Using a system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of a thin elastic orthotropic cylindrical panel with free edges is investigated. To calculate its natural frequencies and to identify the respective vibration modes, the generalized Kantorovich–Vlasov method of reduction to ordinary differential equations is employed. To find the natural frequencies of possible types of vibrations, dispersion equations are derived. An asymptotic relation between the dispersion equations of the problem in hand and of an analogous problem for a rectangular plate with free sides is established. Determined is also a relation between the dispersion equations of the problem and of the boundary-value problem for a semi-infinite orthotropic nonclosed circular cylindrical shell with three free edges. With the example of an orthotropic cylindrical panel, the values of dimensionless characteristics of its natural frequencies are derived.

中文翻译：

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具有自由角的薄弹性正交各向异性圆柱板的自由振动

使用对应于正交各向异性圆柱壳的经典理论的方程组，研究了具有自由边的薄弹性正交各向异性圆柱板的自由振动。为了计算其固有频率并确定各自的振动模式，采用了归约到常微分方程的广义 Kantorovich-Vlasov 方法。为了找到可能的振动类型的固有频率，可以导出色散方程。建立了手头问题的色散方程与具有自由边的矩形板的类似问题的色散方程之间的渐近关系。还确定了问题的色散方程与具有三个自由边的半无限正交各向异性非封闭圆柱壳的边界值问题之间的关系。