Sensitivity of Initially Stressed Un-symmetric Micro-Layered Plate in Large Deflection due to Lateral Load

摘要

The sensitivity of an isotropic un-symmetric layered micro-layered plate under initial tension is formulated analytically. The approach which follows von Karman large deflection plate theory for the case of a un-symmetrically layered isotropic plate was developed, first, followed by neglecting the arising nonlinear terms to have a linear consideration upon the posed problem. The arisen modified Bessel equation for the lateral slope can be solved by the use of modified Bessel functions with arguments defined via a modified tension parameter accounting for stiffness due to un-symmetry. The solutions for geometrical responses are further manipulated to obtain an analytical expression for the mechanical sensitivity for a typical layered micro-sensing plate, using the re-occurrence relationships for integration and differentiation for the modified Bessel functions. The results for a slightly un-symmetric plate are compared to those of a singled layered case available in literature to validate the present approach. The radial variations of the geometrical responses are found to correlate very well with which given by Sheplak and Dugundji, throughout the range of the employed initial tension. In additions, the effects of initial tension, lateral load, as well as the deviation in layer moduli are thoroughly investigated, for typical un-symmetrically.