This book deals with damping or energy dissipation processes in vibrating solids. It includes information on the methods of approach to describing energy dissipation processes in materials. The book contains basic results which describe the dissipative response of anisotropic bodies and composites.Introduction - Phenomenon of Internal Friction in Solids - Energy Dissipation Response - Energy Dissipation in Composites - Elasto-Dissipative Characteristics (EDC) of Anisotropic Bodies - Dissipative Response of Unidirectional FRC: Structural Methods - Effective Viscoelastic Characteristics of FRC - Extreme Properties of the Dissipative Behavior of a Transversely Isotropic Monolayer - Dissipation Properties of Multilayered Composites - Energy Dissipation in Vibrating Composite Bars - Rotational Reinforcement - Appendices