再论端面受到空气阻力的弹性杆的振动

Revisited discussion on vibration of an flexible rod with end surfaces subjected to air resistance

重新研究了端面受到空气阻力的弹性杆振动的分离变量法.建立了复本征函数的广义正交性.用复数形式的本征振动展开一般解.利用正交性求出了一般解中的系数以满足任意给定的初始条件.求解了多种边界条件下的振动,包括两端均受到空气阻力、一端有集中质量物体和弹性连接并受到空气阻力等情况.

The method of separation of variables for the vibration of an flexible rod with end surfaces subject to air resistance is discussed again.Generalized orthogonal relations of the complex eigenfanctions are established.The general solution is expanded in terms of complex eigenvibrations.The orthogonal relations are used to determine the coefficients in the general solution,such that it satisfies arbitrarily given initial conditions.Several cases with many boundary conditions are solved,including the case with both ends subjected to air resistance,and the case with one end fixed and the other connected to a concentrated mass and the latter connected to a spring and subject to air resistance.