Asymptotic Modal Analysis of Structure Borne Noise in Cross Beams

Abstract

The dynamic response (structure borne noise) of two cross beams intersecting perpendicularly to each other is studied for a point load applied vertically at an arbitrary location on one beam. The modal analysis technique is used to analyze the bending and torsional responses of the system of coupled beams. The modal equations of motion are derived from Lagrange’s equations with the coupling constraint at the beam intersection point included via Lagrange multipliers. For the limiting case of a large number of participating modes, an asymptotic modal analysis is performed resulting in simple estimates of the upper and lower bounds of the beam responses. These bound estimates are compared with the corresponding SEA results.