Research on Vibration Reduction Method of Nonpneumatic Tire Spoke Based on the Mechanical Properties of Domestic cat’s Paw Pads

Although there is no risk of puncture, the vibration problem caused by discontinuous structures limits nonpneumatic tire development (NPT). The vibration reduction of nonpneumatic tires is a solvable urgent problem. This current study analyzed the dynamic grounding characteristics and the vibration reduction mechanism of the cat’s paw pads and then applied the mechanical properties to the bionic design of nonpneumatic tire spokes to solve the vibration problem. Domestic cats’ paw pads’ dynamic grounding characteristics were determined using the pressure-sensitive walkway, high-speed camera, and VIC-2D. The results indicated that the mechanical characteristics of swing deformation of paw pads during the grounding process attenuated the grounding stress and buffered the energy storage to achieve the vibration reduction effect. According to the similarity transformation, a finite element model of NPT that could accurately reconstruct the structure and realistically reflect the load deformation was employed. The structure design of asymmetric arcs on the spokes’ side edges was proposed, and it can effectively reduce the radial excitation force of NPT. The three parameters, the asymmetric arc, the thickness, and the curvature of spokes, were used as design variables to maximize the vibration reduction. The orthogonal experimental, the Kriging approximate model, and the genetic algorithm were carefully selected for optimal solutions. Compared with the original tire, the results showed that peak amplitude 1, peak amplitude 2, and the root square of the optimized tire’s amplitudes were reduced by 76.07%, 52.88%, and 51.65%, respectively. These research results offer great potential guidance in the design of low-vibration NPT.

Symplectic Superposition Solution of Free Vibration of Fully Clamped Orthotropic Rectangular Thin Plate on Two-Parameter Elastic Foundation

Based on the method of separation of variables in Hamiltonian system and superposition method, the series expansion solution of the free vibration problem of orthotropic rectangular thin plates (ORTPs) with four clamped edges (CCCC) on two-parameter elastic foundation is obtained. The original vibration problem is decomposed into two subproblems with two opposite sides simply supported, and the general solution of each subproblem is obtained by using the expansion of symplectic eigenvectors. Then by superposing these two general solutions, the series expansion solution of the original problem is obtained. The advantage of this method is that the solution process is carried out in symplectic space, and the validity of variable separation and symplectic eigenvectors expansion ensures the rationality of the solution process, while avoiding the presetting of the solution form. Finally, the correctness of symplectic superposition solution obtained in this paper is verified by calculating three concrete examples of fully clamped rectangular thin plates.