窄带随机激励带集中质量梁的主参激共振

Principal parametric resonance of a slender beam carrying a lumped mass under narrow-band random excitation

以受窄带随机激励带集中质量柔性梁为研究对象,采用多尺度法导出系统单模态主参激共振调谐方程组,结合FPK方程分析了力-幅特性下联合概率密度随激励幅值所出现的随机跳跃现象,结果显示:在三值响应范围内存在一外扇形峰及一内火山口峰,随着激励幅值减小,外扇形峰减弱而内火山口峰增强,表明响应逐渐从非平凡稳态响应向平凡稳态响应跳跃。

A detailed theoretical investigation into the single-mode approximate response of a slender cantilever beam carrying a lumped mass subjected to base excitation,where the narrow-band random excitation characters to feature the very weak fluctuation in frequency of the excitation are taken into consideration, is presented.The multiple scales method is used and the stochastic jumps of amplitude-phase joint probability density of the response have been investigated for the principal parametric resonance of the system under the varying excitation amplitude using finite difference method based on FPK equation.For the force-response domain,there is a region of excitation acceleration within which the joint probability density has two peaks： an outer flabellate peak and a central volcano peak.Results show that the outer flabellate peak decreases while the central volcano peak increases as the amplitude of the excitation decreases,showing stationary response jumping from nontrivial to trivial state.