Distributed parallel computing of the recursive eigenvalue search in the context of transfer matrix method for multibody systems

Abstract

The modeling and solving a transcendental eigenvalue problem are important issues in the transfer matrix method for linear multibody systems. Based on the recursive eigenvalue search algorithm for transfer matrix method for linear multibody system, the distributed parallel approach for assembling overall transfer matrix and searching eigenvalues is proposed. This is achieved based on Message Parallel Interface. The influence of the CPU core number as well as the distributed network environment on the final computational time is analyzed through numerical examples of both a nonuniform beam and a multiple launch rocket system. The results indicate that the computational time is significantly reduced by the proposed parallel computing method, so that the computational efficiency on optimization and design of complex multibody systems can be improved.

Wave Propagation in Shear Beams Comprising Finite Periodic Lumped Masses and Resting on Elastic Foundation

“…V(x, t) = ik s (κGA) A + e ik s x − A − e −ik s x e −iωt (26) where A + and A − are complex wave coefficients, A + e ik s x−iωt and A − e −ik s x−iωt are harmonic waves propagating in the positive and negative x-directions, respectively. When the solution of the wave equation is obtained, it is seen that the characteristic roots of r 1,2 = ±ik s correspond to the wave number, k s .…”

“…The transfer matrix method (TMM) method is one of the most commonly used methods to reveal the dynamic behavior of periodic structures and PCs [21][22][23]. The TMM was used to obtain the dispersion relationship observed in the wave propagation problems of both periodic rods and beams [6,11,[24][25][26][27]]. In the TMM, which is used to model the periodic unit cell, the model is reduced to an eigenvalue problem, and it is thus possible to obtain wave numbers and dispersion curves.…”