关键词: 振动, 等效线性化法, 小振幅假设, 非线性, 柔性悬臂梁

Abstract:

The equivalent linearization method is an efficient and approximate method in analyzing the vibration characteristics of a flexible beam with large deformation, but the small amplitude hypothesis is the precondition of this method. The traditional fully nonlinear methods are usually incapable of characterizing explicitly the influence of geometric nonlinear properties on structure parameters; neither can it satisfy the requirements of the reduced-order models. The present paper considers the vibrating behaviors of a flexible cantilever beam with large deformation, and developes an equivalent linearization method to calculate the vibrating response of this beam. The proposed method can equivalently consider the effects of large static deformation on the vibration properties of a beam as the variations of the cross section moment of inertia and mass density distribution. In order to further determine the limitation of the small amplitude hypothesis, a flexible cantilever beam with large deformation is designed and manufactured, and three frequency response function (FRF) curves under three different vibrating amplitude levels are measured by the fixed frequency steady state exciting method. The comparisons between simulation and experimental results show that, when the ratio of tip dynamic displacement amplitude to static deformation amplitude is less than 10%, the changes of measured FRF curves are very small. So the system can be regarded as a linear system, and the relative error of the proposed equivalent linearization method is equal to or less than 6%, and the approximate method is effective. But when the ratio of tip dynamic displacement amplitude to static deformation amplitude is more than 20%, the value of the measured FRF at a resonant frequency point is significantly decreased, and the relative error of the equivalent linearization method is more than 50%, and this method is no longer suitable. And the nonlinear vibration behavior of the experimental flexible cantilever beam is dominated by the structural damping nonlinear property.

Key words: vibration, equivalent linearization method, small amplitude hypothesis, nonlinearity, flexible cantilever beam