Limitations of an equivalent linearized method on vibration analysis of a flexible cantilever beam

Using an equivalent linearized method to analysis the vibrating behaviors of a flexible cantilever beam with large deformation is a very effective method, but the small amplitude hypothesis is the precondition of this method. This paper discusses the limitations of the equivalent linearized method proposed by D.G. Fertis through the experimental and theoretical investigations. A flexible cantilever beam with large deformation was designed and manufactured, and three frequency responses function (FRF) curves under three different vibrating amplitude levels were measured by the fixed frequency steady state exciting method. The comparisons between experimental and simulation results show that, when the ratio of tip dynamic displacement amplitude and static deformation amplitude is less than 10%, the variations of measured FRF curves are very small. So the system can be regarded as linear system, and the relative error of the proposed equivalent linearized method is less than or equal to 6%, this approximate method is effective. But when the ratio of tip dynamic displacement amplitude and static deformation amplitude is more than 20%, the value of the measured FRF at resonant frequency point is significantly reduced, and the relative error of the equivalent linearized method is more than 50%, and this method will be no longer suitable.