STRUCTURAL INTENSITY IN BEAMS - WAVES, TRANSDUCER SYSTEMS AND THE CONDITIONING PROBLEM

The motion of a beam under flexural vibration is decomposed into wave components to evaluate intensity, energy density and reflection coefficients. Results are presented of experimental measurements made with an array of transducers, both in the presence of a single near field and in a region where two significant near fields exist. The problem of errors that result from small transducer spacings is discussed in terms of the condition of a matrix, and the performance of a measurement system is quantified by a transducer array condition number. This condition number allows different transducer systems to be compared in terms of the sensitivity of the final result to measurement noise and other errors. Additionally, optimizing the array condition number through the use of suitable transducer separations gives the best possible intensity measurement for the particular transducers being used. The use of hybrid measurement systems involving the measurement of more than one vibrational quantity, such as acceleration and strain or translational and rotational acceleration, is discussed. These can offer a significant improvement in array condition number over an accelerometer array. An example of a hybrid measurement system is implemented, by using the frequency response technique, between two closely spaced discontinuities and compared with results obtained by using four acceleration measurements. The improved conditioning offered by the hybrid systems results in substantially more accurate intensity measurement.