Calculation of Natural Vibration Frequencies of a Box Structure with Thermal Protection

The article focuses on calculating the natural vibration frequencies of a box structure with thermal protection, a crucial component in many engineering fields such as mechanical engineering and construction. The thermal protective coating applied to the outer surfaces of the structure adds significant mass and requires consideration in static and dynamic analyses. The study employs nonlinear dynamic analysis to model the flexible, two-layered structure subjected to thermal and force loads. The authors derive a system of nonlinear differential equations for the deflection of the structure using the Bubnov-Galerkin method. They also account for the material properties, including the modulus of elasticity and density of both the box and thermal protection layers. Numerical integration techniques are employed to solve these equations, providing a relationship between dimensionless vibration amplitudes over time. The study demonstrates the applicability of the proposed methodology by calculating the lowest natural frequency for a specific plate configuration and extends this analysis to configurations with stiffening ribs. In conclusion, the approach offers a reliable means for dynamic analysis of similar structures, with potential applications in finite element modeling. The results serve as a reference for validating such models under geometrically nonlinear conditions.