5.4.1 MAXIMUM ALLOWABLE PSD LEVEL OF THE PWB
The natural frequencies (f_{n} ) of the PWB and the
thermal plane must be calculated if hardware does not exist, or measured if
hardware does exist. If a thermal plane exists, the expected deflection (_{ex}) and the maximum allowable deflection
(_{max}) of the PWB and thermal plane must be
calculated and compared. The first step in determining the expected and
maximum allowable deflections is to calculate the natural frequency of the PWB
and the thermal plane. The natural frequency equations are shown in Appendix A
with the material properties located in Appendix B. Once the natural frequency
of the PWB and the thermal plane have been calculated or measured, calculate
the expected Glevel that the board and thermal plane will experience. Using
the Crandall Equation shown as 51, and the input profile of Figure 23(a) as a starting
reference w_{o}= .04 g^{2}Hz), the equation can be reduced to
Equation 52. The Glevel can be placed into Equation 53 and the
expected deflection of the PWB or thermal plane calculated. The expected
deflection of the PWB or thermal plane is the largest deflection that the
board or plane will see during a vibration screen using the input profile of
Figure 23(a).
If a thermal plane is present, the expected deflection for both the PWB and
the thermal plane must be calculated with the smaller value of the two used
for the remainder of this section. The smallest deflection between the PWB and
the thermal plane is used since they bend together and the one with the
smallest expected deflection will generally dominate during vibration.
The maximum allowable deflection (ba) of the PWB and the thermal plane
must be calculated next. The maximum allowable deflection is the largest
distance that the PWB or thermal plane can deflect without damaging the
material properties. The maximum allowable deflection formula is shown as
Equation 54. If a thermal plane exists, the maximum allowable deflections
of the PWB and the thermal plane are compared and the smaller of the two
values is used to calculate the maximum allowable PSD level for the PWB
thermal plane combination.
where: 

_{max} = Endurance
limit (Se) of the PWB or thermal plane, psi.
E = Modulus of elasticity, psi F =
.208 if PWB short sides are simply supported. or F
= .062 if PWB short sides are fixed. 
* If one or more sides are free, use the F
value that most represents the PWA fixturing.
The maximum input PSD level for the PWB and thermal plane can be
calculated from Equation 55 using the smaller of the two expected
defiections and the smaller of the two maximum allowable deflections. The
maximum input PSD level is the maximum level that the PWB and the thermal
plane can withstand without structural damage. The level that is calculated in
Equation 55 is normally an extremely high value in that it
represents a calculation of the maximum input level the PWB material can
withstand. DO NOT ATTEMPT TO USE THIS AS AN INPUT VALUE UNLESS IT IS THE
LOWEST VALUE FOUND, IN THE Z AXIS, AFTER THE PARTS SECTION (SECTION
5.4.2 THROUGH 5.4.4.2) HAS BEEN
COMPLETED.