Vibration of delaminated multilayer beams

A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

“…The DSM model incorporates a total of only three elements; one intact element on each end of the delamination representing the undamaged beam segments (1 and 4) obtained using the methods outlined in [25,26], and one fully delaminated element (Figure 1). The DSM natural frequencies are in excellent agreement with those reported in references [1,7], with a maximum difference of 0.24% (see the last row in Table 1), which could be simply attributed to the extensive use of matrix manipulations in both DSM and CM methods (the results obtained from the CM-based code developed by the authors [23] are not reported here, as they were found to be in perfect match with tabulated frequency data and graphs reported in the literature). It is also worth noting that the authors found a slight dissimilarity between the 2nd natural frequency values (61.67, 60.76, 55.97, 49.00, 43.87, 41.45, 40.93, resp.)…”

“…Figure 5 shows the first opening mode for a delaminated beam with top beam thickness equal to 40% the height of the intact beam, 60% of span, off-midplane delamination, obtained using 3-element DSM and FEM models (FEM nodes visualized). Similar opening modes have also been reported in the literature (see, e.g., [7,8]). …”

“…, 4, as appearing in (4). This solution method, based on finding the coefficient matrix of the system, herein refered to as the "Coefficients Method (CM)," has been used to predict the vibration behavior of different systems of varying complexity (see, e.g., [7,8]). However, it remains a relatively problem-specific solution technique.…”

“…Assembly of element DSM matrices and the application of boundary conditions results in the nonlinear eigenvalue problem of the defective system. In addition, two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature [7,8], taking into account the same continuity conditions, are also developed and used as a benchmark for comparison. The FEM model exploits cubic Hermite interpolation functions of approximation to express the flexural displacement functions, that is, field variables and weighting functions [22,23].…”

“…Alternatively, one can use semianalytical formulations, such as the so-called Dynamic Finite Element (DFE) method [7,8], to carry out structural modal analysis. The hybrid DFE formulation results in a more accurate prediction method than traditional and FEM modeling techniques, allowing for a reduced mesh size.…”