Normal Modes of Uniform Beams

The paper is devoted to the dynamics of building structures excited by-sinusoidal excitation. The analysis indicates that the complicated response curves found for higher modes of some structures are a result of the interference of lower modes of vibration. A procedure is developed which enables the resonant frequency, mode shape and modal damping of the second mode to be recovered from steady-state response data when interference is present from the fundamental mode. This is a condition that has occurred in tests, and the procedure is applied to the second mode response of the Millikan Library Building to illustrate the method. The damping in the second mode is found to be about 3.7% of critical. The analysis also is generalized to apply to the response of higher modes of vibration with interference from any number of lower modes.