On the Dynamics of Non-linear, Coupled Structures with Primary - and Moving Secondary-Oscillating Systems

In past two decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers: (i) coupled dynamics of distributed parameter system carrying one or more moving oscillators, and (ii) transient dynamic analysis of axially moving media (and associated phenomena of parametric resonances). Bridge vehicle interaction falls into the first class of problems and flexible appendage deployed from a satellite or a spacecraft is typical of the second class. Mathematically, these two problems are dual to each other, and they often are highly non-linear in nature and typically involve large overall motion in space with complex effects of convective inertia terms in their governing equations of dynamic equilibrium. Many researchers are trying to formulate the response of these problems, each having a different approach, but applicable only to certain specific details. Moreover, few researchers have concluded that these problems are beyond the scope of present commercial finite element software packages. However, we believe that if the nature and details of these problems are studied properly and carefully, it is immediately possible to simulate these problems in available commercial finite element software packages. An added advantage would also be the avoidance of many unrealistic simplifying assumptions that are often introduced to reduce the mathematical complexity; e.g. neglecting possible separation in beam-moving vehicle problem (Yang & Yau 1997), assuming linear behavior of suspension system, restriction to beam configuration only, etc. For demonstration, we use ABAQUS in a large number of test cases to be presented. The results are compared with those presented in literatures.