A Parametric Approach to System Identification of Nonlinear Vibrating Structures

Abstract

Modal analysis techniques have become an important part of the engineering design and development process. These techniques use the modal properties identified from measured vibration data to validate and update analytical models. The basis of these techniques is the assumption that the structure under test is linear. Thus, any presence of nonlinearity will cause errors which may be too significant to be neglected. To ensure that the nonlinear characteristics of a structure are identified, so that they can be incorporated into future mathematical models, several procedures for identifying the different types of nonlinearities are being developed. This thesis considers the problem of identifying structures incorporating cubic stiffness nonlinearity. To identify the linear and nonlinear mass and stiffness parameters, a parametric method of identification is developed based on the use of frequency-amplitude relations or backbone curves, obtained by the Describing Function method. This method requires however that the character of nonlinearity is known in advance. Methods based on similar approach have previously been mainly limited to the identification of ideal systems in the sense that the analysis was restricted to single degree of freedom systems. A procedure to locate nonlinear elements situated within the structure is also introduced. Under noisy measurement conditions, in order to reduce the bias error, a least squares formulation based on the use of more effective weighting factors as compared to the standard weighted least squares method is also presented. The identification of the damping parameters is carried out using procedures based on the use of limit curves at resonance. The application of these curves has in the past been limited to damping characterisation only. Two approaches are introduced. The first requires that multi-point excitation techniques, using the proper force distribution to excite a single mode, is employed. The second approach uses single-point excitation force which can permit a much simpler experimental set up. The suggested procedures are extensively tested using simulated data and there is evidence that these procedures may also be applied to nonlinear structures not represented by Duffing's equation, provided an analytical expression for the backbone and limit curves can be established.