面内载荷作用下功能梯度板动力屈曲

Dynamic Buckling of the Functionally Graded Material Plate Under In-plane Load

基于Kirchhoff薄板理论与Vogit应变假设,用Hamilton原理,得到面内载荷作用下材料物性参数服从幂律分布的功能梯度板动力屈曲控制方程。联合使用分离变量法和试函数法,获得了功能梯度板在满足边界条件下的动力屈曲临界载荷解析表达式和屈曲解。数值计算讨论了功能梯度板的几何尺寸、梯度指数、屈曲模态阶数以及材料构成对临界载荷的影响。结果表明:功能梯度板的动力屈曲临界载荷随临界长度的增大呈指数式下降,随厚度的增大而增大,随梯度指数k的增大而减小,且k值在区间(0,1)内对临界载荷影响较大。动力屈曲临界载荷随构成材料的弹性模量、泊松比以及模态阶数的增大而增大,且弹性模量影响较为明显。面内载荷越大,越容易激发功能梯度板产生高阶屈曲模态。边界条件对功能梯度板的屈曲模态影响较大。

On the basis of the Kirchhoff thin plate theory and Vogit's strain assumption,the dynamic buckling governing equations of the functionally graded material plate under the in-plane load were obtained by using Hamilton's principle.The analytic expression and the buckling modal solution of the critical load under boundary conditions were obtained by using the variable separation method and the test function method.The influence of the geometrical size,gradient index,buckling mode number and material composition on the critical load was discussed.The results show that the critical load decreases exponentially with the increase of the plate length,and increases with the increase of the plate thickness.The critical load decreases with the increase of the material gradient exponent k,and the influence in the k interval(0,1)is obvious.The critical load increases with the increase of elastic modulus,Poisson's ratio of the constituent materials and modal number,the influence of elastic modulus is more obvious than that of Poisson's ratio.The complicated and high order buckling mode of functionally graded material plate would be stimulated easily with larger in-plane load.The boundary conditions have large influence on the buckling mode of the functionally graded plate.