The transverse vibrations of a pipe containing flowing fluid: Methods of integral equations
Methods are developed to study the problem described in the title. Improvable lower bounds for the first eigenvalue are obtained for the low velocity-thin pipe wall case. It is shown that the eigenvalue changes from real to imaginary as the fluid velocity increases through a "critical" velocity. It is the methods which we wish to emphasize in that while we discuss them only for the present problem they are very general and especially powerful when applied to differential equations with constant coefficients.