Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method

Païdoussis, 1998 Blevins, 1977 Housner, 1952, Bending vibrations of a pipe line containing flowing fluid, Journal of Applied Mechanics, 19, 205, 10.1115/1.4010447 He, 1999, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 257, 10.1016/S0045-7825(99)00018-3 He, 2004, The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151, 287, 10.1016/S0096-3003(03)00341-2 He, 2005, Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitions and Fractals, 26, 695, 10.1016/j.chaos.2005.03.006 He, 2006, Homotopy perturbation method for solving boundary value problems, Physics Letters A, 350, 87, 10.1016/j.physleta.2005.10.005 Biazar, 2007, Homotopy perturbation method for systems of partial differential equations, International Journal of Nonlinear Science and Numerical Simulations, 8, 411 Biazar, 2008, Homotopy perturbation method for solving hyperbolic partial differential equations, Computers and Mathematics with Applications, 56, 453, 10.1016/j.camwa.2007.10.032 Biazar, 2008, Exact solutions for systems of Volterra integral equations of the first kind by homotopy perturbation method, Applied Mathematical Sciences, 2, 2691 Sadighi, 2007, Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods, Physics Letters A, 367, 83, 10.1016/j.physleta.2007.02.082 Gregory, 1966, Unstable oscillation of tubular cantilevers conveying fluid—I, Proceedings of the Royal Society of London A, 293, 512, 10.1098/rspa.1966.0187 Nayfeh, 1973 H.L. Dodds, H. Runyan, Effect of high-velocity fluid flow in the bending vibrations and static divergence of a simply supported pipe, NASA Technical Note D-2870, 1965. Lees, 1999, A perturbation approach to analyze the vibration of structures conveying fluids, Journal of Sound and Vibration, 222, 621, 10.1006/jsvi.1998.2101 Yang, 2005, Allowable span length of submarine pipeline considering damping, The Ocean Engineering, 23, 1