Computer Modeling for the Complex Response Analysis of Nonstandard Structural Dynamics Problems

Over the past several decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers: (1) coupled dynamics of a distributed parameter system traversed by one or more moving oscillators; and (2) transient dynamic analysis of axially moving media (and associated phenomena of parametric resonances). Bridge vehicle interaction falls into the first class of problems, and the analysis of flexible appendages 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 nonlinear in nature and typically involve large overall motion in space with complex effects of convective inertia terms in their governing equations of dynamic equilibrium. The “nonstandard” analytical nature of these problems stems from the fact that we are dealing with one or more of the following peculiarities: (1) variable problem domain; (2) varying spatial distribution of forces over the time duration of the analysis; and/or (3) changing location and type of constraints. 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 the present commercial finite-element (FE) 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 FE programs. 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 (after periods of prior contacts) in beam-moving vehicle problems, assuming linear behavior of suspension systems, and restriction to beam configuration only, among many others. For demonstration, we use ABAQUS in a large number of test cases to be presented. The results are compared with those presented in literatures.