Abstract
AbstractThis paper deals with the differential equation: ẍ + μF(ẋ) + x = ƒ( X, ẋ, t/Tμ) for μ ≫ 1 where F is a piecewise linear function and f is a periodic function of period μT, where T is to be chosen. It is established that periodic forced vibrations exist in an annular domain R(μ) constructed for the free vibration (ƒ ≡ 0), provided ƒ is not of higher order than Subsequently with ƒ = A cos (2πt/μT*), an asymptotic treatment of the forced vibration problem is carried out, by finding the proper initial conditions and the proper period μT* of f. Finally it is concluded that μT* is close to the period of the free vibration.
Publisher
Canadian Mathematical Society
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Direct Asymptotic Methods;Applied Mathematical Sciences;2014-11-11