Nonlinear damping in large-amplitude vibrations of structures: modelling and experiments

An increase in damping is relevant for the passive control of vibrations and noise; therefore, it is very relevant in design. Experimental data show a strong and nonlinear dependence of damping on the vibration amplitude for beams, plates, and shells of different sizes and made of different materials (metal, composite materials, silicone rubber, and graphene). While the frequency shift of resonances due to stiffness nonlinearity is 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 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 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) regimes were obtained and successfully compared to experimental results, validating the nonlinear damping model. **Key Learning Objectives** - How good is it to model damping as linear viscous damping? - Is damping slightly or significantly nonlinear during large-amplitude (nonlinear) vibrations of structural elements? - Nonlinear damping is very important in the design of major systems under extreme conditions, like the core of a nuclear reactor subjected to earthquakes - Ignoring nonlinear damping has the consequence of over-design of structures and systems for extreme events that may never happen during the structure’s life. **Who Should Attend** - Mechanical engineers - Aerospace engineers - Civil Engineers - Researchers/scientists in mechanical sciences and dynamics - Research/Project managers - Heads of research divisions in mechanical design and dynamics