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Introduction to Benchmark Control Problems
Published in Suhasini Madhekar, Vasant Matsagar, Passive Vibration Control of Structures, 2022
Suhasini Madhekar, Vasant Matsagar
The nonlinear evaluation model is evaluated to find the response of the bridge to the selected earthquake ground motions. It is assumed that the properties of the system remain constant during the time increment. Incremental dynamic equations of motion are solved using the Newmark-beta method, in combination with the modal reduction method. The input and output matrices are found using the state-space form of the equation. The global damping matrix is a combination of the distributed 5% inherent Rayleigh damping in the first two modes and soil radiation damping. The basic equations of motion and the nonlinear analysis tool remain the same for all the controllers used in the study. A MATLAB-based nonlinear structural analysis tool is developed for vibration control simulations. This tool is written as S-function and is incorporated into the SIMULINK model. The S-function solves the incremental equations of motion and convergence technique at the overshooting regions. The inputs to the S-function block in SIMULINK are the seismic excitation and control forces provided by the control devices.
SPH Simulation for Short Fibre Recycling Using Water Jet Alignment
Published in International Journal of Computational Fluid Dynamics, 2021
S. Huntley, T. Rendall, M. Longana, T. Pozegic, K. Potter, I. Hamerton
In this work, the Newmark-beta method (Huebner, Byrom, and Thornton 1995) is used to integrate the equations in time as done in Hall et al. (2015). Values of and are used, which gives a constant average acceleration integration and a scheme that is unconditionally stable. The integration scheme is applied to Equations (6) and (7) to give The Newmark-beta method is implicit so the particle acceleration and density rate of change from Equations (6) and (7) are substituted into Equations (16) and (17) to perform the time integration and fixed-point iteration is carried out to converge to a solution for time level n + 1.
Multi-hazard loss analysis of tall buildings under wind and seismic loads
Published in Structure and Infrastructure Engineering, 2018
Ilaria Venanzi, Oren Lavan, Laura Ierimonti, Stefano Fabrizi
Based on the above analyses, it can be stated that for the specific example structure, the estimation of the response using linear analysis is expected to lead to reasonable predictions, even for strong ground motions. Even if a strong earthquake occurs, leading to damage to outer frames, the probability of occurrence of such a strong earthquake is small. The contribution of such rare events to the life-cycle cost is not expected to be large. Therefore, a small error in the prediction of the behaviour of the structure under these rare events, due to the use of linear analysis, is expected to lead to second-order inaccuracies that may be negligible. To compute the structural response, the linear dynamic analysis is carried out adopting the Newmark-beta method.