Investigation of vibrations of a two phase material

Abstract

The model for investigation of vibrations of an elastic structure filled with fluid is proposed. This model is applicable for the analysis of vibrations of soil filled with water and can also be applied for the analysis of vibrations of materials used in various transportation devices. A two-dimensional structure is analyzed and four nodal variables are assumed: displacements of the elastic structure in the directions of the axes of coordinates and displacements of the fluid in the directions of the axes of coordinates. The interaction of the elastic structure and the fluid is assumed through the volumetric strains. This enables to obtain the stiffness and mass matrixes directly applicable for calculation of the eigenmodes of the system. The eigenmode is represented by two figures: the displacements of the elastic structure and the displacements of the fluid. The first eigenmodes of the rectangular structure are obtained and analyzed. An important problem for precise analysis of vibrations of such twophase systems is the accurate determination of physical parameters used in the analysis. Special experimental procedures are to be designed and implemented for their determination. This is the subject of subsequent investigations and is to be presented in future papers.