考虑几何非线性项和阻尼的影响,给出了四边简支的正交各向异性矩形层合板在两项横向简谐激励作用下的非线性振动微分方程,利用伽辽金法导出了相应的达芬型非线性强迫振动方程.应用多尺度法对组合共振问题进行求解,得到了系统在稳态运动下的幅频响应方程.基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件.通过数值算例,分析了不同参数对系统组合共振及其分岔特性的影响.结果表明,随着调谐参数、板厚度、阻尼系数以及激励力等参数的改变,系统存在多幅值现象、滞后现象和跳跃现象,出现不稳定解,且在某些参数点处具有运动性态发生变化的分岔特性,表现出较为复杂的动力学特性.
Considering the effects of geometrical nonlinearity and damping,the vibration differential equation of simply supported rectangular orthotropic laminated plate excited by two-term harmonic forces was established.The non-dimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method.The amplitude frequency response equation of system steady motion under combination resonance was obtained by the method of multiple scales.Based on Lyapunov stable theory,the critical conditions of steady-state solutions' stability were got.By some examples,the influence of different parameters on nonlinear combination resonances and bifurcation properties of system was analyzed.The results show that the detuning parameter,thickness of plate,damping and amplitude of excitation have different influences on combination resonance and bifurcation.With the change of parameters,the jump phenomenon,hysteresis phenomenon and unstable solutions will occur.It is also shown that the system presents relatively complicated dynamics behaviors,and there exists multi-valued phenomenon,and the dynamics behaviors will change in some values.
参考文献
| [1] | 蒋咏秋,陆逢升,顾志建.复合材料力学[M].西安:西安交通大学出版社,1990:1-25. |
| [2] | Crabtree O I,Mesarovic S D,Richards R F,et al.Nonlinear vibrations of a pre-stressed laminated thin plate[J].International Journal of Mechanical Sciences,2006,48(4):451-459. |
| [3] | Eshmatov B K.Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates[J].Journal of Sound and Vibration,2007,300(3/5):709-726. |
| [4] | Sassi S,Ostiguy G L.Effects of initial geometric imperfections on the interaction between forced and parametric vibrations[J].Journal of Sound and Vibration,1994,178(1):41-54. |
| [5] | Harras B,Benamar R.Geometrically non-linear free vibration of fully clamped symmetrically laminated rectangular composite plates[J].Journal of Sound and Vibration,2002,251(4):579-619. |
| [6] | Oh K,Nayfeh A H.Nonlinear resonances in cantilever composite plates[J].Nonlinear Dynamics,1996,11(2):143-169. |
| [7] | 任勇生,孙双双.形状记忆合金纤维正交各向异性层合矩形板的非线性弯曲振动[J].复合材料学报,2007,24(4):185-192.Ren Yongsheng,Sun Shuangshuang.Large amplitude flexural vibration of the orthotropic composite plate embedded with shape memory alloy fibers[J].Acta Materiae Compositae Sinica,2007,24(4):185-192. |
| [8] | 冯世宁,陈浩然.含分层损伤复合材料层合板非线性动力稳定性[J].复合材料学报,2006,23(1):154-160.Feng Shining,Chen Haoran.Nonlinear dynamic instability behavior of delaminated composite laminates[J].Acta Materiae Compositae Sinica,2006,23(1):154-160. |
| [9] | Zhang W.Global and chaotic dynamics for a parametrically excited thin plate[J].Journal of Sound and Vibration,2001,23(9):1013-1036. |
| [10] | Ye Min,Sun Yanhong,Zhang Wei.Nonlinear oscillations and chaotic dynamics an antisymmetric cross-ply laminated composite rectangular thin plate under parametric excitation[J].Journal of Sound and Vibration,2005,287(4/5):723-758. |
| [11] | 韦勇,陈国平,何欢.层合板振动特征值对铺层角的灵敏度[J].复合材料学报,2006,23(5):132-136.Wei Yong,Chen Guoping,He Huan.Sensitivity of the eigenvalues to the ply angles for composite plate[J].Acta Materiae Compositae Sinica,2006,23(5):132-136. |
| [12] | Nayfeh A H,Mook D T.Nonlinear oscillations[M].New York:John Wiley & Sons,1979:56-59. |
- 下载量()
- 访问量()
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%