On the dynamic behavior of mono-coupled continuous structures attached to nonlinear springs - Santo, Douglas Roca (2021)
The use of the concept of periodicity has become an interesting solution for structural vibration reduction in many engineering applications. Structures built using the repetitive assembling of identical elements are called periodic structures, which can be used to achieve frequency regions where the propagating waves are highly attenuated, called attenuation zones. The objective of this work is to investigate the harmonic response of vibrating structures attached to nonlinear springs of the cubic type. The proposed analysis aims at investigating the effect of periodic local nonlinearities on the dynamic behavior and wave propagation properties in waveguide structures. In order to solve the nonlinear dynamic stiffness matrix problem, a closed-form solution using the methodology to solve polynomial equations is proposed. This yields a scalar polynomial equation, which is well suited for accurately computing the nonlinear receptance functions at some point in the structure considering a small number of unit cells. Alternatively, a method based on a perturbation approach is proposed to calculate the nonlinear frequency responses, resulting in a cubic matrix equation that can be solved numerically. It is found that the resonance peaks shift in frequency when compared to the use of linear springs, interesting features for the passive control of these structures. The effects of nonlinear springs on continuous mono-coupled periodic structures based on the concept of transmissibility of a single cell of finite structures are analyzed. Numerical simulations are carried out showing the influence of nonlinear springs over the structure bandgaps. The investigation showed that the vibration control in periodic structures can be improved by the use of nonlinear springs.