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.

An extended computational model of the circulatory system for designing ventricular assist devices.

An extended computational model of the circulatory system has been developed to predict blood flow in the presence of ventricular assist devices (VADs). A novel VAD, placed in the descending aorta, intended to offload the left ventricle (LV) and augment renal perfusion is being studied. For this application, a better understanding of the global hemodynamic response of the VAD, in essence an electrically driven pump, and the cardiovascular system is necessary. To meet this need, a model has been established as a nonlinear, lumped-parameter electrical analog, and simulated results under different states [healthy, congestive heart failure (CHF), and postinsertion of VAD] are presented. The systemic circulation is separated into five compartments and the descending aorta is composed of three components to accurately yield the system response of each section before and after the insertion of the VAD. Delays in valve closing time and blood inertia in the aorta were introduced to deliver a more realistic model. Pump governing equations and optimization are based on fundamental theories of turbomachines and can serve as a practical initial design point for rotary blood pumps. The model's results closely mimic established parameters for the circulatory system and confirm the feasibility of the intra-aortic VAD concept. This computational model can be linked with models of the pump motor to provide a valuable tool for innovative VAD design.