Subharmonic Resonance of Fractional Viscoelastic Films with Varying Density in Flexible Electronic Manufacturing

The emphasis of this paper is placed on the subharmonic resonance of moving viscoelastic films with varying density in flexible electronic manufacturing. The varying density arises from the pattern distribution of each flexible device. Based on the fractional Kelvin-Voigt model, the nonlinear governing equation of moving viscoelastic film is derived from the Hamilton framework, and then the resulting equation is reduced to a fractional ordinary differential equation by using the Galerkin method. The multiple-scale method is applied to analyze the occurrence condition and dynamic responses of subharmonic resonance. The effects of the density parameter and fractional order on the resonance responses are discussed. These analyses gain a deeper understanding about the instability phenomena in flexible manufacturing and therefore contribute to product design and structural optimization.