Abstract
Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.
Highlights
Due to the development of science and technology, new materials have been invented and widely applied in engineering practice, in which, materials reinforced by graphene platelets (GPLs) are one of the next-generation structural forms
Based on the first-order shear deformation beam theory combined with the differential quadrature method, Song et al [2] investigated the nonlinear free vibration of edge-cracked graphene nanoplatelet- (GPL-) reinforced composite laminated beams resting on a two-parameter elastic foundation in thermal environments
Mojiri and Salami [5] combined both Timoshenko beam theory and generalized differential quadrature method to examine the free vibration and Mathematical Problems in Engineering dynamic transient response of a multilayer polymer nanocomposite beam resting on an elastic foundation reinforced by graphene platelets nonuniformly distributed through the thickness direction in a thermal environment
Summary
Due to the development of science and technology, new materials have been invented and widely applied in engineering practice, in which, materials reinforced by graphene platelets (GPLs) are one of the next-generation structural forms. Based on the first-order shear deformation beam theory combined with the differential quadrature method, Song et al [2] investigated the nonlinear free vibration of edge-cracked graphene nanoplatelet- (GPL-) reinforced composite laminated beams resting on a two-parameter elastic foundation in thermal environments. Mojiri and Salami [5] combined both Timoshenko beam theory and generalized differential quadrature method to examine the free vibration and Mathematical Problems in Engineering dynamic transient response of a multilayer polymer nanocomposite beam resting on an elastic foundation reinforced by graphene platelets nonuniformly distributed through the thickness direction in a thermal environment. From the short review above, one can see that there are no works dealing with the mechanical behavior of a functionally graded GPL-reinforced composite (FG-GPLRC) beam resting on an elastic foundation, in which the whole structure is embled in a temperature environment, and rotating around one fixed axis.
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