Transverse vibrations of an Euler-Bernoulli uniform beam carrying two particles in-span (Q1348428)

The author deals with natural frequencies and natural modes of a prismatic beam with two concentrated masses. The beam itself is modeled as Euler-Bernoulli beam with uniformly distributed mass. Concentrated masses are in a general position on the beam axis. A conventional solution of the corresponding differential equation of beam dynamics is presented. Subsequently, an eigenvalue problem with boundary conditions and continuity conditions at points of concentrated masses is composed, and zero points of functional determinant are numerically determined for various combinations of input parameters. The references are adequate, nevertheless references to classical worldwide known resources are missing. The style of derivation and subsequent analysis can be found in various basic monographs dealing with slope deflection method, transition matrices method, etc. A lot of papers discussing this problem in more detailed form have been published in seventies and eighties in many journals.