超声速蒙皮颤振微分积分方程的特征值问题

根据二维线化理论讨论超声速薄钣的动力稳定性,导致一类新颖的数学物理问题:非自共轭Volterra型四阶微分积分方程的复特征值问题.求得这一气动弹性系统的严格解.与其它近似分析对比,本法的临界曲线与实验数据符合良好,在低超声速范围不存在发散问题.此外,在数学物理实质方面,发现:(1)颤振频谱与固有频谱有互为间隔现象;(2)临界Mach数有简并现象.指出本法可以推广应用于三维机翼模型和燃气轮中叶栅的超声速颤振问题.

Eigenvalue Problem for Integro-Differentiai Equation of Supersonic Panel Flutter

The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to study a new problem in mathematical physis:complex eigenvalue problem for a non-self-adjoint integro-differential equation(4-th order) of Yolterra's type.Exact solution for the aeroelastic system is obtained In contrast to various approximate analysis,our resulting critical curve agrees satisfactorily with experimental data, free from divergence in low supersonic region.Moreover, we observe some notable physical behaviors;(1)mutual separation between flutter and vacuum frequency spectrum,(2) degeneracy of critical Mach number.The present method may be generalized in solving the supersonic flutter problems for 3-din ensiunal airfoil models as well as blade cascade in turbo-generator.