Principal Trajectories of Forced Vibrations

Abstract

As shown earlier by Zhuravlev (1992) that harmonically loaded linear conservative systems possess an alternative physically reasonable basis, which is generally different from that associated with conventional principal coordinates. Briefly, such a basis determines directions of harmonic loads along which the system response is equivalent to a single oscillator. The corresponding definition (principal directions of forced vibrations) is loosing sense in nonlinear case, when the linear tool of eigen vectors becomes inapplicable. However, it will be shown in this chapter that nonlinear formulation is still possible in terms of eigen vector-functions of time given by NSTT boundary value problems. Physical meaning of the corresponding nonlinear definitions for both discrete and continual models is discussed.