Engineering computation of fiber laser focusing system

A formula for the diameter definition of the spot of focused laser emission at the known quality parameters of BPP and M2 ray is obtained. A formula for the definition of the optimum focal distance of an optical path in a fiber laser is presented. An alignment chart is formed for the definition of the optimum value of the focal distance of the optical system in a fiber laser.

A Modified Nonlinear Conjugate Gradient Method for Engineering Computation

A general criterion for the global convergence of the nonlinear conjugate gradient method is established, based on which the global convergence of a new modified three-parameter nonlinear conjugate gradient method is proved under some mild conditions. A large amount of numerical experiments is executed and reported, which show that the proposed method is competitive and alternative. Finally, one engineering example has been analyzed for illustrative purposes.

Mass and Stiffness Matrices Updating Using the First Modal Data

This paper presents a new direct approach to simultaneously update the analytical mass and stiffness matrices in an undamped model .First, we assume that the difference between the finite element model and the real model is little. Second, only by utilizing the first order modal data orthogonal normalization conditions and eigen equations , we derive the updated matrices. Third, the method can maintain matrices symmetry and sparsity and preserve system connectivity. The merit of the proposed method is simple and accurate in a practical engineering computation. Finally,a numerical example is given to demonstrate the accuracy and effectiveness of the presented updating method.