共振频率激励下弦振动定解问题的求解

Solution of string vibrating problem under the resonant frequency incentive

对于一端固定、另一端施加正弦激励的弦线振动定解问题,采用分离变量法在共振与非共振两种激励频率下对其进行了求解;通过对两种不同形式解的研究发现:对非共振频率激励下的解求极限,亦可得到共振频率激励下的解;最后通过分析可知:共振频率激励下的解即为无阻尼条件下的驻波状态解.

For the string vibrating problem under the condition that one end is fixed and the other end with sinusoidal incentive, it is solved by the separation of variables under incentive of resonant frequency and non-resonant frequency.Through the study of two different forms of solutions, it is found that the solution under the resonant frequency incentive can be obtained by getting the limit of the solution under non-resonant frequency incentive.Finally, the analysis shows that the solution under resonant frequency incentive is the solution of standing wave state without damping.