Mn-Cu high damping alloy is a twin-type damping alloy. Owing to its martensite twin structure at room temperature, it
can convert vibration energy into heat energy, thereby reducing vibration. Although essentially a nonlinear elastic material,
Mn-Cu damping alloys are treated as linear elastic materials in current engineering practice. However, introducing a
constant damping coefficient alone will produce significant errors when modeling vibration reduction characteristics of
the material, especially under impact loading. In this study, vibration test was performed on Mn-Cu damping alloy cantilever
beam subjected to an impact load and deviation between the test result and the one of existing modeling method
was analyzed. A generalized fractional-order Maxwell model was established to describe the nonlinear constitutive relation
of the Mn-Cu damping alloy. Then, the model was extended to the three-dimensional state and a secondary development
was performed. Finally, various applications for the damping alloy were explored and the effects of the damping
alloy on the vibration characteristics of composite cantilever beam structures subjected to impact loads were investigated
with the aim of better understanding the dynamic characteristics and improving the effectiveness of vibration
reduction applications using Mn-Cu damping alloy in the future.