The axial vibration of the liquid-filled pipes can be represented with a four-equation fluid–structure interaction (FSI) model. When distributed friction was neglected, this model could be solved with an exact solution without computational grid, while the only weakness was the high time cost. A fast meshless solution (FMS) developed earlier used the time-line interpolation rather than the recursive algorithm, to speed the calculation. For the purpose of practical applications, the FMS for supports at pipe end and middle position is proposed, and series connection is also studied in this paper. The support is described by the complex constraint including elastic, damping and inertial effects. A numerical case of the double-pipe water hammer is employed to validate the series connection and end supports. The FMS for the middle support is validated by an existing experiment, where the support can be described by the dry friction. Both numerical and experimental cases indicate the effectiveness and the efficiency of the proposed solution method.

充满液体的管道的轴向振动可以用四方程流体-结构相互作用（FSI）模型来表示。如果忽略了分布式摩擦，则可以用精确的解决方案来求解该模型，而无需计算网格，而唯一的缺点是时间成本高。较早开发的快速无网格解决方案（FMS）使用时间线插值而非递归算法来加快计算速度。出于实际应用的目的，提出了用于管端和中间位置的支架的FMS，并且还对串联连接进行了研究。支撑由复杂的约束条件来描述，包括弹性，阻尼和惯性效应。使用双管水锤的数值案例来验证串联连接和端部支撑。中间支撑的FMS已通过现有实验验证，其中支撑可通过干摩擦来描述。数值和实验案例均表明了所提方法的有效性和有效性。