The ensemble statistics of the band-averaged energy of a random system

This paper is concerned with the response statistics of a dynamic system that has random properties. The frequency-band-averaged energy of the system is considered, and a closed form expression is derived for the relative variance of this quantity. The expression depends upon three parameters: the modal overlap factor m, a bandwidth parameter B, and a parameter α that defines the nature of the loading (for example single point forcing or rain-on-the-roof loading). The result is applicable to any single structural component or acoustic volume, and a comparison is made here with simulation results for a mass loaded plate. Good agreement is found between the simulations and the theory. © 2003 Published by Elsevier Ltd.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.

Selective epitaxial growth in silicon on insulator: Planarity and mass flow

Seeded zone-melt recrystallization using a dual electron beam system has been performed on silicon-on-insulator material, which was prepared with single-crystal silicon filling of the seed windows by selective epitaxial growth. The crystal quality has been assessed by a variety of microscopic techniques, and it is shown that single-crystal films 0.5-1.0 μm thick over 1.0 μm of isolating oxide may be prepared by this method. These films have considerably less lateral variation in thickness than standard material, in which the windows are not so filled. The filling method is suitable for both single- and multiple-layer silicon-on-insulator, and gives the advantages of excellent layer uniformity after recrystallization and improved planarity of the whole chip structure. Experiments using various amounts of seed window filling have shown that the lateral variations of silicon film thickness seen in unplanarized material are due to stress relief in the cap oxide when the silicon film is molten, rather than the effect previously postulated in which they were assumed to be due to the contraction of silicon on melting.

Imaging the femoral cortex: thickness, density and mass from clinical CT.

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm(2)) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex.

Imaging the femoral cortex: Thickness, density and mass from clinical CT

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm 2) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex. © 2012 Elsevier B.V.

A design strategy in the propulsion system attachment to a submarine hull to minimise radiated noise

Vibration modes of a submerged hull are excited by fluctuating forces generated at the propeller and transmitted to the hull via the propeller-shafting system. The low frequency hull vibrational modes result in significant sound radiation. This work investigates the reduction of the far-field radiated sound pressure by optimising the connection point of the shafting system to the hull. The submarine hull is modelled as a fluid loaded cylindrical hull with truncated conical shells at each end. The propeller-shafting system consists of the propeller, shaft, thrust bearing and foundation, and is modelled in a modular approach using a combination of spring-mass-damper elements and continuous systems (beams, plates, shells). The foundation is attached to the stern side end plate of the hull, which is modelled as a circular plate coupled to an annular plate. By tuning the connection radius of the foundation to the end plate, the maximum radiated noise in a given frequency range can be minimised.

A general mass law for broadband energy harvesting

It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. © 2013 The Author.