Free Vibrations of Continuous Grading Fiber Orientation Beams on Variable Elastic Foundations

Free vibration characteristics of continuous grading fiber orientation (CGFO) beams resting on variable Winkler and two-parameter elastic foundations have been studied. The beam is under different boundary conditions and assumed to have arbitrary variations of fiber orientation in the thickness direction. The governing differential equations for beam vibration are being solved using Generalized Differential Quadrature (GDQ) method. Numerical results are presented for a beam with arbitrary variation of fiber orientation in the beam thickness and compared with similar discrete laminate beam. The main contribution of this work is to present useful results for continuous grading of fiber orientation through thickness of a beam on variable elastic foundation and its comparison with similar discrete laminate composite beam. The results show the type of elastic foundation plays very important role on the natural frequency parameter of a CGFO beam. According to the numerical results, frequency characteristics of the CGFO beam resting on a constant Winkler elastic foundation is almost the same as of a composite beam with different fiber orientations for large values of Winkler elastic modulus, and fiber orientations has less effect on the natural frequency parameter. The interesting results show that normalized natural frequency of the CGFO beam is smaller than that of a similar discrete laminate beam and tends to the discrete laminated beam with increasing layers. It is believed that new results are presented for vibrational behavior of CGFO beams are of interest to the scientific and engineering community in the area of engineering design.