本文在受轴向冲击圆柱壳的非冲击端引入轴向、周向、径向和径向旋转四个方向边界弹簧模拟一般边界条件。根据Love薄壳理论得到圆柱壳变形过程中的应力应变，并采用一种改进的Fourier级数方法表示圆柱壳沿坐标轴方向的位移。将应力应变以及位移代入圆柱壳的能量表达式，采用基于Hamilton方程的一阶变分法对能量表达式进行推导和变换，得到一般边界条件下受轴向冲击圆柱壳的自然频率以及动力屈曲临界载荷的判别式。计算分析了一般边界条件对受轴向冲击圆柱壳的自然频率和屈曲临界载荷的影响，以及不同边界条件圆柱壳屈曲模态的类型特点。结果表明：一般边界条件下自然频率随着冲击载荷增大而降低；随着轴向波数的增加圆柱壳自然频率及屈曲临界载荷增大，随着周向波数的增加屈曲临界载荷也增大；轴向、周向、径向和径向旋转各个方向边界刚度对圆柱壳自然频率和屈曲临界载荷的影响都是:刚度系数越小，自然频率越低而临界载荷越大；圆柱壳受轴向冲击，边界条件的改变会影响屈曲模态。
Abstract
Four kinds of springs are introduced at the non-impact end of an axially impacted cylindrical shell to simulate general boundary conditions. These are linear springs distributed along the axial, circumferential, radial directions, respectively, and rotational springs distributed along the radial direction. To study the dynamic characteristics of axially impacted cylindrical shells with general boundary conditions, firstly, the stress and the strain of a cylindrical shell during deformation are obtained based on Love thin shell theory. The displacements of the cylindrical shell are expressed in the form of improved Fourier series. Secondly, the stress, strain and displacements of the cylindrical shell are substituted into energy expression. The energy expression is derived and transformed using first-order variational method which is on the basis of Hamilton equation. Discriminant about natural frequency and critical buckling load is achieved. Finally, the effects of general boundary conditions on the natural frequency and the critical buckling load are calculated. Several numerical examples reveal that the natural frequency decreases with increasing the impact load. The natural frequency and the critical buckling load increase with increasing the axial wave number, and the critical buckling load increases with increasing the circumferential wave number. The lower the stiffnesses of four kinds of springs are, the lower the natural frequency and the higher the critical buckling load will be. Under axial impact, the change of boundary conidtions will affect buckling modal shapes.
关键词
弹性圆柱壳 /
一般边界条件 /
轴向冲击 /
能量方法 /
动力特性
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Key words
elastic cylindrical shell /
general boundary conditions /
axial impact /
energy method /
dynamic characteristics
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