Agnes O'Gallagher

Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

CALCULATED REGENERATOR PERFORMANCE AT 4 K WITH HELIUM-4 AND HELIUM-3

The helium-4 working fluid in regenerative cryocoolers operating with the cold end near 4 K deviates considerably from an ideal gas. As a result, losses in the regenerator, given by the time-averaged enthalpy flux, are increased and are strong functions of the operating pressure and temperature. Helium-3, with its lower boiling point, behaves somewhat closer to an ideal gas in this low temperature range and can reduce the losses in 4 K regenerators. An analytical model is used to find the fluid properties that strongly influence the regenerator losses as well as the gross refrigeration power. The thermodynamic and transport properties of helium-3 were incorporated into the latest NIST regenerator numerical model, known as REGEN3.3, which was used to model regenerator performance with either helium-4 or helium-3. With this model we show how the use of helium-3 in place of helium-4 can improve the performance of 4 K regenerative cryocoolers. The effects of operating pressure, warm-end temperature, and frequency on regenerators with helium-4 and helium-3 are investigated and compared. The results are used to find optimum operating conditions. The frequency range investigated varies from 1 Hz to 30 Hz, with particular emphasis on higher frequencies.