Dynamics of cantilevered fluid-conveying pipes by Galerkin method combined with Laplace-based transfer matrix method

A novel hybrid approach combining Galerkin discretization and LTMM (Laplace-based transfer matrix method) is put forward to study the dynamics of cantilevered fluid-conveying pipes possessing potential periodicity and elastic supports. Firstly, the deduction for normalized modal functions of a periodic cantilevered beam additionally supported by a combination of linear and torsional springs via LTMM is reviewed. Secondly, the motion equation for a cantilevered pipe with the same material and cross-section moment of inertia as the former-mentioned beam is discretized through the Galerkin method. A hybrid method, abbreviated as LTMM-Galerkin, is then proposed by incorporating the obtained modal functions into the Galerkin method. Thirdly, the eigenfunction and steady-state displacement response are deduced by LTMM-Galerkin. Finally, numerical calculations are carried out, and the validity of LTMM-Galerkin is verified compared with existed methods including transfer matrix method, finite difference method, differential quadrature method, Green function method, and differential transformation method. LTMM-Galerkin can be radiated to study dynamics problems of fluid-conveying pipes with other supporting formats. Additionally, the creation process of this method can serve as a model for the development of other hybrid approaches.