Analytical and experimental study on damping ratio of GRP‐reinforced glulam beams

Purpose: The purpose of this paper is to present weighted residual method (WRM) for evaluating damping ratio of unreinforced glued-laminated (glulam) wood beams and also reinforced glulam beams with E-glass reinforced epoxy polymer (GRP) plates. Design/methodology/approach: In this method, created error from the regression curve to the peak points of experimental displacement values is minimized. Several weight functions such as Galerkin weight function, Petrov-Galerkin weight functions, and least square weight function are used for minimizing this error and results from these methods are compared to the existing methods as; logarithmic decrement analysis (LDA), Hilbert transform analysis (HTA), moving block analysis (MBA), and half power bandwidth (HPB). Findings: Because WRM tries to minimize the error function provided from differences between theoretical and experimental fitted curves, comparison among these methods indicate that proposed procedure is useful for any range of damping ratios and it gives better values in comparison with the other methods. Due to the initial conditions and weight function used in Galerkin weighted residual method, damping ratio values obtained from this method have different values from the other weighted residual methods. Among the existing methods, HPB method could not predict damping ratio of the glulam beams accurately. Originality/value: This paper is a high quality research paper that presents weighted residual method (WRM) for evaluating damping ratio of unreinforced glued-laminated (glulam) wood beams and also reinforced glulam beams with E-glass reinforced epoxy polymer (GRP) plates. In this paper, LDA, HTA, MBA, and HPB methods are used and an analytical investigation of damping ratios of glulam beams unreinforced and reinforced with GRP plates is proposed by using weighted residual method (WRM). Although there is a simplifier assumption in some of existing methods, proposed method shows the damping ratio can be calculated without any requirement to simplifier assumption.