摘要
从形状记忆合金(SMA)的等应变拉压实验数据出发,利用van-der-pol环模型模拟了形状记忆合金在加载和卸载过程中的应力应变迟滞环特性。并根据弹性理论和Galerkin方法建立了形状记忆合金简支梁在受轴向激励时的振动模型。随后得出了自由振动系统的分岔特性。在利用待定固有频率法研究了模型的非线性参数对系统固有频率的影响后,根据待定固有频率法的计算结果和时间尺度变化提出了系统Melnikov函数的改进表达式,提高了计算形状记忆合金梁模型在参数激励下发生混沌的阈值的精度。数值模拟的结果证明了该途径的有效性。
Van-der-pol hysteretic cycle was used to describe hysteretic nonlinear characteristic of strain-stress relation of a shape memory alloy（SMA）based on experimental data.A dynamical model with nonlinear damping for a simply supported SMA beam subject to axial excitation was proposed based on elastic theory and Galerkin’s approach.At first,the local bifurcations of the free vibration system were analyzed with the normal form theory.And the global bifurcation was studied with Melnikov approach.Secondly,the undermined natural frequency and normal form methods were utilized to study the influence of the disturbing parameters on the natural frequency.Finally,the improved Melnikov expression for the oscillator was built based on the results of the undermined natural frequency method and time scale transformation to obtain the approximate threshold value of chaotic motion with the homoclinical points of view.The numerical results showed the effectiveness of the theoretical analysis.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第12期103-107,119,共6页
Journal of Vibration and Shock
基金
国家自然科学基金重点资助项目(10732020)
