Analysis of a bi-material strip

A theory-of-elasticity-based analytical (mathematical) model has been developed, in application to an advanced ceramic electrical sensor design, for a bi-material elongated strip experiencing longitudinal displacements distributed over one of its long edges. The actual gage is configured like a thin bi-material plate-like element attached to a thick-and-stiff carrier (substrate). The model assumes, however, that the mechanical behavior of such a gage could be evaluated by considering the behavior of the longitudinal cross-section of the gage and by treating this cross-section like an elongated bi-material strip. Because the substrate is typically much thicker and much stiffer than the strip, the displacements of the substrate determine the longitudinal displacements at the strip-substrate interface, while the displacements of the strip do not affect the displacements of the substrate. The obtained results enable one to determine how thick (high) the two component ceramic strips should/could be made, so that the substrate displacements could be adequately recorded and interpreted from the measured longitudinal displacements at the free edge of the bi-material strip. We have found that if the ratios of the thicknesses (heights) of each of the component strips to the length of the strip in question are below (1/2p) `'? 0.16, i.e., when the approximations sinh u `'? u and cosh u `'? 1 can be applied, the longitudinal displacements at the free edge of the upper strip and the interfacial displacements will not be different from the displacements of the substrate. In addition, we have found that these displacements are independent of the elastic constants of the strip materials. We believe that the obtained solution could be used also in other areas of applied science and engineering, where bi-material strip-like elements of the type in question are employed. The analysis is a generalization of the authors' study conducted earlier for a single material strip.