Optimization Modeling for Vibration of Composite Conical Shell Suitable for A Wide Range of Complex Boundaries: Used for Discontinuous Winding Structure

The study of shell vibration also has clear engineering significance and scientific value.

In practical engineering, the spring stiffness configuration of the classical boundary is difficult to simulate the actual boundary situation, which in turn requires the use of elastic boundaries for simulation.

Given this, this paper is a pioneering proposal to optimize the spring stiffness setting by introducing an intelligent optimization algorithm. Firstly, the vibration model of an isotropic truncated conical shell is established by applying a modified Fourier series method. Then the new characteristic equation is derived by setting the artificial spring stiffness as the parameter to be optimized. The objective function is then obtained from the deviations of the modal parameters to build the optimization model. Subsequently, the optimized model is optimized using an improved particle swarm algorithm and an immune algorithm. Finally, the optimized semi-analytical solution is compared with the finite element analysis results for verification.

The results show that the method in this paper can find a better spring stiffness configuration to simulate complex boundary conditions.

Proposed optimization algorithm can be applied to the cone, column, spherical shell, and other shells and combination shells. The stator end winding is used as an example. Similarly, and characteristic equation under the theory of composite materials are innovatively established; the objective function is extended to the optimization model of characteristic equation for stator-winding. To solve the vibration optimization model of complex structural constraints, the pathological characteristics of data introduced by the numerical difference between the small vibration and the order of magnitude of constraint stiffness are solved. The spring stiffness of small-diameter end of the boundary spring for the stator-winding model has been optimized.