研究了流体负载下的无穷大双周期加强板，在周期谐振力作用下的振动响应和声辐射，并提出了一种基于有限元和空间波数法的半解析半数值方法．首先利用有限元的方法对周期结构进行单元离散，并将结构对薄板的作用力等效为节点力的作用．然后通过周期结构的振动方程，结合薄板与结构的位移边界条件，建立了节点力与薄板节点位移的函数方程．最后应用空间波数法和傅里叶变换，并采用数值计算的方法求解出薄板的节点位移，得到了周期加强板关于离散节点位移的振动和辐射声压方程．在数值算例中，对该方法的正确性进行了验证，并且分析了周期结构对薄板的振动和声辐射的影响．%The vibration response of and sound radiation from an infinite fluid-loaded plate, stiffened by two dimensional periodically spaced structures and excited by a time-dependent plane harmonic pressure, are investigated in this paper. A semi-analytical approach based on the finite element method （FEM） and space harmonic method to study the stiffened plate is also presented. To obtain the reaction forces of the periodic structures acting on the plate, the FEM is applied by discretizing each structure into a sufficient number of elements and nodal points, and the reaction forces are approximated by the equivalent nodal forces. Then using the vibration equations of the periodic structures combined with the displacement boundary conditions between them and the plate, the nodal forces are expressed in terms of the corresponding discrete point displacements of the plate. Based on the space harmonic method and Fourier transforms, the vibro-acoustic equations of the stiffened plate are finally derived as functions of these point displacements of the plate, which are calculated numerically. In numerical examples, the validity of the present approach is demonstrated and the effects of the periodic structures on the vibro-acoustic responses of the plate are also analyzed.
展开▼
