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利用特征函数展开法对台阶式变深水槽中推板式造波机造波问题进行了研究,建立了相应速度势和波面的解析表达式.与高阶边界元方法(HOBEM)数值结果进行了对比,验证了本解析解的正确性.通过数值试验,研究了台阶对入射波的影响,同时分析了造波板所在位置(上部台阶)水深、水槽工作区(下部台阶)水深、造波板运动周期和造波板水平位置等因素对生成波浪高度的影响.由此选择合适的造波板所在位置及水深来得到所需要的波浪高度,进而根据需要生成波浪的周期和波幅来反演造波板的运动.“,”Based on the eigenfunction expansion technique, an analytical study on the wave generated by a piston wave generator in a depth-varied water-flume in step type is carried out. The corresponding velocity potential and wave elevation in the flume are developed. The analytical solution is verified by a higher-order boundary element method (HOBEM). Numerical experiments are carried out to study the effect of the step on the generated wave height due to the step, the ratio of water depths at the up and low steps, the wave generator position, and the period of the wave generator motion. According to research, the suitable water depths and the wave generator position can be chosen to reach the required wave height Meanwhile, the amplitude of the wave generator motion can be deduced according to the expected wave period and amplitude.