A spectral finite element model for analysis of axial–flexural–shear coupled wave propagation in laminated composite beams

Development of numerical technique by Galerkin approach of spectral element method for hybrid beam

“…11 Hence the equation (7) is derived in more specific form of composite beam. In the literature, 1,3-7,10 spectral components by using force displacement method for the hybrid beam without damping and axial force were developed by Gopalakrishana and Mahapatra 1 (6) were developed in Lee and Jang 9 by using variational approach.…”

“…There are only few studies in which the axial loaded hybrid beams phenomenon has been discussed. Gopalakrishnan and Mahapatra 1 and Sierakowski and Vinson 2 considered the impact of axial loading in the structure of Bernoulli-Euler beam theory. The effects of rotary inertia and shear deformation depending upon FSDT were considered by Yang and Chen, 3 Chandrashekara et al, 4 Abramovich, 5 Dong et al 6 and Palacz et al 7 for shear bending hybrid beams.…”

The partition of unity finite element method for elastic wave propagation in Reissner–Mindlin plates

“…For > cut-off , the imaginary pair k 3,4 become a purely real pair and they introduce the propagating shear waves. Also, k 5,6 remain imaginary at frequencies less than another cut-off frequency. In a low frequency or in a medium frequency wave propagation problem, the in-plane rotational wave components can be neglected, since such rotational waves are purely imaginary (attenuating) in these frequency ranges.…”

“…Parallel to the research and development in hp-FE, there have been quite remarkable progresses on exact methods, which rely on the strong form of the boundary value problem (BVP) as opposed to its weak form as in the FE method. For simple 1D geometry with general boundary conditions and for 2D or 3D geometries with periodic or semi-infinite boundary conditions, asymptotic solutions have been employed to develop various numerical methods, namely the transfer function matrix method [1], dynamic stiffness matrix method [2], space-time FE method [3], strip element method [4], spectral FE method for beams [5,6] and Levy-type plate [7] etc. Moreover, in the recent times, a new and general numerical methodology, namely the partition of unity finite element method (PUFEM) has been developed by Melenk and Babuska [8] for various mechanics problems.…”

Locating Delamination in Composite Laminated Beams Using the Zero-Order Mode of Lamb Waves

“…Also, tremendous efforts have been put to the delamination identification, which could be treated as a problem of inverse pattern recognition using calibrated numerical methods such as artificial neural network [6]. The interaction between Lamb waves and delamination has also been investigated numerically and theoretically [7][8][9]. However, the complex wave scattering phenomenon in a delamination area has not been clearly understood in these studies.…”