Abstract
In this study, an efficacious method for solving viscoelastic dynamic plates in the time domain is proposed for the first time. The differential operator matrices of different orders of Bernstein polynomials algorithm are adopted to approximate the ternary displacement function. The approximate results are simulated by code. In addition, it is proved that the proposed method is feasible and effective through error analysis and mathematical examples. Finally, the effects of external load, side length of plate, thickness of plate and boundary condition on the dynamic response of square plate are studied. The numerical results illustrate that displacement and stress of the plate change with the change of various parameters. It is further verified that the Bernstein polynomials algorithm can be used as a powerful tool for numerical solution and dynamic analysis of viscoelastic plates.
Highlights
Plate and plate structure are widely used in many realms of mechanical, building and aerospace [1]
In order to apply plate structure more widely in real life, many scholars are committed to the research of plate vibration
Scholars analyzed the linear vibration of plates
Summary
Plate and plate structure are widely used in many realms of mechanical, building and aerospace [1]. Few studies directly solve such equations in time domain and analyze the dynamic behavior combined with three-dimensional plates For these reasons, it is necessary to combine the fractional order model with a new calculation method to settle the above problem. The Bernstein polynomials algorithm is proposed to numerically simulate differential equations of the plate and analyze the effects of parameters on the numerical solutions of the displacement and stress. This algorithm has good applicability to calculate the fractional governing equation of threedimensional plates in the time domain.
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