Efficient modeling of printed circuit boards structures for dynamic simulations

Printed circuit boards (PCB) are complex geometrical and functional systems that may be exposed to a combination of external and internal loads. In order to evaluate the dynamic behaviour of PCBs in early stages of the development process, modal finite element (FE) simulations are used. Realistic results for a wide frequency range can only be achieved if all the geometrical features, such as PCB assembly, copper layer thicknesses, prepreg structures, etc. with the appropriate material properties are taken into account. To model a printed circuit board including all details such as glass fiber-epoxy compounds and copper traces is possible, but is found to be very time-consuming. A method to model PCBs was developed taking into account the corresponding functional board layout and assembly. In order to ensure an appropriate representation of the layout-dependent local material properties for FE applications without considering the geometry in full detail, a simplified approach based on general composite theory, domain-specific mixture rules and generalized laminate theory was developed. The analytically calculated material property distributions of the PCB such as local stiffness values and densities can be transferred to the meshed geometry. To verify the developed method by comparison with experimentally achieved results, operational modal analysis (OMA) for a frequency up to 25 kHz was carried out by piezo patch transducer. It can be shown that both simulated mode shapes and natural frequencies of the non-assembled board show a very good agreement with the experimental results.