Dynamic response of a rectangular plate to a shock load, with application to portable electronic products

The ability to predict and possibly minimize the adverse consequences of dynamic loading on electronic equipment is especially important for portable electronic products, both because they can be easily dropped and because the minimum displacement (stopping distance) in such products, when subjected to shock loads, has to be made very short. This leads to high accelerations and, as a consequence of that, to elevated dynamic stresses, and can possibly result in failures of vulnerable elements. In this analysis, we examine the dynamic response of an element having a shape of a rectangular plate (e.g., liquid crystal display), and packaged in a “double box” system, (e.g., a chassis and a cabinet). The analysis is carried out, assuming that the outer box (cabinet) does not rebound. The purpose of the analysis is to evaluate the effect of the masses (weights) of the element itself and the inner box (chassis), as wed as the effect of the spring constants of the cushionings, on the maximum displacement and the maximum acceleration of the plate´s support contour. On the basis of the performed analysis, we developed engineering guidelines for the preliminary selection of the spring constants of the cushionings, so that not to compromise the dynamic stability of the package, e.g., to keep the induced displacements and accelerations at a sufficiently low level. We show that this stability can be ensured by designing the package in such a way that the lower natural frequency of vibrations of the two-degree-of-freedom dynamic system in question (plate/chassis assembly) differs considerably from its higher frequency. For the given masses of the plate element and the inner box (chassis), this can be achieved by making the inner cushioning (gasket) substantially stiffer than the outer one (grommet). We show also that the strength of the plate element can be improved, if it is made thick enough and is clamped by the support contour. Finally, we demonstrate that a probabilistic approach can be successfully applied to design a package with a low probability of failure