Vibration Analysis of the Multiple-Hole Membrane by using the Coupled Diem-Fe Scheme

This paper presents a 2D dynamics infinite element method (DIEM) for modeling the multiple-hole membrane for vibration analysis. A new concept involving converting the DIEM into a super element that can adjust the hole size and free and fixed boundary conditions around the hole is also proposed. The special element, embedded with an elastic membrane, is formulated on the basis of the conventional finite element method (FEM) by using the similarity mass/stiffness property of isoparametric elements and Craig-Bampton matrix reduction procedures. A DIEM-FE coupling scheme is also developed and self-programmed into the software MATLAB to conduct the vibration analysis of a membrane with multiple holes. The DIEM-FE approach is validated to study the vibration of the rectangular membranes by using the corresponding analytical solutions and the solutions obtained using the conventional FEM. The DIEM-FE is then applied to analyze imbedded L-shaped and circular opening problems. The effects of varying hole diameters and the free or fixed boundary condition along the hole are also examined. Finally, the last example shows that to perform vibration analysis of the multiple-hole membrane, only one DIEM mass/stiffness matrix must be calculated for all holes with an identical circular shape. Overall, this study provides a flexibility and efficient scheme for analyzing a wide variety of membrane vibration problems. The number of degrees of freedom and the corresponding PC memory storage are substantially reduced through the computation.