Vibration isolation of a rigid body on compliant mounts has many engineering applications. An analysis for solving these problems using a rigid body simulation and a penalty function optimization is discussed. The simulation is used to calculate natural frequencies and mode shapes, which are a function of the mount design parameters. Laboratory testing results are presented which verify the accuracy of the simulation. The optimization procedure penalizes natural frequencies in an undesirable frequency range and also large design changes. This penalty function is minimized by changing the mount design paramters consisting of the location, stiffness, and/or orientation. The result is a set of design parameters defining a vibration isolation system with natural frequencies moved away from the center of the undesirable frequency range. An interactive computer program was written which allows the engineer to use this technique as a design tool.

This urticlr qitunti'jes errors arising from vcirious integrcition methods and,from sampling density in thti numerical rstimcition i?f'cdorimrtric integrcils,e.g. tristimirlus ual-i4e.Y. Both dutu sumpling dtwsity and uarious numerical itrtegrtttion method errors will be distingitished. A test is presrntrd to yriantib sampling intrrual rryuirrmrnts f o r acrurutr cdorimetric calculations j b r various illuminunt.s. Cj I992 John Wile? & S o w , Inc.

Few actual sound fields are representative of ideal acoustic pressure responses and ideal boundary conditions, such as those nearly found in anechoic or reverberant rooms. Normally encountered enclosures have complicated responses that are difficult to relate to a boundary condition that is inbetween these two ideal extremes. Yet, the propagating-and standing-wave responses associated with absorptive and reflective boundary conditions seen in the ideal cases are fundamental bases to understand these more complicated problems. An analytical method is developed to decompose a one-dimensional acoustic pressure response associated with a specified partially absorptive boundary condition into an equivalent summation of propagating and standing waves usually.associated with absorptive and reflective boundary conditions, respectively. The propagating-and standing-wave responses are scaled and shifted in phase by factors that are dependent on the boundary absorptivity and frequency, but are independent of the spatial location. The complicated mixed response is decomposed into varying amounts of the ideal responses, which can be helpful during a design analysis.

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