The method of experimental study of the effect of local damage from a low-energy impact on the non-ideally elastic resistance of woven carbon fiber composites of a multilayer structure is considered. The amplitude-dependent logarithmic decrement of vibrations is taken as a characteristic of the non-ideal elasticity of the material. The presented experimental technique makes it possible to obtain experimental data on the dissipative properties of intact and damaged samples of materials under the conditions of their pure bending.