Damping Matrix and Modal Parameters Identification of Dynamic Structure by Sub-Structuring Technique

摘要

One major accomplishment of this research paper is developing a method to identify damping matrix and modal parameters in frequency domain of a dynamic system by sub structuring technique. The dynamic system is divided into a series of subsystems each one of them is then analysed and the vibration responses, here spectral densities of velocities and displacements, to an impulsive loading, of the overall system are then obtained by a suitable combination of subsystem data, that is mobility and re-ceptance coupling technique. The spatial coupling is first employed within finite element model (FE) for damping matrix identification. In the second step, The modal coupling, the complex inversion and the FRF coupling methods for damping and modal parameters identification are used to identify the proportional damping matrix and the modal parameters. It should be noted that the velocity and displacement data are transformed to spectral density matrices before the identification technique is applied. Application of the proposed method requires an N×N velocity and displacement matrices .N being the model order or the number of modes of the dynamic system. In practice, it is not possible to gather such an amount of data. Therefore, a minimum set of data should be used for economy concern. Hence It is shown how the N×(N-1) velocity or displacement response matrices in time domain are completed from the knowledge of only one row or column of response matrices of velocities or displacements. In practice, once the response matrices, velocities or displacements, are identified in time domain, they are transformed into frequency domain data. The derivation and application of the proposed method for damping matrix and modal parameters identification is possible because of the connection between frequency domain and time domain data. To simulate real life data, a white noise with Gaussian distribution and zero mean is added to analytical, that is noise free, data. The method is applied to deliberately chosen simple analytical lumped mass systems.