An Inverse Approach for the Determination of\\ Viscous Damping Model of Fibre Reinforced Plastic Beams using Finite Element Model Updating

Abstract

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.

Estimation of Viscous Damping Parameters of Fibre Reinforced Plastic Plates using Finite Element Model Updating

“…16 Also, similar observations have been made for FRP beams. 30 The regenerated FRF curves-as shown in Fig. 3- continually matched as additional modes were added into the simulation, indicating that the updated parameters of the identified damping matrix are globally representative.…”

“…In fact, the plate has been extracted from a much bigger plate fabricated for the purpose of experimentation on beam samples as well as for the plate. 30 The average thickness and the mass density of the plate was 10.12 mm and 2012 kgm −3 respectively. 30 Modal testing was carried out on the FRP plate under free-boundary conditions, using impact excitation imparted through an impact hammer; Responses were picked up by an accelerometer.…”

“…30 The average thickness and the mass density of the plate was 10.12 mm and 2012 kgm −3 respectively. 30 Modal testing was carried out on the FRP plate under free-boundary conditions, using impact excitation imparted through an impact hammer; Responses were picked up by an accelerometer. The Frequency Response Functions (FRFs) were directly measured, and frequencies and mode shapes were extracted using modal analysis software MEScope.…”

“…Such modal testing is standard in current practice-details of similar modal testing on pultruded FRP composite beam may be obtained from investigations carried out earlier. 30,31 Figure 5(a) shows the modal test setup, in which the free boundary condition was realised by suspending the FRP plate using soft elastic strings from a rigid support. The finite element modelling of the plate was performed using the same shell element (S8R) with adequate discretization to get converged values of the modal properties.…”

“…29 The procedure includes detailed experimental modal testing and subsequent data analysis, precise finite element modelling with appropriate discretization, correlating finite element results to the experiment, and updating selected parameters using a robust gradient-based optimization technique. 30 The methodology is established by a numericallysimulated example, followed by a real experimental case study on a pultruded FRP plates under free-boundary conditions. A set of relaxation parameters has been defined to model nonviscous damping for FRP plates.…”