Mathematical Modeling of Stress in Circuit Cards Represented by Mechanical Oscillatory Systems

The represented paper is aimed at stress calculation in circuit cards with their representation as a type of mechanical oscillatory systems in purpose of their strength assessment especially in resonance conditions. Three types of oscillatory systems are researched: single-mass; multiple mass and oscillatory system with uniformly distributed mass. In all types the cylindrical bending of circuit cards is considered to be a set of beam-strips with rectangular cross-sections so their stress calculation is performed by conventional methods applied in strength of materials and civil engineering. Mathematical model has been developed for maximal dynamic stress and deflection estimation in circuit card assemblies represented by unique oscillatory system as prismatic beam set on two oscillating supports under inertial resonance excitation generated by constant dynamic force. Comparative analysis of mathematical modeling, MatLab simulation and experimental determination of maximal dynamic stress and deflection accomplished for three types of oscillatory systems verified proximity of obtained results. Single-mass oscillatory system is proposed as equivalent to multiple mass or uniformly distributed oscillatory systems on condition of their equal mass, geometric, elastic and dissipation characteristics in resonance frequency correspondent to the main mode of oscillation, so mathematical model designed for single-mass oscillatory system is recommended for strength and stiffness assessment in engineering calculations where possible difference in determination of stress in equivalent systems can used as safety factor.