For the plane problem with an orthotropic material, show that the characteristic Eq. (11.5.7) reduces to the quadratic equation in μ²:

Justify the isotropic case where β_1,2 = 1. Finally, determine β_1,2 for each of the four composite materials given in Table 11.2. See MATLAB code C.10 for numerical methods to calculate b-parameters.

Table 11.2

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S11+(2S12 + S66) + S22 = 0 Explicitly solve this equation for the roots ui, and show that they are purely complex and thus can be written as 1,2 = i1.2, where 32= - 25 11 { - (2512 + S66) (2512 + S66) - 4511 $22}