Natural Frequencies and Associated Mode Shapes for a Two-Branch Structure with an Arbitrary Geometry
ABSTRACT NATURAL frequencies and associated vibrational mode shapes of a continuous structure having a rigidly fixed base, a fork with two branches and an ar-bitrary geometrical configuration were investigated. A transfer matrix technique with lumped parameters was used to account for the generalized structural geometry and the interdependence of bending, longitudinal and torsional vibrations. By properly applying the boundary conditions at the fixed and both free ends of the structure a complete solution to the transfer matrix problem was achieved. A forked aluminum structure was observed ex-perimentally and used to validate the transfer matrix ap-proach and the associated computational routines re-quired to predict resonant frequencies, nodal positions and mode shape.