波纹夹层板固有频率的一阶Zig-Zag理论计算方法

Calculation method on corrugated core panel natrural frequency applying first order Zig-Zag theory

在波纹夹层板微振动时,认为面板不仅承受弯曲作用,还承受剪切作用;心层承受剪切作用,同时仅承受波纹母线方向的弯曲作用。在夹层板的上下面板和心层分别应用一阶Zig-Zag理论,根据波纹心层的具体形状,列出夹层板的几何方程。通过Hamilton原理,建立夹层板的微振动微分方程。根据边界条件,用双傅里叶级数的方法求解方程,确定特征值,求得夹层板的振动频率。经过算例验证,该方法计算的前8阶固有频率与有限元法或其他文献结果相吻合。

It is taken into account that corrugated core face sheets endure not only bending but also shearing,and core endure bending along corrugation generating line direction as well as shearing along double directions when the corrugated core panel tiny vibrates.Based on the core practical shape,geometry equations were demonstrated by applying first order Zig-zag theory to upper and lower face sheet and core.Tiny vibration diffrential equations were established according to Hamilton principle.Eigenvalue was determined and vibration frequency was calculated by solving the equations using double Fourier series according to boundary conditions.In the calculation example,the results of the first to eight order frequency of this proposal method are of good agreement with FEM or other literatures.