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This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) material nonlinearity and (c) combined geometric and material nonlinearity. The material nonlinearity also included both third and fourth nonlinear elasticity terms. The frequency response equation of these models were further evaluated quantitatively and qualitatively. The models capture the hardening effect, i.e., increase in resonant frequency as a function of forcing amplitude for geometric nonlinearity, and the softening effect, i.e., decrease in resonant frequency for material nonlinearity. The model is applied on the first three bending modes of the cantilever beam. The effect of the fourth-order material nonlinearity was smaller compared to the third-order term in the first mode, whereas it is significantly larger in second and third mode. The combined nonlinearity models shows a discontinuous frequency shift, which was resolved by utilizing a set of transition assumptions. This results in a smooth transition between the material and geometric zones in amplitude. These parametric models allow us to fine tune the nonlinear response of the system by changing the physical properties such as geometry, linear and nonlinear elastic properties. 

Zinc (Zn) alloys, particularly those incorporating magnesium (Mg), have been explored as potential bioabsorbable metals. However, there is a continued need to enhance the corrosion characteristics of Zn-Mg alloys to fulfill the requirements for biodegradable implants. This work involves a corrosion behavior comparison between severe-plastic-deformation (SPD) processed cast Zn-Mg alloys and their hybrid counterparts, having equivalent nominal compositions. The SPD processing technique used was high-pressure torsion (HPT), and the corrosion behavior was studied as a function of the number of turns (1, 5, 15) for the Zn-3Mg (wt.%) alloy and hybrid and as a function of composition (Mg contents of 3, 10, 30 wt.%) for the hybrid after 15 turns. The results indicated that HPT led to multimodal grain size distributions of ultrafine Mg-rich grains containing MgZn2 and Mg2Zn11 nanoscale intermetallics in a matrix of coarser dislocation-free Zn-rich grains. A greater number of turns resulted in greater corrosion resistance because of the formation of the intermetallic phases. The HPT hybrid was more corrosion resistant than its alloy counterpart because it tended to form the intermetallics more readily than the alloy due to the inhomogeneous conditions of the materials before the HPT processing as well as the non-equilibrium conditions imposed during the HPT processing. The HPT hybrids with greater Mg contents were less corrosion resistant because the addition of Mg led to less noble behavior.