A generalized bilinear amplitude and frequency approximation for piecewise-linear nonlinear systems with gaps or prestress
A generalized bilinear amplitude and frequency approximation for piecewise-linear nonlinear systems with gaps or prestress
复制标题
具有间隙或预应力的分段线性非线性系统的广义双线性幅值和频率近似
DOI：
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发表时间：
2017
期刊：
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通讯作者：
Kiran D’Souza
中科院分区：
文献类型：
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作者：
Meng;Kiran D’Souza
对于各种民用、机械和航空航天结构来说，分段线性动力系统的分析是至关重要的，这些结构含有由裂纹、分层、接缝或部件之间的界面引起的间隙或预应力。最近，一种被称为双线性振幅近似(BAA)的技术被用来估计无间隙或无预应力的双线性系统的响应。该方法基于这样一种思想，即双线性系统的动力学可以处理为两个时间间隔内的线性响应的组合，这两个时间间隔的系统都表现为不同的线性系统：(1)打开状态和(2)闭合或滑动状态。然后应用几何约束和动量约束作为状态之间的兼容性条件，以耦合每个时间间隔的线性振动响应。为了更一般地估计体系中存在间隙或预应力的情况下的响应，本文提出了一种推广的BAA方法。新方法需要考虑接触刚度和阻尼来模拟滑动状态下的接触行为，并为每个状态建立新的平衡位置以建立适当的坐标。新方法还求出了系统的双线性频率，但由于双线性频率近似方法只适用于零间隙和无预应力的情况，因此不能用该方法来计算。在单自由度体系、三自由度体系和裂纹悬臂梁模型上对不同间隙尺寸和不同预应力水平下的广义BAA方法进行了验证。
Analysis of piecewise-linear nonlinear dynamical systems is critical for a variety of civil, mechanical, and aerospace structures that contain gaps or prestress that are caused by cracks, delamination, joints or interfaces among components. Recently, a technique referred to as bilinear amplitude approximation (BAA) was developed to estimate the response of bilinear systems that have no gap or prestress. The method is based on an idea that the dynamics of a bilinear system can be treated as a combination of linear responses in two time intervals both of which the system behaves as a distinct linear system: (1) the open state and (2) the closed or sliding state. Both geometric and momentum constraints are then applied as compatibility conditions between the states to couple the linear vibrational response for each time interval. In order to estimate the response for more general cases where there are either gaps or prestress in the system, a generalized BAA method is proposed in this paper. The new method requires inclusion of contact stiffness and damping to model contact behavior in the sliding state, and new equilibrium positions for each state to establish proper coordinates. The new method also finds the bilinear frequency of the system, which cannot be computed using the bilinear frequency approximation method previously developed since that method is only accurate for the zero gap and no prestress case. The generalized BAA method is demonstrated on a single degree of freedom system, a three degree of freedom system, and a cracked cantilever beam model for various gap sizes and prestress levels.