Frequency reduction mechanism of variable stiffness trapezoidal sandwich plates under cantilever constraints

Trapezoidal plates, such as aircraft vertical tails, are highly susceptible to structural vibrations under complex aerodynamic environments. Variable stiffness composites are often employed to improve structural performance, but the coupling effects between curvilinear fibers and boundary conditions vary significantly. This paper investigates the coupling mechanism between variable stiffness and boundary conditions in trapezoidal sandwich plates. A structural evaluation model is established based on a higher-order shear theory combined with a discrete numerical approach, balancing high computational accuracy and efficiency for irregular domains. Quantitative analysis indicates that the dynamic effectiveness of variable stiffness designs is strictly dependent on boundary conditions. Under simply supported boundaries, curvilinear fibers fully stimulate bend-twist coupling, yielding a 6.71% increment in the fundamental frequency. Conversely, under cantilevered boundaries, the strong root fixation alters this coupling effect, consequently causing a severe frequency reduction of 16.05%. This study elucidates the physical competition among geometric configuration, variable stiffness paths, and boundary conditions, thereby suggesting application adjustments for variable stiffness composites under varying boundaries. These findings provide a reference for the dynamic design of trapezoidal sandwich plates in engineering applications.