This study presents a technique for the optimal design of composite structures made of different materials with the purpose of reducing vibration amplitudes at dynamic loads. The characterization of damping is important in making accurate predictions of both the true response and the frequency response of any structure dominated by energy dissipation. It is also necessary to design the structure to be controlled for optimum performance. The process of modeling damping matrices and experimental verification is challenging because damping can not be determined via static tests as can mass and stiffness. The stiffness and mass distributions are quite well determined, but there is great uncertainty regarding the energy dissipating mechanism provided by the damping of the structure because it is the least well understood, the damping must be estimated. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping, such as structure soil system. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. The effect of damping on the natural frequencies of tower structure is discussed. It is shown that in classically damped systems increasing the damping decreases the natural frequencies of the system; with non-classical damping some of the natural frequencies of the damped system may be greater than the corresponding natural frequencies of the un-damped system.