弹性边界下圆弧拱的自由振动分析

发布时间：2018-08-06 20:59

【摘要】：工程中圆弧拱的边界不能总被简化为理想的简支或固支形式。为了研究弹性支承对圆弧拱自由振动特性的影响规律,将力、位移等变量无量纲化。根据平衡方程和坐标转换推导得出极坐标下圆弧拱在水平、竖直和转动方向支撑条件为弹性时的边界条件方程。并采用考虑弯曲和轴向变形而忽略剪切变形及转动惯量的自由振动的运动控制方程。运动方程在边界条件情况下,其解仅为关于矢跨比f,细长比s和无量纲刚度阵[K]的函数。采用Runge-Kutta法和行列式搜索法求解运动方程的特征值即无量纲频率Ωi以及特征向量即振型。通过计算发现,与理想支撑相比,弹性支承情况下细长比s对拱自振频率的影响要明显下降。理想支撑情况下圆弧拱的自振频率越高,则弹性支承对其自振频率的影响越小。与水平和竖向弹性支承相比,转动方向弹性支承仅对圆弧拱基频有较大影响。
[Abstract]:In engineering, the boundary of arc arch can not always be simplified to ideal simple support or fixed support form. In order to study the influence of elastic support on the free vibration characteristics of arc arch, the variables such as force and displacement are dimensionless. According to the equilibrium equation and coordinate transformation, the boundary condition equation of arc arch with elastic support condition in horizontal, vertical and rotational direction under polar coordinates is derived. The governing equation of free vibration considering bending and axial deformation and ignoring shear deformation and moment of inertia is adopted. In the case of boundary conditions, the solution of the equation of motion is only a function of the vector-span ratio f, the slenderness ratio s and the dimensionless stiffness matrix [K]. Runge-Kutta method and determinant search method are used to solve the eigenvalue of motion equation, i.e. dimensionless frequency 惟 I and eigenvector mode. It is found by calculation that the effect of slenderness ratio s on the natural vibration frequency of the arch is obviously decreased when compared with the ideal bracing. The higher the natural frequency of arc arch is, the less the effect of elastic support on its natural vibration frequency is. Compared with the horizontal and vertical elastic supports, the rotation direction of the elastic support only has a greater effect on the fundamental frequency of the arc arch.
【作者单位】：解放军理工大学爆炸冲击防灾减灾国家重点实验室;南京理工大学机械工程学院;
【分类号】：O327

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