VIBRATION MODE LOCALIZATION IN RANDOMLY DISORDERED WEAKLY COUPLED TWO-DIMENSIONAL SYSTEMS

摘要

In this paper, a general method of regular perturbation forrnlinear eigenvalue problems is presented, in which the orders ofrnperturbation terms are extended to infnity. The method ofrnregular perturbation is applied to study vibration mode local-rnization in randomly disordered weakly coupled two-dimensionalrncantilever-spring arrays. Localization factors, which characterizernthe average exponential rates of decay or growth of the ampli-rntudes of vibration, are defned in terms of the angles of orienta-rntion. First-order approximate results of the localization factorsrnare obtained using a combined analytical-numerical approach.rnFor the systems under consideration, the direction in which vi-rnbration is originated corresponds to the smallest localization fac-rntor; whereas the diagonal" directions correspond to the largestrnrate of decay or growth of the amplitudes of vibration. Whenrnplotted in the logarithmic scale, the vibration modes are of a hillrnshape with the amplitudes of vibration decaying linearly awayrnfrom the cantilever at which vibration is originated.