Background
Viscoelastic oscillator (VEO) is the basic element for viscoelastic damping structures and displays intermediate mechanical properties between purely Newton damping and purely Hooke spring. The modeling and prediction of the dynamic response of VEO are a challenging research task. Recently, fractional calculus is well used to model VEO and, however, fails to taking account into geometric factor by modeling the VEO as a rheological model.
Objective
Our objective was to establish a fractional Maxwell model of VEO (MFVEO) considering the geometric elements and derive its frequency response.
Method
The system equation of MFVEO was established by substituting the vibration equation and the geometric relation into the fractional Maxwell constitutive equation. The amplitude frequency function (AFF) and phase frequency function (PFF) of MFVEO were deduced by Laplace transform of fractional derivative as well as the linear and superposition properties. Finally, the variations of frequency responses of MFVEO under different system parameters were numerically studied.
Results
The system parameters, namely natural frequency, fractional orders, geometric factor and damping ratio, exert considerable effects on PFF and AFF of MFVEO at the specific frequency ratio. In addition, the harmonic peak exists for AFF and the corner frequency exists for PFF.
Conclusions
These results indicate that the frequency response of MFVEO is under influence of multiple factors and fractional orders; geometric factor should be optimized and designed for engineering applications.