Free Vibration Characteristics of Moderately Thick Spherical Shell with General Boundary Conditions Based on Ritz Method

In this paper, the Ritz method is adopted to investigate the vibration characteristics of isotropic moderately thick annular spherical shell with general boundary conditions. The energy expressions of the annular spherical shell were established based on the first-order shear deformation theory (FSDT). The spring stiffness method is introduced to guarantee continuity and simulate various boundary conditions on the basis of the domain decomposition method. Under the current framework, the displacement admissible function along axial direction and circumferential direction of the shell structure are, respectively, expanded as the unified Jacobi polynomials and Fourier series. The final solutions can be obtained according to the Ritz method. The validity of the proposed method is proved by comparing the results of the same condition with those obtained by the finite element method (FEM) and published literatures. The results show that the current method has fast convergence and delightful accuracy through the comparative study. On this basis, the vibration characteristics of isotropic moderately thick annular spherical shell are further studied by a series of numerical examples

The effects of two free-floating plants (Eichhornia crassipes and Pistia stratiotes) on the burrow morphology and water quality characteristics of pond loach (Misgurnus anguillicaudatus) habitat

Loach exhibit conspicuous drilling behaviors in the mud of shallow waters, yet their burrow morphology and the factors affecting this behavior have received little attention. We characterized the burrow morphology and water quality of the pond loach Misgurnus anguillicaudatus in three scenarios: in tanks without plants, tanks with the free-floating plant water hyacinth Eichhornia crassipes, and tanks with water lettuce Pistia stratiotes. Water hyacinth effectively removed water TN, COD, NO3-N and NH4-N, and water lettuce removed water TP and NH4-N. Water hyacinth and water lettuce markedly reduced water turbidity and DO, increased TOC and EC. Water hyacinth purified water more effectively than water lettuce, providing a suitable habitat for loach feeding, living and burrowing. The burrow structures were V-shaped, Y-shaped, inverted L-shaped, or complicated dendritic networks composed of multiple V shapes. The hyacinth treatment was characterized by the greatest burrow volume, length, depth, and structural complexity, but the opening size was reduced by dense root mat coverage. Burrows in the water lettuce treatment were characterized by intermediate volume, length, branches and sinuosity, but they had the largest opening and pit size. The control treatment had a flat bottom with the smallest, shortest burrows. This study indicates that free-floating plants improve habitat suitability and change burrow morphology and may be used to improve loach breeding methods