Nonlinear dynamic response of a ‘flexible-and-heavy’ printed circuit board (PCB) to an impact load applied to its support contour

Abstract

Based on the developed simple and physically meaningful analytical (‘mathematical’) stress model, we evaluate some major parameters (amplitude, frequency, maximum acceleration, stresses and strains) of the response of a ‘flexible-and-heavy’ square simply supported printed circuit board (PCB) to an impact drop load applied to its support contour. The analysis is restricted to the first mode of vibrations and is carried out in application to the PCB design employed in an advanced accelerated test setup (test vehicle). This setup is aimed at the assessment of the performance, in accelerated test conditions on the board level, of packaging materials (and, first of all, BGA solder joint interconnections) subjected to dynamic (drop or shock) loading. It is anticipated that heavy masses could be mounted on the PCB to accelerate its dynamic response to an impact load. These masses are expected to be small in size, so that while changing the total mass of the board and generating significant inertia forces, they do not affect the board's flexural rigidity or its stiffness with respect to the in-plane loading. The PCB's contour is considered non-deformable, which is indeed the case in many practical situations. This circumstance, if the drop height and/or the induced inertia forces are significant, leads to elevated in-plane (‘membrane’) stresses in the PCB and, as a result of that, to the nonlinear response of the board to the impact load: the relationship between the magnitude of the load (determined by the initial impact velocity) and the induced PCB deflections becomes geometrically nonlinear, with a rigid cubic characteristic of the restoring force. The carried out numerical example, although reflects the characteristics of the PCB and loading conditions in an actual experimental setup, is merely an illustration of the general concept and is intended to demonstrate the abilities of the suggested method. Predictions based on this method agree well with the finite element analysis (FEA) data. The model can be helpful in understanding the physics of the addressed problem. The obtained results can be easily generalized, if necessary, for PCBs of different aspect ratios and with other boundary conditions, for different distributions of the added masses, etc, and applied, with adequate modifications, to PCBs in actual use conditions as well. The model can be used, along with FEA simulations, in the analysis, structural (‘physical’) design and accelerated testing of electronic systems of the type in question, and particularly of 'flexible-and-heavy' PCBs, both in accelerated tests and in actual operation conditions.