Classification of the vibration conditions on the natural frequency and the maximal displacement using response surface methodology (RSM)

Static and free vibration analyses of a straight beam with four general boundary conditions on elastic foundation are performed. In this study, the effects of beam material, boundary conditions, beam geometry (cross-sectional area), and inertia moment on natural frequencies and maximal displacements in free vibration were experimentally investigated. Optimal vibration conditions for each performance level are established, and the relationship between the variables and the physical parameters is determined using a quadratic regression model. The results show that the natural frequency is influenced principally by the boundary conditions and in the second level by the beam material. Also, it is indicated that the beam material is the dominant parameter affecting maximal displacement.