不等间距加筋圆柱壳的振动局域化研究

Localization of vibration on a disordered framed cylindrical shell

对圆柱壳采取不等间距加筋配置将导致其振动在通频带局域化,从而可实现对圆柱壳结构振动进行控制。将加筋圆柱壳模型的振动等效为耦合振子链的振动,利用耦合振子链的无序局域化因子理论公式定量预报不等间距加筋圆柱壳的无序局域化因子:与耦合振子链等效的圆柱壳振动参数由基于有限元结合波数分析技术所获得的加筋圆柱壳色散曲线给出;与耦合振子链等效的圆柱壳无序参数由圆柱壳弯曲波动理论和统计理论给出。在给出不等间距加筋圆柱壳无序局域化因子的基础上,开展了无序局域化因子影响规律的研究。针对不等间距加筋圆柱壳实例的数值分析表明,利用不等间距加筋配置来实现圆柱壳结构振动局域化控制具有可行性,所采取的无序局域化因子预报方法具有有效性。

It has been observed that vibration energy of disordered reinforced cylindrical shells will be confined to the source in the pass bands.Disordered stiffeners are one of the measures to control the vibration of cylindrical shells.An investigation on localization of a disordered reinforced cylindrical shell will be presented.The vibration of the reinforced cylindrical shell is analogized to that of coupled oscillator chain system.The localization factors of the reinforced cylindrical shell are predicted using formula derived for a coupled oscillator chain system.Vibration parameters of equivalent oscillator chains can be acquired by the disperse curves,which can be identified by wave number analysis based on finite element analysis.Disordering parameter of the reinforced cylindrical shell can be acquired using the theory on flexural wave in cylindrical shells and theory of statistics.On the basis of the disordered localization factor of stiffened cylindrical shells with unequal spacing,the regularity of the disordered localization factor is studied.Numerical results on some disordered reinforced cylindrical shells are presented,and are used to verify both the feasibility of vibration control by disordered stiffeners and the method on predicting the localization factors in the paper.