An efficient equivalent static methodology for simulating electronic packages subjected to resonant vibrations

Modeling of electronic packages under vibrations is quite an interesting and important problem. The Finite element method (FEM) is the most common tool that is used in simulating the vibration-induced deformations and stresses of electronics. Therefore, this paper aims to present an equivalent static solution, instead of the dynamic solution, to simulate this mechanical problem. Towards this goal, the mathematical derivation of the equivalent static loading is thoroughly discussed. This analytical derived solution is then validated with the results of experimentally acquired data and with dynamic finite element analysis (FEA) simulations in terms of the board transverse deflections and solder array stresses. The validation study showed great agreement with all solutions. The validity of this approach is certified through a case study. Thus, the use of the equivalent static loading method is highly recommended as, unlike dynamic analysis, it allows for the crucial inclusion of the nonlinear mechanical properties of the solder interconnects in computationally effective simulations. • An efficient methodology to use static solutions in simulating electronic packages under vibration is presented. • The theoretical basis of this methodology is fully introduced using simple vibrations principles. • The results of this method were validated with measurements and with FEA. • A case study is conducted to test efficiency of the use of this equivalent static analysis is presented.