具有内部纵板的水下有限圆柱壳体的强迫振动

摘要

By utilizing Lagrangian equations, an approximation formulation is developed for the vi-brations of a submerged finite cylindrical shell joined (hinged or clamped) to an internal longitudi-nal plate. The displacements for the cylindrical shell and its internal plate are respectively expand-ed as modal series while the displacement compatibilities at their junctions are enforced by La-grange multiplier method. Fluid loading induced by the vibration of the shells is also taken into ac-count, which is expressed in terms of the integral of harmonic Green’s function multiplied by bound-ary velocities over the vibrating surfaces. The numerical results for the natural frequencies and forced dynamic responses of shell structures agree well with the analytical solutions and FEM results, which demonstrates that the proposed method has great potential to address the dynamics of sub-merged finite cylindrical shell joined with an internal plate.%运用拉格朗日方程，导出具有内部纵板铰接或固接的水下有限圆柱壳体的振动方程。平板和圆柱壳体的位移场皆采用假设振型展开形式，而壳体和平板之间的位移连续条件通过引入拉格朗日乘子法实现。壳体振动诱发的流体负载采用格林函数和边界振速乘积的边界积分方程表示。采用文中方法得到的壳体结构自然频率和强迫响应同解析法、有限元结果符合良好，表明该方法对于处理具有内部平板结构的有限圆柱壳体的动力学问题有较好适用性和较大潜力。