Abstract
1. Sridhar R, Chakraborty A, Gopalakrishnan S. Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method. International Journal of Solids and Structures 2006; 43(16):4997–5031. https://doi.org/10.1016/j.ijso.... CrossRef Google Scholar
Highlights
Analytical and numerical techniques, are available in the open literature, to investigate the effects of Structures made of functionally graded materials cracks on the linear and non-linear vibration (FGM) have a very wide area of industrial characteristics in both the free and forced regimes
Yang and Chen analytically studied the damages in the form of cracks may be influence of an open edge crack on the free vibration observed in these materials during their operational and elastic buckling of functionally graded beam (FGB) using the Eulerlife as a result of various external or internal
Akbaş used the total Lagrangian finite element method to investigate the geometrically non-linear vibration of an edge cracked Timoshenko beam [19] and more recently Panigrahi and Pohit studied the free vibration of a cracked FGB, based on the neutral surface approach, the Ritz method and an iterative technique [20]
Summary
Analytical and numerical techniques, are available in the open literature, to investigate the effects of Structures made of functionally graded materials cracks on the linear and non-linear vibration (FGM) have a very wide area of industrial characteristics in both the free and forced regimes. Akbaş used the total Lagrangian finite element method to investigate the geometrically non-linear vibration of an edge cracked Timoshenko beam [19] and more recently Panigrahi and Pohit studied the free vibration of a cracked FGB, based on the neutral surface approach, the Ritz method and an iterative technique [20]. The purpose of the present contribution is the application of the non-linear forced vibration model previously reported in [25] using a multimode response approach and combined with the homogenization procedure based on the neutral surface approach previously adopted in [26,27] This allowed an explicit calculation of multidimensional non-linear frequency response curves, the corresponding amplitude dependence deflection shapes and the associated curvatures distributions of a multi-cracked FGB subjected to a uniformly distributed harmonic force applied over the beam length.
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