Linear and Nonlinear Vibrations Caused by Periodic Impulses

Abstract

et al. [21] suggested a shock-protective suspension design for printed circuit boards (PCBs), including those used in portable electronics. Dynamic response of a PCB in a portable electronic product to a drop impact was addressed by Seah et al [66]. Suhir [52][53][54][55][59][60][61] emphasized the nonlinear effects in the PCBs subjected to shock loads applied to the support contour of the PCB. He examined cases of periodic shocks [51, 53] and a suddenly applied constant acceleration [54]. Exact solutions to highly nonlinear problems described by von Karman's equations (see, e.g., [52]) were obtained using elliptic functions and elliptic integrals. Later on He and Fulton [57] and He and Stallybrass [58] also addressed some nonlinear problems in the mechanical behavior of PCBs subjected to dynamic loading.Various aspects of drop impact in application to portable electronics products and chip-size packages (CSPs) were recently analyzed by numerous investigators (see, e.g., Lim and Low [67], Lim et al. [68,69], Zhu [22,33,70], Zhu and Marcinkiewicz [43], Luan and Tee [27,32,35,37,41,45,46], and Wang [34]). The role of viscous damping in a SDOF linear system experiencing a drop impact was investigated in detail by Suhir [15]. It has been demonstrated, particularly, that although elevated damping always has a favorable effect on maximum displacements leading to lower maximum displacements, it can have a strong adverse effect on the maximum accelerations (decelerations): Elevated damping can result in accelerations (decelerations) that are significantly larger than the accelerations in a damping-free system.In many cases drop test conditions can be adequately substituted by shock tests provided that the drop test conditions are correctly predicted and the shock tester is appropriately "tuned" [20]. The incentive for substituting drop tests with shock tests is due to the fact that shock tests might be easier to conduct as well that the shock impact's magnitude and duration can be easily prescribed and, hence, predicted, while the characteristics of the drop impact pulse have to be determined during the experiment itself.By employing nonlinear shock protection elements (materials) and multi-degree-offreedom shock protection systems, one could improve such a protection dramatically. Substantial improvement in the performance of a shock protection system can be achieved, particularly, by employing a two-degree-of-freedom system ("box-in-a-box" type). This should be done, however, with an appropriate selection of the masses and spring constants, so that resonance conditions that might lead to a "rigid impact" are avoided [55,56]. The analysis and design concepts addressed in [62] were developed in the application to a liquid crystal display design. A detailed analysis of the shock response spectrum of a portable device with a shock protection system was carried out by Goyal et al. [64].Many recent studies were devoted to the investigation of the effect of a short-term loading on solder materials and solder joints in portab...

Shock Protection of Portable Electronic Devices Using a “Cushion” of an Array of Wires (AOW)

“…Periodic (repetitive) impact loading could occur in micro-and opto-electronic devices during operation of some micro-and opto-electronic equipment, particularly those used in some military systems, such as rapidly shooting artillery or machine-guns [10,11]. The repetitive nature of loading (i.e., the interaction of the vibrations caused by sequential impacts) should be considered if the damping in the system is low and/or the impacts are significant and therefore the vibrations due to the given impact do not fade away completely by the time of the application of the next impact.…”