For the nonsymmetrical laminated beam of Problem 29 in Chapter 7, determine the effects of \(B_{i j}\)-type coupling on the flexural vibration frequencies.

Data From Problem 29 Of Chapter 7:

The nonsymmetrically laminated beam shown in Figure 7.71 consists of a substrate material having Young's modulus \(E_{\mathrm{S}}\) and a coating material having Young's modulus \(E_{\mathrm{C}}\), and both materials are linear elastic, isotropic, and homogeneous. Using a modified laminated beam theory, derive the equation for the flexural modulus \(E_{\mathrm{f}}\) for the beam. Your answer should be in terms of the given parameters.

Figure 7.71:

Transcribed Image Text:

X Substrate, Es Coating, Ec