By Farzad Ebrahimi
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Extra info for Advances in Vibration Analysis Research
99% of the natural frequencies because the displacements cannot be evaluated as the true value of the natural frequency is approached. As can be seen in Figures 3, all the mode shapes are dominated by radial displacements. 225 m) would make the beam appear nearly straight). 2 Clamped-Clamped (C-C) end conditions The next test case uses the same beam properties as the previous example, with clampedclamped end conditions. The results of the DFE, and 3- and 4-DOF/node FEM formulations along with those reported by Ahmed (1971,1972) are listed in Table 2 below.
Closed form solution) for any of the natural frequencies of the beam, or beamstructure, with the use of a single continuous element characterized by an infinite number of degrees of freedom. , systems with Free Vibration Analysis of Curved Sandwich Beams: A Dynamic Finite Element 39 constant geometric and material properties and only a certain number of boundary conditions. , to fuse the adaptability of classical FEM with the accuracy of DSM. Therefore, the approximation space is defined using frequency dependent trigonometric basis functions to obtain the appropriate interpolation functions with constant parameters over the length of the element.
J. Nonlin. , 34, 1999, 699-708. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Nonlin. , 35, 2000, 37-43. H. He, An elemantary introduction to the homotopy perturbation method, Computers and Mathematics with Applications, 57(2009), 410-412. H. He, New interpretation of homotopy perturbation method, International Journal of Modern Physics B, 20(2006), 2561-2568. H. He, The homotopy perturbation method for solving boundary problems, Phys.
Advances in Vibration Analysis Research by Farzad Ebrahimi