端面受到空气阻力的弹性杆的振动

Vibration of a flexible rod with one end subjected to air resistance

研究了一端固定、一端受到空气阻力的弹性杆的振动.建立了受阻力端的近似边界条件.本征振动模式含有阻尼振动特有的指数衰减因子,但不具有分离变量的形式.因为边界条件不属于斯特姆-刘维型,所以关于本征函数的完备性和正交性的一般定理不适用于本问题.用拉普拉斯变换法求解了任意给定初始条件下的振动.

The vibration of a flexible rod with one fixed end and the other subjected to air resistance is studied.The boundary condition for the end with air resistance is established approximately.The eigen modes of vibration involve an exponentially decaying factor characterizing damp vibration,but are not of factorized form.Because the boundary conditions are not of Sturm-Liouville type,the theorem on the completeness and orthogonality of the eigenfunctions is not applicable. The vibration satisfying arbitrarily given initial conditions is found by the method of Laplace transform.