Analytical models for shock isolation of typical components in portable electronics

Theoretical models can help to guide the cushion design for portable electronics. In the theory of shock isolation, mass-spring model has been mostly adopted to describe the shock response of a system. However, since the mass-spring model ignores the deflection of the fragile equipment and the coupling of the equipment with its supports, it may not be adequate to apply to flexible electronic components such as printed circuit board. In the present paper, a comprehensive study is carried out for both mass-spring systems and flexible beam structures. Particular attention is paid to the maximum force sustained by the connecter, the maximum relative displacement and the vibration amplitude with respect to shock duration. It is found that as long as the shock duration exceeds 0.3 times of the basic period, the beam structure can still be simplified as mass-spring model. However, about 10 vibration modes should be considered in order to achieve a good estimation, if the shock duration is much shorter than the natural period. Results show that better cushion effect can be achieved when the shock duration exceeds 2.5 times of the natural period of the response system. A notable phenomenon found in this research is that the maximum strain is independent of the dimension of the beam.