Efficient optimization strategy of multibody systems is developed in this paper.Augmented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly.Then methods based on second order sensitivity are used to solve the unconstrained problem,where the sensitivity is solved by hybrid method.Generalized-α method and generalized-α projection method for the differential-algebraic equation,which shows more efficient properties with the lager time step,are presented to get state variables and adjoint variables during the optimization procedure.Numerical results validate the accuracy and efficiency of the methods is presented.
In this paper,a fractional differential equation is introduced to describe the transverse vibrations of an axially moving viscoelastic string.An iterative algorithm is constructed to analyze the dynamical behavior.By conveying the memory effect of the fractional differential terms step by step,the computation cost can be greatly reduced.As a numerical example,the effects of the viscoelastic parameters on a moving string are investigated.
