If the complex moduli of the \(0^{\circ}\) and \(90^{\circ}\) plies in a laminated beam are the same as those described in Example 8.12, but the laminate has a stacking sequence of \([90 / 0 / 90]_{S}\) instead of \([0 / 90 / 0]_{S}\), determine the corresponding flexural loss factor. Compare and contrast these results with those of Example 8.12.

Example 8.12:

A \([0 / 90 / 0]_S\) symmetric laminated beam consists of six plies of equal thickness and the plies have the following complex Young's moduli at a certain frequency:
For the \(0^0\) plies:
\[
E_1^*=E_1^{\prime}+\mathrm{i} E_1^{\prime \prime}=\left[\left(5 \times 10^6\right)+i\left(5 \times 10^3\right)\right] \mathrm{psi}
\]

For the \(90^{\circ}\) plies
\[
E_2^*=E_2^{\prime}+\mathrm{i} E_2^{\prime \prime}=\left[\left(1.5 \times 10^6\right)+i\left(1.5 \times 10^4\right)\right] \mathrm{psi}
\]

Find the flexural loss factor, \(\eta_{i f}\) for the beam, assuming that the complex moduli for the plies and the laminate are all determined at the same frequency. Note that the subscript \(f\) here refers to flexural, not fiber.