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Abstract
Structures, freely moving in space and having some geometric symmetry, are analyzed for damped free linear vibrations by employing group representation theory. The symmetry adapted basis vectors are determined corresponding to various invariant subspaces for the irreducible representations present in the reducible representation of the configuration space. The kinetic, the damping and the strain energy are written in terms of the symmetry adapted co-ordinates. The Lagrangian equations of motion for damped free systems are expressed in the symmetry adapted co-ordinates for each subspace. These equations of motion are solved for natural frequencies and the normal mode vectors in terms of the symmetry adapted basis vectors. The constant coefficients for the general solution are determined for some initial displacements.
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