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首页> 外文会议>DE-vol.119; CED-vol.11; American Society of Mechanical Engineers(ASME) International Mechanical Engineering Congress and Exposition; 20061105-10; Chicago,IL(US) >DEVELOPING POD OVER THE COMPLEX PLANE TO FORM A DATA PROCESSING TOOL FOR FINITE ELEMENT SIMULATIONS OF STEADY STATE STRUCTURAL DYNAMICS
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DEVELOPING POD OVER THE COMPLEX PLANE TO FORM A DATA PROCESSING TOOL FOR FINITE ELEMENT SIMULATIONS OF STEADY STATE STRUCTURAL DYNAMICS

机译：在复杂平面上开发POD，以形成用于稳态结构动力学有限元模拟的数据处理工具

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摘要

To analyze the steady state response of structural dynamical systems with multi-field response (example, Timoshenko shearable rod) given complex-valued databases (finite element simulations of complexified equations of motion), we have developed a Complex Proper Orthogonal Decomposition (C-POD) transform. Like the regular multi-field POD, the development of the C-POD is based on the primitive space and frequency auto-correlation operations. These data fusion operations give rise to complex Hermitian operators whose solution determines the C-POD transform. The eigen-values of the complex Hermitian operators are strictly positive and it is shown that they represent the energy fractions of the autocorrelation energy contained in the POD modes. The POD modes have both amplitudes and shapes that are complex-valued scalar functions. The C-POD transform is verified by applying it to characterize the finite element simulations of the steady state dynamics of planar beams and arches. It turns out that the real part of the shape of a POD mode coincides with the shape of the linear POD; whereas its amplitude is a localized function of frequency at a critical frequency which is identical to a natural frequency.
机译：为了分析具有给定复杂值数据库（复杂运动方程的有限元模拟）的具有多场响应（例如Timoshenko可剪切杆）的结构动力系统的稳态响应，我们开发了复杂正确的正交分解（C-POD） ） 转变。像常规的多场POD一样，C-POD的开发基于原始空间和频率自相关运算。这些数据融合运算产生了复杂的Hermitian运算符，其解决方案确定了C-POD变换。复数Hermitian算子的特征值严格为正，并且表明它们表示POD模式中包含的自相关能量的能量分数。 POD模式的幅度和形状均为复数值标量函数。通过将C-POD变换应用于平面梁和拱的稳态动力学的有限元模拟，可以对其进行验证。事实证明，POD模式的形状的实部与线性POD的形状重合。而其幅度是与自然频率相同的临界频率处的局部频率函数。

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