Assessing the vibrational response and robustness of electronic systems by dissolving time and length scale

This paper presents a methodology to holistically analyse the effects of vibrational loads on electronic systems. An equivalent multi degree-of-freedom (DOF) damped system discretizes the complex structure and sets up the equation of motion. After modal testing the damping and stiffness coefficients, a numerical finite element model (FEM) is developed to identify critical components based on the mass participation factor. Including the system vibration behaviour by means of the characteristic transfer functions, the critical components are linear sub-modelled in the frequency domain to minimize calculation times. The statistical stress configuration caused by normally distributed random vibration cycles reveals electrical devices prone to significant damage. The mechanical damage in terms of high cycle fatigue is quantified in a second hierarchic linear submodel that considers both transfer functions and stress configuration of the critical components. By Inverse Fast Fourier transforming this input load from frequency to the time domain, it finally enables non-linear material models in the device submodel and the calculation of cumulative damage.