A Modal Test Method Based on Vibro-acoustical Reciprocity

Abstract

A modal test method that uses sound pressure transducers at fixed locations and an impact hammer roving over a test structure is developed in this work. Since sound pressure transducers are used, the current method deals with a coupled structural-acoustic system. Based on the vibro-acoustic reciprocity, the method is equivalent to the one, where acoustic excitations at fixed locations are given and the resulting acceleration of the test structure is measured. The current method can eliminate mass loading due to the use of accelerometers, which can destroy the existence of repeated or close natural frequencies of a symmetric structure, avoid the effects of a nodal line of a mode and an inactive area of a local mode, and measure all the out-of-plane modes within a frequency range of interest, including global and local ones. The coupling between the structure and the acoustic field in a structural-acoustic system introduces asymmetry in the model formulation. An equivalent state space formulation is used for a structurally damped structural-acoustic system and the associated eigenvalue problem is derived. The biorthonormality relations between the left and right eigenvectors and the relations between the structural and acoustic components in the left and right eigenvectors are proved. The frequency response functions associated with the current method are derived and their physical meanings are explained. The guidelines for using the current method, including the types of structures that are suitable for the method, the positions of the sound pressure transducers, and the orientation of the test structure relative to the transducers, are provided. Modal tests were carried out on an automotive disk brake using the traditional and current methods, where multiple accelerometers and microphones were used to measure its dynamic responses induced by impacts, respectively. The measured natural frequencies and mode shapes by the two methods are almost the same. The differences between the measured natural frequencies using the current method and those from the finite element model of the disk brake are less than 3% for the first 18 elastic modes, and the modal assurance criterion values of the associated mode shapes are all above 90%.