Vibration analysis of thick-section sandwich structures in thermal environments

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.