An interesting material that appears to be fit to possibly all future mechanical vibration textbooks

Abstract

A material is suggested for future mechanical vibration textbooks. Both mathematically and conceptually it is simpler than most of the material that is already included in the existing textbooks. It pertains to the inverse vibration problem for inhomogeneous beam, i.e. the beam with the modulus of elasticity that varies along the axial coordinate. Specifically, the solution of the following problem is presented: Find a distribution of the modulus of elasticity of an inhomogeneous beam such that the beam would possess the preselected simple, polynomial vibration mode shape.