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Nonlinear plate aeroelastic response with uncertain stiffness and boundary conditions

机译：刚度和边界条件不确定的非线性板气动弹性响应

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The probabilistic response of a nonlinear panel in supersonic flow is investigated using a new computational methodology. The aeroelastic system is modelled by coupling the von Karman plate equations with piston theory aerodynamics. Baseline deterministic results are compared to published data to establish validity of the aeroelastic model. Uncertainties in modulus of elasticity and boundary conditions (BCs) are considered, with their impact on panel response being quantified in terms of limit-cycle oscillation (LCO) onset pressure and panel amplitude. The panel's uncertain BCs are modelled using rotational springs in place of ideally fixed boundary conditions. The panel's uncertain elastic modulus is modelled as a second-order, spatially homogeneous, isotropic, random field. The boundary spring stiffness values are spatially constant for each random realization assuming either a uniform or Weibull distribution. Probabilistic response distributions are obtained through Monte Carlo simulation (MCS) for selected values of flowfield dynamic pressure. MCS is run for the case of random modulus only, as well as random modulus combined with either random BC distribution. It is observed that uncertainties have the greatest nonlinear influence on LCO amplitude near the deterministic point of LCO onset. Furthermore, panel response is much more sensitive to location of the modulus fields' extreme values than the correlation length used to generate the field. Novel aspects of the computational methodology include (1) the use of random fields (as opposed to a random variable) to model uncertainty in the elastic modulus, and (2) the use of proper orthogonal decomposition (POD) to yield insight into the local factors that govern the global response of the panel, permitting enhanced response prediction based on the nature of the random field realizations.
机译：使用一种新的计算方法研究了超音速流中非线性面板的概率响应。通过将von Karman板方程与活塞理论空气动力学耦合来对空气弹性系统进行建模。将基线确定性结果与已发布的数据进行比较，以建立气动模型的有效性。考虑到弹性模量和边界条件（BCs）的不确定性，并根据极限循环振荡（LCO）起始压力和面板振幅来量化其对面板响应的影响。使用旋转弹簧代替理想的固定边界条件来模拟面板的不确定BC。面板的不确定弹性模量建模为二阶，空间均匀，各向同性的随机场。对于每个随机实现，边界弹簧刚度值在空间上都是恒定的，假设是均匀分布或威布尔分布。通过蒙特卡罗模拟（MCS）获得流场动压选定值的概率响应分布。仅针对随机模量以及随机模量与随机BC分布相结合的情况运行MCS。可以看出，不确定性对LCO起始点附近的LCO振幅具有最大的非线性影响。此外，面板响应对模量场极值位置的敏感度远大于用于生成场的相关长度。计算方法的新颖方面包括：（1）使用随机字段（与随机变量相对）来模拟弹性模量中的不确定性，以及（2）使用适当的正交分解（POD）来了解局部控制面板全局响应的因素，可以根据随机场实现的性质增强响应预测。

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