Analysis Methods For Structures With Local Nonlinearities And Applications In Spacecraft Structure

Reasonable and accurate calculation and analysis of dynamic characteristics of spacecraft can provide an accurate reference for the design of structure and control system of spacecraft, and thus can ensure the design quality and enhance the performance of spacecraft. To achieve better performances and integrate more functions, many spacecraft structures have been becoming larger and more complicated. In general, spacecraft can be considered as an assembled structure of which several physically existing substructures that are connected by different kinds of connectors. These connectors usually have obvious influences on the dynamic characteristics of spacecraft, especially when their nonlinearities cannot be ignored. Thus they make the dynamic analysis of spacecraft more complicated. In engineering practices, spacecraft are often idealized as finite element models with many degrees of freedom (DOFs). However, the number of DOFs associated with nonlinear connectors usually constitutes only a small part of the model. If such structures are taken as globally nonlinear in the dynamic analysis, great difficulties will be certainly brought to the analysis and design process. And it is unavoidable that design costs will be added and design time will be extended. Therefore, an alternative approach is to take them as local nonlinear structures. From this point of view, the structural dynamics of spacecraft is investigated.As the nonlinearities of spacecraft are usually distributed and local, an approach is proposed to calculate the transient response of large-scale structure with local nonlinearities. The approach is based on general dynamic reduction method and the Newmark's method, which is commonly used in direct time integration method. DOFs that are of interest, those on which external forces act, and those associated with nonlinearities are expressed in physical coordinates, but the remaining DOFs are transformed into modal coordinates. In this way, the proposed method can solve strongly nonlinear problems and improve the accuracies of the results. With a transformation, the iterations in each time step are only related to nonlinear DOFs. Consequently, the computational effort of the approach can be significantly reduced.A method is proposed to study the forced harmonic response of large-scale structures with local nonlinearities. It is combining the describing function (DF) and frequency response function (FRF). With the method, fundamental and multi-harmonic response analysis is discussed, respectively. In the method, the dynamical equations of motion are firstly converted into a set of nonlinear algebra equations. Subsequently, with FRF, the computational efficiency of the approach can be significantly enhanced, and only associated with nonlinear DOFs. In addition, the method can be also used to study the steady state periodic response of nonlinear structures. In the approach, FRF are obtained by using linear normal modes (LNMs). As the LNMs can be obtained by the well developed standard linear modal analysis procedures, the method can be easily cooperated with commercial finite element (FE) softwares.Following a brief review of most commonly used coupling methods with their merits and shortcomings, a quasilinear FRF coupling method is established by using the DF. The purpose of the method is the treatment of complicated nonlinear joints, which are called general nonlinear joints. Fundamental and multi-harmonic receptance coupling are discussed. In the method, the dynamical equations of motion of general nonlinear joints are firstly quasi-linearized with the DF. Then a linear FRF coupling method is extended, modified and adopted to calculate the forced harmonic response. In comparison with current nonlinear coupling methods in the frequency domain, the present method is more general.In the last part of the dissertation, parametric study for the forced harmonic response of local nonlinear structures is presented. By using the pseudo-arclength continuation scheme, the effects of modifying nonlinear parameters and/or changing excitation levels on the forced harmonic response can be easily obtained. The approach can be also used to calculate the steady state periodic response of a local nonlinear structure when its nonlinear parameter is modified. Besides, sensitivity analysis (SA) of the forced harmonic response with respect to nonlinear parameters and excitation levels are presented. Moreover, focused on two kinds of typical frequency response cure, the calculations of simple turning points, resonant points, and their corresponding amplitudes are discussed. Their SA with respect to nonlinear parameters and excitation levels is presented.