Abstract
By the constitutive model of variable fractional order, in the time domain, the partial differential equation of axially moving variable fractional order viscoelastic plate is established. From the known definition of the shifted Legendre polynomials, the partial differential equation is solved numerically directly in the time domain. Through error analysis and solution of dimensionless equation, the feasibility and accuracy of the shifted Legendre algorithm are proved. Then, the dynamic analyses of axially moving viscoelastic plate are carried out, and the displacement changes of moving plate at different speeds and different external excitations are analyzed.
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