Vibration Analysis of Structures with Rotation and Reflection Symmetry

Abstract

The article applies group representation theory to the vibration analysis of structures with C_nv symmetry, and presents a new structural vibration analysis method. The eigenvalue problem of the whole structure is divided into much smaller subproblems by forming the mass and stiffness matrices of one substructure and than modifying them to form mass and stiffness matrices in each irreducible subspace, resulting in the saving of computer time and memory. The modal characteristics of structures with C_nv symmetry are derived from theoretical analysis. Computation and modal testing are used to verify the validity of the theoretical deductions.