Longitudinal vibration of an isotropic, particle-reinforced composite bar may be modeled by using the 1D wave equation

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Longitudinal vibration of an isotropic, particle-reinforced composite bar may be modeled by using the 1D wave equation (Equation 8.99) if the material is linear elastic. Derive the equation of motion for longitudinal vibration of the bar if it can be assumed to be a Kelvin-Voigt linear viscoelastic material having the stress-strain relationship given by Equation 8.39.

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