stationary earthquake excitations, to enquire the achievable level of seismic isolation. It is shown that this leads to a consistent passive TMD in such a transient excitation context, apt to mitigate the average response. Additionally, the present tuning forms a necessary optimum background for a possible upgrade to a hybrid TMD, with the potential addition of an active controller to the so-optimised TMD, to achieve even further control performance, once turned on, specifically for abating the peak response, too.
TOPICS: Dampers, Excitation, Displacement, Transients (Dynamics), Impulse (Physics), Control equipment, Shock (Mechanics), Optimization, Vibration, Calibration, Earthquakes, Laplace transforms, Steady state, Passive control
research-article  
Le Hung Tran, Tien Hoang, Denis Duhamel, Gilles Foret, Samir Messad and Arnaud Loaec
J. Vib. Acoust   doi: 10.1115/1.4040392
Existing analytical models for the railway track consider only one rail supported by a continuous foundation or periodic concentrated supports (called the periodically supported beam). This article presents an analytical model for a railway track which includes two rails connected by sleepers. By considering the sleepers as Euler-Bernoulli beams resting on a Kelvin-Voigt foundation, we can obtain a dynamic equation of a sleeper subjected to the reaction forces of the rails. Then, by using the relation between the rail forces and displacements from the periodically supported beam model, we can calculate the sleeper responses with the help of Green's function. The numerical applications shows that the sleeper is in flexion where the displacement at the middle of the sleeper is greater than those at the rail seats. Moreover, the deformed shape of the sleeper is non-symmetric when the loads on the two rails are different. The result of the model agrees well with measurements performed using instrumented sleepers in-situ.
TOPICS: Prestressed concrete, Railroads, Rails, Shapes, Stress, Displacement
research-article  
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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