MATHEMATICAL MODELING FREE AND KINEMATIC GENERATED OSCILLATIONS FOR PRINTED CIRCUIT BOARD OF ELECTRONIC EQUIPMENT

Abstract

The paper is aimed at performing complex mathematical modeling of dynamic processes in mechanical system of printed circuit board, which includes calculation of natural frequencies and oscillation modes of the board, as well as determination of the amplitude-frequency response for kinematic excited oscillations of the system. Modeling the stress-strain condition and oscillation processes in the printed circuit board is performed on the basis of application of calculation model for the printed circuit board represented in the form of multi-span beam with concentrated and distributed masses, hinged at the ends, what significantly simplifies dynamic analysis of  mechanical system. The paper represents the discrete mathematical model for free oscillations of the printed circuit board, the discrete mathematical model for kinematic excited oscillations of the printed circuit board and the continuous-discrete mathematical model for free oscillations of the printed circuit board. Calculation is performed to determine oscillation shape of displacements and maximum normal stresses in the cross-sections of printed circuit board at 4 critical oscillation frequencies on 9 variants for concentrated and uniformly distributed masses of electronic components layout on the surface of printed circuit board. The significant influence of vibrations on electronic equipment operating conditions has been illustrated. The possibility for resonant oscillations occurrence of the printed circuit board during operation has been substantiated not only at lower but also at higher frequencies. Elimination of these dangerous phenomena can be accomplished only on the basis of dynamic processes detailed analysis in the mechanical system of the printed circuit board.