THE FREE VIBRATION ANALYSIS OF A BAEM PARTLY IMMERSED IN A FLUID ON COUPLED ELASTIC FOUNDATION

The transversal free vibration of an elastically supported cantilever beam carrying a tip mass in a fluid is investigated. Taking the compression axial force due to the tip mass into account, the mathematical model of a cantilever beam, in which constrains of the elastic horizontal displacement and elastic rotation are coupled, is presented. Due to the inertial force and inertial moment of the tip mass, the boundary conditions of the mathematical model are frequency dependent. The frequency equation and the generalized orthogonal condition for the vibration modes are derived analytically. The influences of the draft ratio, tip mass, moment of inertia, location of the tip mass and coupled spring-stiffness on the natural frequencies and vibration modes are discussed numerically.