Damping plays an important role in structural stability and vibration control and different methods have been developed to design structures with maximum possible damping capacity. The most effective measure to date is perhaps the viscoelastic damping treatment. However, the dynamic properties of viscoelastic materials are generally frequency and temperature dependent. This makes the dynamic characterization of viscoelastically damped structures a tremendously difficult task. Conventional approximate methods, such as the direct frequency response method and the modal strain energy method, become quite inaccurate when the damping of a structure to be analyzed becomes high. An iterative complex eigensolution algorithm, though it is exact, requires a tremendous amount of computational effort since, for each mode, repeated complex eigensolutions are required until converged results are obtained. In the present paper, a new iterative complex eigensensitivity‐based characterization method is presented. Based on...