Abstract
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different types of modeling techniques and constraints, were briefly examined. The Galerkin-type weighted residual method was applied to convert the coupled differential equations of motion into a discrete problem using a polynomial interpolation function in the finite element method. In the dynamic finite element method, trigonometric shape functions were implemented to describe the equations in terms of nodal displacements. The eigenvalue problem resulting from the discretization along the length of the beam was solved in order to determine the system’s natural frequencies and modes. The results, showing the effects of axial load, end moment, and combined loading on natural frequencies, are discussed and are followed by some concluding remarks. <br><div><br></div>
Highlights
Many situations arise in various engineering applications, ranging from terrestrial to aerospace structures, in which layered composite materials are used
It is well known that composite structures can be placed under axial force and end moment simultaneously when used in the above applications
The doubly coupled natural frequencies for a variety of prestressed composite beam configurations were studied, and excellent agreement was found between the dynamic finite element (DFE), finite element method (FEM), and published results
Summary
Many situations arise in various engineering applications, ranging from terrestrial to aerospace structures, in which layered composite materials are used. Hashemi and Borneman [3] used a simplified beam model and the dynamic (frequency-dependent) finite element method (FEM) to investigate the coupling between bending and torsion in free vibration analysis of composite wings. Exploiting the conventional FEM formulation and the frequency-dependent approximation space from the DSM method, Hashemi and his coworkers developed the dynamic finite element (DFE) formulation to investigate the vibrations of various homogeneous and laminated composite beam configurations (see, e.g., [3,4,14,15]). In addition to the material coupling between bending and torsion displacements caused by the ply angle in a laminated composite beam, which has been treated and reported many times in the literature, the system was characterized by another geometric coupling resulting from the end moment, bringing more complexity to the vibration analysis of such prestressed structural elements.
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