The primary objective of this paper is to investigate the accuracy of the finite element (FE) smeared properties approach for the determination of the mode shapes and frequencies of a printed wiring board (PWB) populated with electronic modules. Smearing of the material and/or structural properties is a recognized means of reducing a complicated structure to a less complicated approximation. Comparisons of both the natural frequencies and mode shapes are made between the smeared FE model and those obtained from vibration testing. The extent of correlation between the mode shapes is characterized by the modal assurance criterion (MAC). Since the intent of this study is to examine the effectiveness of the smearing technique, free boundary conditions are assumed. It is shown that the smearing technique can produce good correlation of both natural frequencies and mode shapes of PWBs populated with modules. A case study of a PWB with both surface mount technology (SMT) and pin-in-hole (PIH) components is presented.
Reduced-order mass weighted proper orthogonal decomposition (RMPOD), smooth orthogonal decomposition (SOD), and state variable modal decomposition (SVMD) are used to extract modal parameters from a nonuniform experimental beam. The beam was sensed by accelerometers. Accelerometer signals were integrated and passed through a high-pass filter to obtain velocities and displacements, all of which were used to build the necessary ensembles for the decomposition matrices. Each of these decomposition methods was used to extract mode shapes and modal coordinates. RMPOD can directly quantify modal energy, while SOD and SVMD directly produce estimates of modal frequencies. The extracted mode shapes and modal frequencies were compared to an analytical approximation of these quantities, and to frequencies estimated by applying the fast Fourier transform to accelerometer data. SVMD is also applied to estimate modal damping, which was compared to the estimate by logarithmic decrement applied to modal coordinate signals, with varying degrees of success. This paper shows that these decomposition methods are capable of extracting lower modal parameters of an actual experimental beam.
is a Research Scientist in The Center for Engineering Education Research (CEER). She received her Ph.D. in Plant Biology from Purdue University. Her scholarly interests include: improvement of STEM teaching and learning processes in higher education, and institutional change strategies to address the problems and solutions of educational reforms considering the situational context of the participants involved in the reforms. She is involved in several research projects focusing on competenciesbased curriculum redesign and implementation aimed to integration across curricula; increasing the retention rate of early engineering students; providing opportunities for STEM graduate students to have mentored teaching experiences.
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