Most of the nonlinear system identification techniques described in the existing literature required force and response information at all excitation degrees-of-freedom (DOFs). For cases, where the excitation comes from base motion, those methods cannot be applied as it is not feasible to obtain the measurements of motion at all DOFs from an experiment. The objective of this research is to develop the methodology for the nonlinear system identification of continuous, multimode, and lightly damped systems, where the excitation comes from the moving base. For this purpose, the closed-form expression for the equivalent force also known as the pseudo force from the measured data for the base-excited structure is developed. A hybrid model space is developed to find out the nonlinear restoring force at the nonlinear DOFs. Once the nonlinear restoring force is obtained, the nonlinear parameters are extracted using “multilinear least square regression” in a modal space. A modal space is chosen to express the direct and cross-coupling nonlinearities. Using a cantilever beam as an example, the proposed methodology is demonstrated, where the experimental setup, testing procedure, data acquisition, and data processing are presented. The example shows that the method proposed here is systematic and constructive for nonlinear parameter identification for base-excited structure.

Predictive analysis of the life of an electronic package requires a sequence of processes involving: (i) development of a finite element (FE) model, (ii) correlation of the FE model using experimental data, and (iii) development of a local model using the correlated FE model. The life of the critical components is obtained from the local model and is usually compared to the experimental results. Although the specifics of such analyses are available in the literature, a comparison among them and against the same electronic package with different user printed circuit board (PCB) thicknesses does not exist. This study addresses the issues raised during the design phase/life analysis, by considering a particular package with a variable geometric thickness of the user PCB. In this paper, the effect of stiffening the user PCB on the fatigue life of a ball grid array (BGA), SAC305 solder joint is studied. The board stiffness was varied by changing the thickness of the PCB, while the size of the substrate, chips, and solder balls were kept constant. The test vehicle consisted of BGA chips soldered to a user PCB. The thickness of the user PCB was varied, but the surface area of the BGA chip remained identical. The test vehicle was then modeled using a finite element analysis tool (ANSYS). Using a global/local modeling approach, the modal parameters in the simulations were correlated with experimental data. The first resonance frequency dwell test was carried out in ANSYS, and the high-cycle fatigue life was estimated using the stress-life approach. Following the simulation, the test vehicle was subjected to resonance fatigue testing by exciting at the first mode resonance frequency, the mode with the most severe solder joint failure. The resistance of the solder joint during the experiment was monitored using a daisy-chain circuit, and the point of failure was further confirmed using the destructive evaluation technique. Both the experimental and simulation results showed that stiffening the board will significantly increase the fatigue life of the solder joint. Although the amplitude of the acceleration response of the test vehicle will be higher due to board stiffening, the increase in natural frequencies will significantly reduce the amplitude of relative displacement between the PCB and the substrate.

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In this paper, the nonlinearity detection, characterization and identification of a bolted beam assembly is presented. The methodology utilized in this work is based on the force reconstruction using the base excitation as an input and the nonlinear system identification. The force reconstruction procedure was carried out by exciting the bolted beam assembly at very low excitation with fully tightened bolt condition. The nonlinear effect in the bolted beam assembly was induced by reducing the bolt clamping loads. A collection of frequency response functions (FRFs) are shown at different clamping loads to detect and characterize the nonlinearities. Once the nonlinearities are detected and characterized, the restoring force surface method using the reconstructed force was used to identify the nonlinear parameters in the modal space. Four different base excitation (energy) levels with three different tightening torques were considered in the tests in order to study the energy dependence of the damping nonlinearities. In all the cases, the nonlinear system identification methodology employed was successful in identifying the damping and stiffness nonlinearities.