Wave motion in pipe bends is much more complicated than that in straight pipes, thereby changing considerably the propagation characteristics of guided waves in pipes with bends. Therefore, a better understanding of how guided waves propagate in pipe bends is essential for inspecting pipelines with bends. The interaction between a pipe bend and the most used non-dispersive torsional mode at low frequency in a small-bore pipe is studied in this paper. Experiments are conducted on a magnetostrictive system, and it is observed that T(0,1) bend reflections and mode conversions from T(0,1) to F(1,1) and F(2,1) occur in the pipe bend. The magnitude of the T(0,1) bend reflections increases with increasing propagation distance and excitation frequency. The amplitude of the mode-converted signals also increases with increasing propagation distance, but it decreases with increasing excitation frequency. Because of their longer bent path, the test signals for a pipe bend with a bending angle of 180X are much more complicated than those for one with a bending angle of 90X. Therefore, it is even more difficult to scan a bent pipe with a large bending angle. The present findings provide some insights into how guided waves behave in pipe bends, and they generalize the application of guided-wave inspection in pipelines.

The central theme of this work was to analyze high aspect ratio structure having structural nonlinearity in low subsonic flow and to model nonlinear stiffness by finite element-modal approach. Total stiffness of high aspect ratio wing can be decomposed to linear and nonlinear stiffnesses. Linear stiffness is modeled by its eigenvalues and eigenvectors, while nonlinear stiffness is calculated by the method of combined Finite Element-Modal approach. The nonlinear modal stiffness is calculated by defining nonlinear static load cases first. The nonlinear stiffness in the present work is modeled in two ways, i.e., based on bending modes only and based on bending and torsion modes both. Doublet lattice method (DLM) is used for dynamic analysis which accounts for the dependency of aerodynamic forces and moments on the frequency content of dynamic motion. Minimum state rational fraction approximation (RFA) of the aerodynamic influence coefficient (AIC) matrix is used to formulate full aeroelastic state-space time domain equation. Time domain dynamics analyses show that structure behavior becomes exponentially growing at speed above the flutter speed when linear stiffness is considered, however, Limit Cycle Oscillations (LCO) is observed when linear stiffness along with nonlinear stiffness, modeled by FE-Modal approach is considered. The amplitude of LCO increases with the increase in the speed. This method is based on cantilevered configuration. Nonlinear static tests are generated while wing root chord is fixed in all degrees of freedom and it needs modification if one requires considering full aircraft. It uses dedicated commercial finite element package in conjunction with commercial aeroelastic package making the method very attractive for quick nonlinear aeroelastic analysis. It is the extension of M.Y. Harmin and J.E. Cooper method in which they used the same equations of motion and modeled geometrical nonlinearity in bending modes only. In the current work, geometrical nonlinearities in bending and in torsion modes have been considered.