Dynamic behavior of a populated circuit card assembly

A new approach for predicting the dynamic response and natural frequencies (NF´s) of a non-uniform bending plate is presented. The plate simulates a circuit card, assembled with different types of electronic components (EC´s). The NF´s are affected differently by the stiffness, mass, geometry and location of each component. Therefore, it is important to develop a method to estimate the effect of these non-uniformities on the natural frequencies of any deterministic case and also find the statistical behavior when the circuit´s information is given by stochastic measures. In this study, the functional perturbation method (FPM) and the Rayleigh-Ritz approximation are combined in order to analytically find the NF´s of electronic cards. An important advantage of the FPM is by uniquely producing functional derivatives of the target function (here, NF) with respect to the non-uniformities field. Thus, each particular case is solved by a direct convolution without re-solving the whole problem. The analytical results are compared to a finite element (FE) solution and experiments on real electronic cards. Excellent correlations were found between the experimental results, FE and the FPM even for large local variations of the non uniform parameters. Higher order frequencies were examined and compared with experiments and FE. It was found that in order to have accurate results for the N order frequency, at least 2N shape functions should be selected. The new tool is now available for predictions of the fundamental natural frequency (FNF) of circuit card assembly (CCA) taking into account its electronic components, and therefore improving the mechanical design