The nonlinear parametric resonance of a cantilever under axial base excitation is examined while capturing extremely large oscillation amplitudes for the first time. A geometrically exact model is developed for the cantilever based on the Euler-Bernoulli beam theory and inextensibility condition. In order to be able to capture extremely large oscillation amplitudes accurately, the equation of motion is derived for centreline rotation while keeping trigonometric terms intact. The developed model is verified for the static case through comparison to a three-dimensional nonlinear finite element model. The internal energy dissipation model of Kelvin-Voigt is used to model the system damping in large amplitudes more accurately. The Galerkin modal decomposition scheme is utilised for discretisation procedure while keeping the trigonometric terms intact. It is shown that in parametric resonance region, the oscillation amplitudes grow extremely large even for smallest possible amplitudes of the base excitation, which highlights the significant importance of employing a geometrically exact model to examine the parametric resonance response of a cantilever.

检查悬臂在轴向基础激励下的非线性参数共振，同时首次捕获极大的振荡幅度。基于欧拉-伯努利梁理论和不可扩展条件，为悬臂建立了几何精确模型。为了能够精确地捕获非常大的振荡幅度，在保持三角学项不变的情况下，针对中心线旋转导出了运动方程。通过与三维非线性有限元模型进行比较，对开发的模型进行了静态验证。Kelvin-Voigt的内部能量耗散模型用于更精确地对大振幅的系统阻尼建模。Galerkin模态分解方案用于离散化过程，同时保持三角项完好无损。