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首页> 外文期刊>Journal of thermal stresses >VIBRATION OF THERMALLY POST-BUCKLED ORTHOTROPIC CIRCULAR PLATES
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VIBRATION OF THERMALLY POST-BUCKLED ORTHOTROPIC CIRCULAR PLATES

机译：热屈曲后正交异性圆板的振动

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摘要

Axisymmetric vibrations of a statically buckled polar orthotropic circular plate due to uniform temperature rise have been studied numerically. Effects of geometric nonlinearities have been incorporated into the problem formulation. The problem is challenging because the buckled configuration is unknown a priori. By assuming that the amplitude of plate's vibration and the additional strains induced in it are infinitesimal, and its response harmonic, the non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations; one for the thermal post-buckling, and the other for linear vibrations of the plate superimposed upon the post-buckled configuration. The plate's boundary is taken to be either clamped or simply supported but restrained from moving in the radial direction. The two sets of coupled boundary value problems are solved numerically by a shooting method. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and post-buckled plates, have been computed, and characteristic curves of the frequency versus temperature rise for different values of material anisotropy parameters are plotted. It is found that the three lowest frequencies of the pre-buckled plate decrease with an increase in the temperature, but those of a buckled plate increase monotonically with the temperature rise. The fundamental frequency of the deformed plate approaches zero at the onset of buckling.
机译：数值研究了静态屈曲的正交异性正交圆板由于均匀升温引起的轴对称振动。几何非线性的影响已纳入问题表述中。这个问题是具有挑战性的，因为弯曲的配置是先验未知的。通过假设板的振动幅度和在其中引起的附加应变为无穷小，以及其响应为谐波，将非线性偏微分方程简化为两组耦合的常微分方程。一个用于热后屈曲，另一个用于叠加在后屈曲构型上的板的线性振动。可以将板的边界夹紧或简单地支撑，但要限制其在径向上移动。通过射击方法可以数值求解两组耦合的边值问题。对于前屈曲板和后屈曲板，计算了前三个频率对温度升高的依赖性，并绘制了不同材料各向异性参数值下频率对温度升高的特性曲线。可以发现，预屈曲板的三个最低频率随温度的升高而降低，而屈曲板的三个最低频率随温度的升高而单调增加。变形的板的基本频率在屈曲开始时接近零。

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