Modeling And Dynamic Response Of Continuous Systems With Nonlinear Connections And Restraints

The modern spacecrafts are mostly assembled using functional modules andload-bearing structures, the non-linear vibration problems are prominentgradually with new type light materials widely adopted, payloads increased andthe overall structures complicated. The genetic mechanism of the phenomenon socalled ‘frequency-shift’ which was proposed in the Cassini satellite ground testsince1997has long been attached much importance. Some viewpoints believethat the connections and composite materials widely applied in the structures arekey contributing factors but final verdict still remains uncertain, however thestudy on the mechanism has great significance for not only guarantee of thelaunch security but also satellite-rocket mechanical environmentfitness-optimization. This paper aims at studying the mechanism of spacecraftfrequency-shift, from the view of nonlinearities in the connections, thecontinuum of beam with connections and restraints is taken as investigatingobject, and affects of certain nonlinear factors on the frequency-shiftphenomenon are discussed. The in-depth research on the theory of continuousdynamical modeling method with nonlinear boundary conditions and restrictionsis conducted, a method is put forward, and good results are achieved.There are various types of connections in a particular spacecraft, andcommonly existing nonlinear factors in these connections includes gap,hysteresis, in-plane friction, etc. The two categories of methods when dealingwith dynamical problem of continuous systems with nonlinear boundaryconditions are Force Integration Method (FIM) and Mode Transfer Method(MTM), the classical MTM can deal with the gap nonlinear boundary problem,but it has not been reported in the literature using MTM to study the othercomplex nonlinear boundary condition problems, such as hysteresis boundaryproblem, etc. It can be said that the MTM has narrow applications, and to fix thisshortcoming, a new method named Relative Mode Transfer Method (RMTM) isproposed in this paper. The dynamical problem of a continuous beam withhysteresis boundary condition is firstly studied based on the principle of modetransfer using RMTM with the hysteresis force-displacement relationship discreteby Iwan model. The effect of hysteresis on the frequency-shift is revealed, andparameter study is conducted to discuss the effects of settings on thefrequency-shift. An optional form of Iwan mode which is time-driven is putforward to convenient the solving process of the system equations.The dynamical response of a typical continuum beam with double stop at the end is studied using RMTM, the multi-periodic motion and chaotic motion of thesystem are revealed, parametric studies are investigated, the effects of stopstiffness, modal damping etc on the system response are discussed.The connections are not only just at the end but may exist at any location ofthe beam. Based on the variation principle, an approach of RMTM to analysisvibration problems of continuous systems with arbitrary discrete piecewise-linearconstraints or nonlinear constraint which can be converted to piecewise-linearform is derived, which extends the scope of application of RMTM. The processof the derivation validates the correctness of RMTM, and a study case of aclamped-clamped beam with a constraint at the middle point is conducted.Considering the prevalent nonlinear factors existing in the connections,taking a beam which is clamped at one end and restraint by connection at theother end as object, the effects of these nonlinear factors on the frequency-shiftphenomenon are studied, especially the effects of in-plane friction, axialrestoring force, and gap characteristics. The frequency-shift phenomenon of ‘softspring-hard spring’ similar to the satellite ground test is obtained whenconsidering the effect of gap in the presence of preload, and the conclusion thatthe in-plane friction can make the system exhibiting soft spring characteristic isgained, too.