Hamilton体系下介电弹性体圆形薄膜的 动力学建模与辛求解 Hamilton体系下介电弹性体圆形薄膜的 动力学建模与辛求解 Hamilton体系下介电弹性体圆形薄膜的动力学建模与辛求解

The symplectic algorithm is used to study the dynamic response of the circular membrane of dielectric elastomer in a Hamiltonian system.Firstly,this model is introduced into the dual Hamiltonian variable system,and the generalized momentum and Hamilton functions of the system are obtained by means of Legendre transformation.The canonical equation is obtained by using the variational principle to the Hamilton function.Secondly,for the obtained canonical equations,the calculation scheme of the symplectic Runge-Kutta algorithm is given.Finally,the two-stage and fourth-order symplectic Runge-Kutta algorithm is adopted for the numerical solution.Numerical simulation results show that the two-stage and fourth-order symplectic Runge-Kutta algorithm has an advantage of preserving energy and long-time numerical stability by comparing with the four-stage and fourth-order classic Runge-Kutta algorithm.In addition,this example also illustrates the limitations of step dependence of the four-stage and fourth-order classical Runge-Kutta algorithm.