A methodology has been proposed to estimate non-proportional viscous damping matrix of beams from measured complex eigendata using finite element model updating technique. Representation of damping through a proportional damping matrix ignoring the complexity of eigenvectors may not be appropriate when external damping devices are employed. The current literature of determination of non-proportional damping matrix demands measurement of a large number of complex modes which is extremely difficult in practice. A gradient based finite element model updating algorithm implementing inverse eigensensitivity method has been presented through a series of numerically simulated cantilever beams. The method can accurately predict the non-proportional damping matrix even if the measured eigenvectors are polluted with random noise. The novelty of the current method is that it can sustain a high level of modal and coordinate sparsity in measurement. The method assumes prior determination or updating of the mass and stiffness matrices.
Investigations have been carried out both numerically and experimentally to settle with a practically feasible set of proportional viscous damping parameters for the accurate prediction of responses of fibre reinforced plastic beams over a chosen frequency range of interest. The methodology needs accurate experimental modal testing, an adequately converged finite element model, a rational basis for correct correlations between these two models, and finally, updating of the finite element model by estimating a pair of global viscous damping coefficients using a gradient-based inverse sensitivity algorithm. The present approach emphasises that the successful estimate of the damping matrix is related to a-priori estimation of material properties, as well. The responses are somewhat accurately predicted using these updated damping parameters over a large frequency range. In the case of plates, determination of in-plane stiffness parameters becomes easier, whereas for beam specimens, transverse material properties play a comparatively greater role and need to be determined. Moreover, for damping matrix parameter estimation, frequency response functions need to be used instead of frequencies and mode shapes. The proposed method of damping matrix identification is able to reproduce frequency response functions accurately even outside the frequency ranges used for identification.
Recently, the use of sandwich composites in different fields of engineering such as aerospace, marine, automobile, pipelines, bridge structure, industrial work, has attracted significant attention. Sensitivity analysis of structures made of sandwich composites is necessary to design them properly and maintain their longevity. The present study analyzes stiffened sandwich composite bridge deck panels and focuses on its sensitivity analysis. The lack of control in the manufacturing of the sandwich composites may lead to non-uniform material properties, and thus variation in its behavior. The variation in the dynamic responses obtained through the free vibration analysis of the bridge deck panel models of stiffened composites due to is studied. The free vibration analysis is implemented using a finite element method. The analysis is carried out with the stiffeners located in different positions and alignments. The glass fiber-reinforced plastic (GFRP) and polyvinyl semi-rigid foam are considered in the face and core layer for modeling the deck panels, respectively. The sensitivity of the bridge deck panels is also observed with the presence of holes of different diameters in the core layer of the sandwich composite plate without stiffeners and with a transverse stiffener. It has been noticed that dynamic response, i.e. the eigenvalue, is sensitive concerning the in-plane parameters of the face layers compared to other parameters. Moreover, an increase in the size of the hole in the core layer results in a decrease in the dynamic response of the stiffened sandwich composite bridge deck panel. The knowledge of the sensitivity of the sandwich composites will be helpful to update the model and also to design the bridge deck for better performance and improved longevity.
The dynamic performance of any structure is function of existing material properties and boundary stiffness parameters which may deteriorate or become more flexible due to prolonged use. These parameters are estimated inversely through optimization of a suitable objective function. The gradient based optimization methods are preferred due to their faster convergence from a set of initial guess points, but suffers mostly from lack of reliable methodology to select appropriate step sizes. Arbitrary selection of step sizes may sometimes work well, depending upon the judgment of the user, but is case specific. The present work describes the estimation of existing material properties and boundary stiffness of isotropic and orthotropic plates from measured frequencies and mode shapes using a new gradient based step size controlled inverse eigensensitivity algorithm. The method takes a strategy that the step sizes automatically become smaller when the change in gradient of objective function is having a high value and similarly, takes larger steps when the gradient is remaining fairly constants in subsequent iterations. The results obtained from the investigations are encouraging, as some convergences could be achieved by this new adaptive step size control only, whereas methods adopting arbitrary or no step size control diverged.
A complex eigenvector is a result of nonproportional damping present in a structural system. However, it is difficult to identify the accurate damping matrix considering the modal sparsity and coordinate sparsity. A nonproportional viscous damping parameter identification is formulated as an unconstrained optimization problem in the present study. The damping coefficient of each element is considered as the design variable for the optimization problem. The objective function is defined using the incomplete complex eigenvectors, which are generated because of the presence of external damping devices in the structure. This objective function is then minimized using standard particle swarm optimization to identify the damping coefficient of the damping matrix. The accuracy and efficiency of the particle swarm optimization are investigated by solving a few numerical problems with simulated measured data. The proposed method works well with the incomplete measured modal data. The current methodology performs satisfactorily with and without noisy data. A comparison study is performed with the existing gradient-based method, and the results show that the proposed method performs better than the existing gradient-based method for the present problem with and without noisy measurement data.
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