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Published Articles

The Volume 16, No 4, December 2011

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Finite Element Vibration Analysis of Damped Composite Sandwich Beams

Samir Assaf


In this study, a finite element model for the vibration analysis of cross-ply laminated sandwich beams is presented. This formulation is an extension of our previous work on predicting the acoustic and vibration responses of sandwich beams and plates with homogeneous elastic faces and a viscoelastic core. The formulation is based on a layerwise linear axial displacement through the beam thickness. The formulation assumes the classical lamination theory for the faces and Timoshenko theory for the core. The governing equations of motion are obtained using Hamilton’s principle. A finite element method and a beam element are further developed to predict the natural frequencies and modal loss factors. In order to validate the proposed model, several free vibration analyses of composite sandwich beams with different boundary conditions, length-to-thickness ratios and face laminations are presented. The results are then compared with solutions available in the literature and with those obtained by the PATRAN/NASTRAN finite element software package. These results show the validity of the present formulation. Finally, the effects of ply-stacking sequence, core-to-face stiffness ratio and core-to-face thickness ratio upon the natural frequencies and modal damping are investigated.

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Gearbox Damage Diagnosis usingWavelet Transform Technique

Mohamed S. El-morsy, Shawki Abouel-seoud and El-Adl Rabeih


Vibration-based schemes are founded on the assumption that vibration signals from gearboxes measured using accelerometers reflect their condition accurately. A large number of vibration based techniques are used to make this reflection. They include various spectral analyses such as traditional Fourier transform, short-time Fourier transform, amplitude phase modulation and time synchronous averaging and non-parametric special estimation. Recently,Wavelet Transform (WT) has been proven to be more suitable for analysis of vibration signals, since most of the time-vibration signals have instantaneous impulse trains and exhibit a transient (non-stationary) nature. This paper uses an adaptive wavelet filter, based on the Morlet wavelet, applied on the torsional vibration data measured from a single-stage gearbox with artificially induced cracks in the gear. This is done to extract some parameters and check their diagnostic behavior in an effort to search for those with the most potential and appropriateness for future health monitoring schemes. The results demonstrate that the adaptive wavelet filter is found to be very effective in detection of symptoms from vibration signals of a gearbox with early tooth cracks. Moreover the influence of crack depth, speed, and load on the wavelet entropy are interduced. Multi-hour tests were conducted and recordings were acquired using torsional vibration monitoring. The transitions in the wavelet entropy values with the recording time were highlighted suggesting critical changes in the operation of the gearbox.

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Prediction of Breakout Noise from a Rectangular Duct with Compliant Walls

B. Venkatesham, Mayank Tiwari and M. L. Munjal


Breakout noise from HVAC ducts is important at low frequencies, and the coupling between the acoustic waves and the structural waves plays a critical role in the prediction of the transverse transmission loss. This paper describes the analytical calculation of breakout noise by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The first step in the breakout noise prediction is to calculate the inside duct pressure field and the normal duct wall vibration by using the solution of the governing differential equations in terms of Green's function. The resultant equations are rearranged in terms of impedance and mobility, which results in a compact matrix formulation. The Green's function selected for the current problem is the cavity Green's function with modification of wave number in the longitudinal direction in order to incorporate the terminal impedance. The second step is to calculate the radiated sound power from the compliant duct walls by means of an equivalent unfolded plate model. The transverse transmission loss from the duct walls is calculated using the ratio of the incident power due to surface source inside the duct to the acoustic power radiated from the compliant duct walls. Analytical results are validated with the FE-BE numerical models.

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Mistuning Effects Evaluation on Turbomachine Dynamic Behaviour using Genetic Algorithms

Gennaro Scarselli, Leonardo Lecce, Elisa Castorini


This paper presents a new approach to evaluating the mistuning effects on turbomachinery blades that is classified as neither deterministic nor statistical - it is based on the employment of genetic algorithms. A genetic algorithm has been exploited to find the structurally mistuned configuration that leads to the maximum value of blade vibration amplitude for an assigned domain of variations. A test case has been fixed and subjected to an assigned forcing field; the target of the test case was to perform a smart search of the worst mistuned configuration. The test case was a twenty-blade disc on which one thousand forced frequency response analyses have been performed. A comparison with the results, based on the Monte Carlo methods, proved the suitability and the relevance of the proposed approach. The investigation has demonstrated the applicability of this new possible engineering approach to the study of systems with uncertain properties.

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A degenerate case of the Timoshenko beam problem with boundary damping: an asymptotic and numerical study

Matthew P. Coleman and Les Schaffer


Recently, the Timoshenko beam, and generalizations thereof, have been considered as models for the vibration of single and multiple walled carbon nanotubes. Further, it has been shown that, in some instances, carbon nanotubes and nanotube sheets possess the common property that their Poisson's ratio is negative. In these cases, the degenerate case of the Timoshenko beam problem, where $E = k'G$, becomes physically realizable. The asymptotic derivation of the vibration spectrum in this case is qualitatively different from that for the nondegenerate case. We performed such a derivation, and we compared the asymptotic results with numerical results. Further, we performed parameter studies based on the exact frequency equation for the undamped case for values of $E/k'G$ on intervals including $E/k'G = 1$. The results show very interesting and complex behavior throughout a fairly large interval about $E/k'G = 1$.

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