Research On Dynamics And Inverse Problems Of Thermo-elastic Beam And Plate Structures

High-speed vehicles are subject to very tough aerodynamic load and heating during their missons in the Earth’s atmosphere, either to and from space or in sustained flight. Aerodynamic heating is extremely important because the induced high temperature can affect the structural behavior in several detrimental ways. First of all, high temperature degrades the ability of structural materials to withstand loads because elastic properties such as Young’s modulus are significantly reduced. Moreover, thermal stresses are introduced because of restrained local or global thermal expansions or contractions. Such stresses increase deformation, change buckling loads, and alter flutter behavior. Therefore, the studies of the dynamic characteristics of beam or plate under time-varying high temperature environment are helpful to understand and explain the complicated behaviors of spacecraft thermal structures.Using the linear and nonlinear finite element modeling technology to establish the thermo-elastic beam and plate model, this dissertation studies the forward and inverse problems of dynamic analysis of the thermal structure under unsteady high temperature environment. The major contributions of the dissertation can be summarized as follows.1. The finite element models for thermo-elastic beam with axially elastic support and plate with in-plane elastic support are built. A systematic identification method based on the Time-Varying Auto-Regressive(TVAR) model is proposed for the time-varying modal parameters of thermo-elastic structure under unsteady heating conditions.By the combination of Bayesian Information Criterion(BIC) and grey correlation analysis, a new approach is proposed to determine the order of TVAR model and the dimension of basis functions. The identification method is applied to estimating the time-varying modal parameters of theo-elastic beam and palte subjected to different kinds of unsteady heating.2. A new strategy is proposed to identify the temperature-dependent properties of a thermo-elastic structure in an unsteady temperature environment, where time-varying material properties and thermal stresses are taken into account. The identification problem is formulated as an updating procedure of the finite element model. The temperature-dependent properties are expressed as low-order polynomials first. Then, an integrated objective function is established for the particle swarm optimization to minimize the above objective function to simultaneously determine the coefficient and the order of the polynomials. To demonstrate the effectiveness of the proposed procedure, the identification of a simply supported beam with an axially movable boundary subjected to an unsteady, uniformly distributed temperature field is presented.3. An experimental study is made for the identification procedure of time-varying modal parameters and the finite element model updating technique of a beam-like thermal structure in both steady and unsteady high temperature environments. Based on the identified modal parameters, a finite element model for the structure is updated by using Kriging meta-model and optimization-based finite element model updating method. The experimental results demonstrate the effectiveness of the time-varying modal parameter identification method and show that the instantaneous natural frequencies of the updated model well track the trends of the measured values with high accuracy.4. To study the nonlinear large deformation behavior such as thermal buckling of themo-elastic beam, a reduced thermo-elastic beam element based on Absolute Nodal Coordinate Formulation(ANCF) is proposed. Based on this beam element, solving the dynamic equations, modal analysis, linear buckling and nonlinear buckling are studied. Numerical examples are presented to study the large deformation and buckling of a cantilever beam, the pre-buckling and post-buckling behaviors of a simply-supported beam under steady temperature environment, and the identication of time-varing modal paramets of a simply-supported beam with axially elastic support under unsteady temperature environment.