S. R. Ibrahim

An upper Hessenberg sparse matrix algorithm for modal identification on minicomputers

The time domain modal identification problem is here reduced to an eigenvalue problem of a sparse upper Hessenberg matrix. Such a matrix has only a number of elements equal to its order (one column), subdiagonal elements of unity and all the other remaining elements are zeros. The one vector elements of this matrix are obtained by using Cholesky decomposition to solve a positive definite system of equations which is constructed by using a structures free decay or impulse time histories. Any number of measurements may be used, from one or more tests with a single or multiple shaker. The direct use of an upper Hessenberg matrix eliminates the need of transforming a full matrix to such a form and consequently greatly reduces the computational requirements when the QR algorithm is used for the eigensolution. In addition to reducing computer time and storage, the proposed technique has more flexibility than other comparable time domain approaches. It also produces higher identification accuracy especially in the identified damping factors. Sample results are presented with comparisons to those of other time domain algorithms.

Time domain identification of standing wave parameters in gas piping systems

Abstract A method for experimentally determining the natural frequencies and modal pressures of an air or gas piping system is presented. Such information is of interest in installations where pressure pulsations caused by pumps or compressors are of importance. In the method a time domain based technique is used which was originally developed as an alternative to frequency response methods for determining the vibration parameters (natural frequencies, modes, damping factors) of structures, to avoid difficulties often encountered in interpreting complex and non-conclusive frequency response data such as arises from systems having numerous modes, some of which may be highly damped or closely spaced in frequency. In this application, a straight steel pipe with a sound source at one end and closed at the other end was used. Two microphones were used to measure the pressure at two locations in the pipe. The free pressure response following a rapidly swept sinewave input was recorded, digitized and then used in a computational procedure based on a lumped parameter representation of the system. The natural frequencies and the corresponding modal pressure ratios at the two stations, thus obtained, are compared with mention here that although in the experiment reported here an external frequency sweep excitation was used, the technique works as well with free decay response after a system shut-off, impulse response or random responses from normal system operation.