Vibration Analysis of GRA Rotating Truncated Conical Shell in Thermal Environment under Unified Boundary Condition

As a part of the rocket structure, the truncated conical shell will undergo extremely high temperature changes during the launch and flight of the rocket, which is particularly important for the selection of materials. The graphene-reinforced aluminum-based composites (GRA) are widely used as a new type of high-performance material. This paper mainly studies the natural vibration characteristics of the graphene-reinforced aluminum-based rotating truncated conical (GRA-RTC) shell under the unified boundary conditions by the traveling wave vibration. The innovation is to consider the temperature change with thickness in the GRA-RTC shell, and there are five uniformly distributed artificial springs at the large and small end radii of the rotating conical shell, which can obtain different elastic support boundary conditions. Three graphene distribution types are obtained along the thickness direction. The impact of the Coriolis force and initial ring tensor on the vibration of the rotating conical shell is examined in the structure. According to the first-order shear deformation theory (FSDT), strain-displacement relationship and constitutive relationship, the kinetic energy and potential energy are obtained for the GRA-RTC shell. While solving, the mode shapes of the circumferential direction and generatrix direction of the rotating conical shell are given by using trigonometric functions and Chebyshev polynomials. The ordinary differential equations of the GRA-RTC shell are attained by the Rayleigh-Ritz method, and the frequency and mode shapes are further solved for the GRA-RTC shell. This paper compares the results with Sanders' shell theory and ANSYS Workbench, which fully verifies the accuracy of the results in this paper. The influences of the spring stiffness, graphene mass fraction, distribution type, temperature, boundary conditions and rotational speed on the frequency and mode are investigated for the GRA-RTC shell. In the study of free vibration processes, it is found that changes in rotational speed can cause mode exchange, critical resonance speed, and critical speed phenomena, which are very dangerous and can cause structural failure and damage. It provides a foundation for further research on nonlinear traveling vibration of the rotating conical shells. This paper presents a novel approach to studying rotating cylindrical and conical shells with various boundary conditions.