Nonlinear damping in large-amplitude vibrations: modelling and experiments

Experimental data clearly show a strong and nonlinear dependence of damping from the maximum vibration amplitude reached in a cycle for macro- and microstructural elements. This dependence takes a completely different level with respect to the frequency shift of resonances due to nonlinearity, which is commonly of 10–25% at most for shells, plates and beams. The experiments show that a damping value over six times larger than the linear one must be expected for vibration of thin plates when the vibration amplitude is about twice the thickness. This is a huge change! The present study derives accurately, for the first time, the nonlinear damping from a fractional viscoelastic standard solid model by introducing geometric nonlinearity in it. The damping model obtained is nonlinear, and its frequency dependence can be tuned by the fractional derivative to match the material behaviour. The solution is obtained for a nonlinear single-degree-of-freedom system by harmonic balance. Numerical results are compared to experimental forced vibration responses measured for large-amplitude vibrations of a rectangular plate (hardening system), a circular cylindrical panel (softening system) and a clamped rod made of zirconium alloy (weak hardening system). Sets of experiments have been obtained at different harmonic excitation forces. Experimental results present a very large damping increase with the peak vibration amplitude, and the model is capable of reproducing them with very good accuracy.