Hyperbolic‐Parabolic Shear Beam Model With Kelvin‐Voigt Damping

ABSTRACT This study investigates the dynamic behavior of a shear beam model incorporating Kelvin‐Voigt type damping. The well‐posedness of the system is established via the Faedo–Galerkin method, ensuring the existence and uniqueness of weak solutions. Subsequently, for the stabilization analysis, an energy perturbation technique is employed. It is shown that the system exhibits exponential stability when the Kelvin‐Voigt mechanism acts either on both the shear force and bending moment, or exclusively on the shear force. In contrast, if the Kelvin‐Voigt damping is applied solely to the bending moment, the system exhibits only polynomial decay. Owing to the absence of rotational inertia in the shear model, the governing equation for the angle of rotation takes an elliptic form, thereby precluding exponential decay under such partial damping. This intrinsic structural property is briefly discussed from a physical perspective.