Investigation on dynamic characteristics of two pole continuous elements by matrix description approach

PDF(935 KB)

Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (9) : 142-145.

论文

Investigation on dynamic characteristics of two pole continuous elements by matrix description approach

LI Jiang-tao1,2;WANG Wei-bo2;WU You-sheng2

Author information +

History +

Abstract

Relationships between state vectors and solutions of differential equations of an Euler-Bernoulli beam and a rod were deduced respectively in element coordinating system. Analytical formulae of forward transfer matrix, reverse transfer matrix, impedance matrix and mobility matrix were derived separately when the positive definition of state vectors were assumed the same. The characteristics of the four matrices were studied. Analytical formulae of the four matrices of a general beam were given by combining the corresponding formulae of Euler-Bernoulli beam with those of the rod. Numerical examples showed that the results of the present method and those of the finite element method were nearly the same. The relationship between dynamic matrix description method and static matrix description method was discussed in the final part. It was also showed that matrix description methods facilitated solving dynamic questions using computer programming. Analytical formulae in this paper can be used in dynamic analyses of continuous systems to achieve good precision with less computation.

Key words

dynamics / Euler-Bernoulli beam / rod / transfer matrix / generalized mechanical impedance method

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LI Jiang-tao;WANG Wei-bo;WU You-sheng. Investigation on dynamic characteristics of two pole continuous elements by matrix description approach[J]. Journal of Vibration and Shock, 2010, 29(9): 142-145