Natural angular frequencies and eigenmodes of orthotropic rectangular parallelepiped with sliding boundary conditions for all faces

Abstract

Natural angular frequencies and natural vibration modes of the three-dimensional orthotropic rectangular parallelepiped that is not made of layers are investigated. The natural angular frequencies and eigenmodes are calculated as the eigenvalues and eigenvectors of the frequency equation that is derived from the relationship between stress and strain in the x-, y- and z-axes, the equations of motion and the admissible functions of displacements. In the numerical examples, we investigate a three-dimensional orthotropic material and an isotropic material. In the relationship between the dimensions and the natural angular frequencies, there are three ranges where the natural angular frequencies vary linearly, they are almost constant and the intermediate range between them regardless the type of the materials. In the case of the three-dimensional orthotropic material, two natural angular frequencies were almost the same only in the range where the natural angular frequencies vary linearly. All eigenmodes are changed in the intermediate range and are unchanged in the other ranges regardless the type of the materials. In the case of the isotropic material, there is always only one dominant component of eigenvectors, while in the case of the three-dimensional orthotropic material, there are sometimes two.

Keywords

• continuous system
• anisotropy
• orthotropy
• natural angular frequency
• eigenmode