Dynamic Beam Modification Using Dimples

In this paper, a design method to modify the vibration characteristics of a beam by creating cylindrical dimples on its surface is investigated. In particular, the vibration response of a beam with several dimples is formulated using the impedance method. The dimpled beam is divided into two kinds of structural segments: one, a curved beam that is modeled as the dimple and the other, a straight beam. The frequency equation is derived by assembling the impedance of each structure segment based on conditions of force equilibrium and velocity compatibility. Then a novel method for shifting the natural frequencies of a beam to preassigned values by creating cylindrical dimples on this structure is introduced. The dimple size and its location on the structure can be determined analytically, so the time consuming process using the traditional optimal search method is thereby avoided. Several examples using this technique are demonstrated.