Simplified calculation method for transverse seismic response of aqueducts considering fluid-structure interaction

Aqueduct is the key structure in water conveyance engineering, which may be damaged during earthquake. Although numerous water conveyance designs have been built, the current state of researches on aqueduct aseismic design is inadequate. In this paper, based on the fluid-structure interaction dynamics and response spectra analysis, a simplified analysis method was proposed to evaluate the transverse seismic response of aqueducts, and the simplified calculating results were compared with the results of the nonlinear finite element calculation of fluid-structure interaction and experimental results. The results showed that the simplified analysis method put forward in this paper could be used to evaluate the transverse seismic response of aqueducts. In the condition that the pier height is less than 40 m, the first-order lateral vibration mode of the aqueduct has a higher model contribution rate; the simplified calculation method can achieve extremely high accuracy. The simplified calculation precision decreases as the height increases when the pier height exceeds 40 m

Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation

The generalized forced Boussinesq equation, utt−uxx+[f(u)]xx+uxxxx=h0, and its periodic traveling wave solutions are considered. Using the transform z=x−ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relation between the ordinary differential equation and a Hammerstein type integral equation is then established by using the Green's function method. This integral equation generates compact operators in a Banach space of real-valued continuous periodic functions with a given period 2T. The Schauder's fixed point theorem is then used to prove the existence of solutions to the integral equation. Therefore, the existence of nonconstant periodic traveling wave solutions to the generalized forced Boussinesq equation is established