Effects of geometric variation and residual stress on the dynamic response of multilayerd thin membrane structures

Tai Chun Han

Thin-film structures have found a wide variety of applications in emerging technologies. Along with the hardware development, there is also a need for a design methodology for such structure. The methodology would allow the designer to be able to predict the performance of these structures before they are fabricated. The currently available methodology assumes that the membrane structures are flat and all the dimensions can be precisely measured. However, in reality, there are always some variations on the dimension measurements. Furthermore, the structures usually have somewhat distorted shapes due the residual stress introduced during the fabrication process. The objective of the current study was to gain insights into the dynamic responses of thin membrane structures. Specifically, the effects of dimensional variations and shape changes due to residual stress on the fundamental frequencies of the structures were examined. The approach used was numerical simulation with ANSYS. It was found that the increase of thickness and decrease of in-plane dimensions would increase the resonance frequencies. However, a 15% variation of these dimensions as deemed reasonable from the practical point of view still could not bring up the predicted frequencies within the experimentally observed range. For the effects of shape change, it was found that the domed shape has the highest frequency compared to other shapes with the same size and out-of-plane displacement, but multiple curvatures. To get a correlation between the shape change and residual stress, thermal cycling simulation was also performed. In this simulation, the structure was subjected to 25-1000-25° C thermal cycling and the resultant deformed shape was then used as an input for the subsequent dynamic analysis. It was found that the deformed shape obtained from thermal cycling simulation would still underestimate the frequencies quite significantly. However, with a combination of dimensional variation and shape change, the predicted frequencies could be brought into closer to the experimentally observed values. It was concluded that dimensional variation and shape change due to residual stress could significantly vary the dynamic response of the thin membrane structures. However, the quantitative evaluation of the contribution from residual stress requires further study on the source and realistic simulation of residual stresses.

Effects of geometric variation and residual stress on the dynamic response of multilayerd thin membrane structures

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