An ultra-light sandwich structure with a thin ceramic-based composite face sheet bonded to a thick thermal insulator is developed as an integrated thermal protection system (ITPS) structure to protect the substructure of a hypersonic flight vehicle. For vibration fatigue assessment and failure prediction, the global dynamic response of the three-dimensional ITPS structure when subjected to a combination of thermal and harmonic excitation is desired. In this study, a novel unified model for vibration analysis of a thick-section sandwich structure is proposed based on the variational asymptotic method. The original 3D sandwich structure problem is reduced to one-dimensional through-the-thickness analysis and two-dimensional (2D) reference plane analysis. The stiffness matrices, including an equivalent transverse shear matrix, are obtained; hence, a shear correction factor is not required. The mechanical response of the 2D reduced-order plate under general boundary conditions in thermal environments is investigated. The static thermal deformation and forced vibration of the sandwich structure with the temperature gradient in the thickness direction are determined using a set of algebraic orthogonal polynomials through the Gram–Schmidt procedure. The thermal deflection is first introduced into the kinematic relationship to modify the total strain energy for the sandwich plate with temperature-independent material properties. To demonstrate the validity and applicability of the model, some numerical results relating to displacements and fundamental frequencies of simply supported sandwich plates are presented and compared to those obtained by other models. The effects of temperature gradients in the thickness direction, boundary conditions, core thickness, and temperature-dependent material properties on the dynamic characteristics and forced vibration of the sandwich structure are discussed by a detailed parametric study. The global dynamic strain response is first obtained using the plate model, which is desirable to determine the 3D local stress and strain field and predict vibration fatigue failure for the ITPS structure.

开发了一种超轻夹层结构，其薄的陶瓷基复合面板与厚的隔热体粘合在一起，作为集成热保护系统 (ITPS) 结构来保护高超音速飞行器的子结构。对于振动疲劳评估和故障预测，需要三维 ITPS 结构在受到热和谐波激励组合时的全局动态响应。在这项研究中，提出了一种基于变分渐近法的厚截面夹层结构振动分析的新统一模型。原来的 3D 夹层结构问题简化为一维全厚度分析和二维 (2D) 参考平面分析。获得包括等效横向剪切矩阵在内的刚度矩阵；因此，不需要剪切修正系数。研究了热环境中一般边界条件下二维降阶板的机械响应。在厚度方向上具有温度梯度的夹层结构的静态热变形和受迫振动是通过 Gram-Schmidt 程序使用一组代数正交多项式确定的。首先将热变形引入运动学关系，以修改具有与温度无关的材料特性的夹层板的总应变能。为了证明模型的有效性和适用性，给出了一些与简支夹层板的位移和基频有关的数值结果，并与其他模型获得的结果进行了比较。通过详细的参数研究，讨论了厚度方向的温度梯度、边界条件、核心厚度和与温度相关的材料特性对夹层结构的动态特性和受迫振动的影响。首先使用板模型获得全局动态应变响应，这有利于确定 ITPS 结构的 3D 局部应力和应变场并预测振动疲劳失效。