Modal decomposition and modal cluster decomposition on two-dimensional frequency domain (sensor placement based realization)

This paper describes the basic theory for modal decomposition and modal cluster decomposition on two-dimensional frequency domain, based on the two-dimensional Fourier transform of array sensor outputs. At first, the concept of modal cluster decomposition was introduced. Then, an objective function was derived to determine the sensor placement to place each modal cluster on any selected line in two-dimensional frequency domain. As a numerical example, the optimal sensor placement was computed for a simply supported beam in case the number of sensor is two. It is shown that this decomposition is used for suppressing several selected modal amplitudes, or placing each modal cluster on any selected line. Moreover there exists the sensor placement that is used for suppressing multiple modal cluster simultaneously.