Free vibration of a PCB rectangular thin plate with 4-side clamped support under thermal environment

PCB board in SMT (surface mount technology) can be simplified as a rectangular thin plate with 4-side clamped support. Based on the small deflection theory, the free vibration differential equation of a rectangular thin plate subjected to thermal load was derived. The differential equation showed that the thermal load applied on the PCB thin plate is equivalent to a uniform in-plane tension of the plate, so the clamped plate vibration under thermal environment can be converted into a clamped thin plate vibration with uniform in-plane tension. Using the virtual displacement theory, the methods to calculate natural frequencies and deflections of the plate were presented. The influences of geometric size and temperature on the natural frequencies of the plate were discussed. Some valuable conclusions were drawn.