The coordinate function in the problem of the nonlinear dynamic response of an elongated printed circuit board (PCB) to a drop impact applied to its supports

Abstract

We consider an elongated printed circuit board (PCB) whose long edges are support-free and the short edges are either simply supported or rigidly clamped. The board experiences a significant impact loading applied to the short edges. In such a situation the reactive in-plane (“membrane”) forces (stresses) are large and result in a geometrically nonlinear dynamic response of the board. The analysis is limited to the fundamental mode of vibrations, and the method of principal coordinates is used to evaluate the dynamic response of the board. The objective of the analysis is to find out if it is sufficient to consider the nonlinear behavior of the principal coordinate (because of the in-plane stresses) only, or it is necessary to account also for the effect of these stresses on the coordinate function. Based on the developed simple and physically meaningful analytical (“mathematical”) stress model, we conclude that the effect of the in-plane tension on the coordinate function does not have to be considered for a simply supported board, but has to be accounted for in the case of a clamped board. This could be done, if necessary, using the results of the analysis.