An alternative solution to the flutter equation with a true damping representation is presented. The p-L method transforms the nonlinear eigenvalue problem into a linear generalized eigenvalue formulation by interpolating the nonlinear aerodynamic term with help of the Loewner and shifted-Loewner matrices, avoiding any kind of approximation. Subsequently an equivalent generalized state-space formulation in the time-domain is obtained, which stability can be determined by solving a standard generalized eigenvalue problem. The proposed method is shown to describe the aerodynamic term throughout the complex plane by analytic continuation of the interpolating rational functions over the imaginary axis, whereas expansions based on polynomial basis functions have a limited validity for excursions outside it. Further, the p-L method matches the generalized aeroelastic analysis method (GAAM) framework representing true damping but requiring only samples of the aerodynamic term along the imaginary axis, avoiding additional computations for non-zero damping. Unlike methods which solve the nonlinear eigenvalue problem whereby some roots of the flutter equation may be missed, the p-L method is able to find all roots at once. The method is applied to well-known flutter benchmark cases from the literature, namely, several two-dimensional flutter cases and the AGARD 445.6 wing aeroelastic benchmark case.

提出了具有真实阻尼表示的颤振方程的替代解决方案。该PL通过在Loewner矩阵和shifted-Loewner矩阵的帮助下对非线性空气动力学项进行插值，避免了任何形式的近似，该方法将非线性特征值问题转换为线性广义特征值公式。随后获得时域中的等效广义状态空间公式，可以通过解决标准广义特征值问题来确定其稳定性。通过在虚轴上插补有理函数的解析连续性，表明所提出的方法可描述整个复杂平面上的空气动力学项，而基于多项式基函数的展开对于其外部偏移的有效性有限。此外，pL该方法与代表真实阻尼的通用航空弹性分析方法（GAAM）框架相匹配，但只需要沿虚轴的空气动力学项样本即可，从而避免了非零阻尼的额外计算。与解决非线性特征值问题（可能会丢失颤动方程的某些根）的方法不同，pL方法能够一次找到所有根。该方法适用于文献中众所周知的颤振基准案例，即几个二维颤振案例和AGARD 445.6机翼气动弹性基准案例。