According to the basic idea of classical yinyang complementarity and modern dualcomplementarity

the unconventional Hamiltontype variational principle in phase space for dynamics of Timoshenko beam with linear damping is established

which can fully characterize the initialboundaryvalue problem of this dynamics. And its Euler function has symplectic structure character. Based on this variational principle in phase space

a symplectic space finite element—time subdomain method is presented. This new method is the result of combining finite element method in space domain with time subdomain method by applying the Lagrange interpolation polynomials as approximation to the time subdomain. The numerical results show that the stability

convergence

computational accuracy and efficiency of this new method obviously improve those of widely used Wilsonθand Newmarkβ methods.