Summary
An increase in damping is relevant for the passive control of vibrations and noise; therefore, it is very relevant in design. Experimental data shows a strong and nonlinear dependence of damping on the vibration amplitude for beams, plates and shells of different size and made of different materials (metal, composite materials, silicone rubber and graphene). While the frequency shift of resonances due to stiffness nonlinearity is commonly of 10 to 25 % at most for common structural elements, a damping value up to several times larger than the linear one can be obtained for vibrations of thin plates when the vibration amplitude is about twice the thickness. This is a huge change in the damping value! Therefore, the nonlinear nature of damping affects structural vibrations much more than stiffness nonlinearity. Despite of this experimental evidence, nonlinear damping has not been sufficiently studied yet. A model of nonlinear damping was derived from linear viscoelasticity for single-degree-of-freedom systems and for rectangular plates by taking into account geometric nonlinearity. The resulting damping model was nonlinear and the model parameters were identified from experiments. Numerical results for forced vibration responses of different structural elements in large-amplitude (nonlinear) regime were obtained and successfully compared to experimental results, validating the nonlinear damping model. Then, identification of dissipation in case of hyperelastic and viscoelastic materials was introduced and applied to soft biological tissues. Loss factors and damping from cyclic loads were obtained from hysteresis loops at different force levels and frequency for human aortic tissue.
