Formulation of mechanical impedance for a composite laminate

Substituting Equation (27.9) into Equation (27.1) and pre-multiplying the result by and using Equations (27.7) and (27.8), we get

(27.10)

in which

(27.11)

Since the actual response of the system is

(27.12)

The homogeneous solution of Equation (27.1) is

(27.13)

The complete solution of Equation (27.1) is

(27.14)

Thus, the actual response becomes

(27.15)

The velocity can be obtained from the transformed equation for general dynamic system as

(27.16)

The mechanical impedance of the system could be obtained as

(27.17)