An experimental study on the vibration control of a single-degree-of-freedom model is carried out to verify market-based control (MBC) strategy effect. Results show that the MBC strategy can reduce both displacement and acceleration responses. Additionally, the MBC strategy is applied to a long-span bridge considering the travelling wave effect. Numerical simulations indicate that the displacement and acceleration responses of the long-span bridge with the travelling wave effect are smaller than those without, and the larger the velocity of travelling wave is, the better the control effect of MBC is. Based on the MBC theory and multimarket-based control (MMBC) presented here it is further applied to a large-space structure considering multiple dimensional features of structural model and ground motions. It is concluded that the MMBC strategy reduces the displacement response of the large-space structure, especially on vertical displacements, but has limited control effects on accelerations.

A quartic B-spline method is proposed for solving the linear sixth order boundary value problems. The method converts the boundary problem to solve a system of linear equations and obtains coefficients of the corresponding B-spline functions. The method has the convergence of two order. It develops not only the quartic spline approximate solution but also the higher order approximate derivatives. Two numerical examples are presented to verify the theoretical analysis and show the validity and applicability of the method. Compared with other existing recent methods, the quartic B-spline method is a more efficient and effective tool.

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. This paper proposes a conjugate gradient method which is similar to Dai-Liao conjugate gradient method (Dai and Liao, 2001) but has stronger convergence properties. The given method possesses the sufficient descent condition, and is globally convergent under strong Wolfe-Powell (SWP) line search for general function. Our numerical results show that the proposed method is very efficient for the test problems.

A new vibration model is built by introducing the head-cover vibration transfer path based on a previous analysis of the vertical vibration model for hydropower station units and powerhouses. This research focuses on disturbance- and parameter-related transfer paths in a practical situation. In a complex situation, the application of the stochastic perturbation method is expanded using an algebra synthesis method the Hadamard product, and theoretical analyses, and numerical simulations of transfer paths in the new vibration model are carried out through the expanded perturbation method. The path transfer force, the path transmissibility, and the path disturbance ranges in the frequency domain are provided. The results indicate that the methods proposed in this study can efficiently reduce the disturbance range and can accurately analyze the transfer paths of hydraulic-source vertical vibration in hydropower stations.