In-plane vibration analyses of curved pipes conveying fluid using the generalized differential quadrature rule

In-plane vibrations of curved pipes conveying fluid are investigated by using the generalized differential quadrature rule (GDQR) proposed. The “modified inextensible” theory for the curved pipes is considered, and the steady-state combined force is taken into account. Several examples of curved pipes conveying fluid with different boundaries are presented to illustrate the validity of the GDQR. The obtained natural frequencies compare quite well with those predicted by the finite element method. Based on the GDQR, the effect of some key parameters on the natural frequencies of the pipe system is further discussed. Compared with other methods, GDQR is more convenient to deal with the boundary conditions of the pipe and gives acceptable precision in the numerical results. This method can be useful for further study of the nonlinear dynamics of pipes conveying fluid.