In this work, two new techniques of the Boundary Elements Method are coupled for solving eigenvalues in three-dimensional piecewise scalar problems. The Domain Superposition Technique (DST) is used to approach the sectorial homogeneities, modeling the domain as a sum of a homogeneous surrounding sector and other complementary ones with different constitutive properties. The Direct Interpolation Technique (DIBEM) with Radial Basis Functions transform domain integrals, in this case referring to the inertia, into boundary integrals. Thus, after discretization, a classical boundary element matrix system is formed in which the natural frequencies are achieved solving an eigenvalue problem. Considering the absence of analytical solutions for three-dimensional dynamic problems, benchmarks are taken by the Finite Element Results, using finer meshes.

在这项工作中，结合了边界元素法的两种新技术来求解三维分段标量问题中的特征值。域叠加技术（DST）用于逼近扇区同质性，将域建模为周围均匀的扇区和其他具有不同本构性质的互补扇区之和。具有径向基函数的直接插值技术（DIBEM）将域积分（在这种情况下是指惯性）转换为边界积分。因此，在离散化之后，形成了经典的边界元矩阵系统，在该系统中实现了固有频率的求解特征值问题。考虑到没有三维动力学问题的解析解，有限元结果使用更精细的网格作为基准。