【摘要】 提出了一种分析滑移边界各向同性和正交各向异性矩形板振动特性的数值方法—双向样条离散法。该方法适用于各种可能组合边界矩形板的自由振动分析;边界包括自由、简支、固定和滑移边界。在x和y方向,板被离散成N和M个等分区间。为适应任意边界,修改N+3和M+3维B3样条函数向量的最前和最后三个函数,得到x方向N+1个点、y方向M+1个点和x-y方向两个附加点的修正的B3样条函数向量,并以此作为板的位移试函数。在给定边界下,修正的B3样条函数向量对位移、位移的一阶导数和二阶导数都仅保留一个未知系数。基于矩形板的势能泛函导出其特征方程。与有限元法和样条有限条法相比,本文方法具有自由度少、计算效率高和输入数据少等优点。数值计算结果表明,本方法具有高的计算精度。更多还原

【Abstract】 The authors present a numerical analysis procedure,referred to as the bidirectional spline discretization procedure,for vibration analysis of an isotropic and orthotropic rectangular plate with possible combinations of the three classical boundary conditions of free(F),simply supported(S), and clamped(C) edges with one guided(G) boundary condition.By discretization through,respectively,dividing the plate into N and M equal subintervals in the x and y directions,the modified B3-spline functions,consisting of the(N+3) and (M+3) local B3-spline functions(The first three and the last three local B3-spline functions have been modified for accommodating to any type of boundary conditions.) with respect to the(N+1) points and two extended additional points in the x direction and the(M+1) points and two extended additional points in the y direction,are employed as the displacement trial functions.Making use of the modified B3spline functions,only one unknown coefficient is required to be determined,respectively,for the deflection(displacement) and the first and the second derivatives of the deflection at a given bound.Characteristic equation of a rectangular plate is derived based on its potential energy functional.In comparison to the finite element method(FEM) and the spline finite strip method(FSM),the present procedure has remarkably fewer numbers of degree of freedom(DOF),and thus it is computatively more efficient.Likewise,the computational program,with minimal preparation of input data,can be developed through the proposed formulation.The numerical results indicate that the proposed method can render a very high accuracy.更多还原