Numerical solution and sensitivity analysis of time–space fractional near-field acoustic levitation model using Caputo and Grünwald–Letnikov derivatives.

The modeling of engineering systems considering fractional approach configures a tendency as due to the generalization of traditional models that use integer order and to the number of applications in different science fields that can benefit from this approach. The present contribution aims to analyze the physical parameters of a near-field acoustic levitation system, as described by the Reynolds equation, and to evaluate the influence of fractional orders on the obtained profiles. For this purpose, both time and space fractional derivatives found in the fractional differential model are approximated using Caputo and Grünwald–Letnikov formulas, respectively. The discretized nonlinear algebraic system is solved considering the Newton method. The proposed methodology was able to solve the time–space fractional near-field acoustic levitation model for both integer and fractional orders. The performed sensitivity analyses demonstrated the influence of the model parameters and the fractional orders on the pressure fields and levitation force. Physically, for a squeeze film levitation system, the increase of the squeeze number is necessary for levitation purposes. In addition, the maximum achievable levitation capacity of a squeeze film levitation system is determined by the excitation amplitude. As expected, the levitation domain is reduced as the mass increases and the reduction rate of the integer model is higher than the one of the fractional order. In this case, for mass bigger than 1.629 Kg, the levitation domain is larger for the fractional order model. It is worth mentioning that the proposed methodology can be used to solve other dynamic systems modeled by time–space fractional differential equations. [ABSTRACT FROM AUTHOR]