Analytical Modeling and Advanced Experimental Analysis of Natural Frequencies in Printed Circuit Boards

This paper presents a combined theoretical, numerical and experimental investigation of the vibrational behaviour of automotive printed circuit boards (PCBs), focusing on natural frequencies, mode shapes and the spatial distribution of the dynamic response. Two classical plate formulations, Kirchhoff–Love and Reissner–Mindlin theory, are implemented in MATLAB to predict modal parameters for two automotive electronic control unit (ECU) case studies (Audi A4 and Volkswagen Polo). Because analytical models cannot fully reproduce the behaviour of populated boards, experimental validation was performed using Laser Doppler Vibrometry, including full-field out-of-plane scanning, three-dimensional (SMART 3D-Scan) vibration analysis and single-point 3D sensing, in accordance with ISO 16750-3. The correlation between numerical and experimental results supports early-stage design assessment, optimized component placement and improved solder-joint reliability, providing a consistent methodology for evaluating PCB dynamic performance under realistic automotive operating conditions.