Probabilistic hazard model of inelastic response of SDOF system based on equivalent linearization technique

2011 ◽  
pp. 891-898
Author(s):  
Y Mori ◽  
S Kojima ◽  
K Ibuki
Keyword(s):  
Hazard Model ◽  
Equivalent Linearization ◽  
Inelastic Response ◽  
Linearization Technique ◽  
Sdof System

scholarly journals Equivalent Linearization Methods for a Control System with Clutching Inerter Damper

2019 ◽  
Vol 9 (4) ◽  
pp. 688 ◽  
Author(s):  
Luyu Li ◽  
Qigang Liang ◽  
Han Qin
Keyword(s):  
Control System ◽  
Numerical Study ◽  
Integrated Design ◽  
Inertial Mass ◽  
Structural Vibration ◽  
Equivalent Linearization ◽  
Sdof System ◽  
Linearization Methods ◽  
Study Results ◽  
And Control

Inerter-based dampers have gained great popularity in structural vibration control. In this paper, equivalent linearization methods (ELMs) for a single-degree-of-freedom (SDOF) system with a clutching inerter damper (CID) are studied. The comparison of a SDOF system with a CID and an inertial mass damper (IMD) shows the advantage of the CID. Considering that the system with the CID is nonlinear, which is problematic for its performance evaluation and the integrated design of the structure and control system, three equivalent linearization methods based on different principles are proposed and discussed in this paper. The CID is considered to be equal to a combination of an IMD and a viscous damper. The equivalent inertance and damping can be calculated using the obtained formulas for all methods. In addition, all methods are compared in a numerical study. Results show that the ELM based on period and energy is recommended for small inertance-mass ratios.

Capability for Growth in Nonlinear Response of SDOF With Bilinear Hysteresis

2009 ◽  
Author(s):  
Tomoyo Taniguchi
Keyword(s):  
Energy Method ◽  
Nonlinear Response ◽  
Damping Ratio ◽  
Spring Constant ◽  
Equivalent Linearization ◽  
Displacement Method ◽  
Force System ◽  
Sdof System ◽  
The Mean ◽  
Ductility Ratio

To approximate nonlinear response of structures subjected to an earthquake excitation, the displacement method in U.S. or the energy method in Japan has been practically used. However, unless these methods include the nature of dynamics of nonlinear structure well, the nonlinear response is not adequately calculated. Applying the equivalent linearization technique to a Single Degree Of Freedom (SDOF) system with bilinear hysteresis subjected to white noise base acceleration, this paper mathematically quantifies deterioration in a spring constant and increase in a damping coefficient with the progress of nonlinearity in the restoring force system as a function of the ensemble ductility ratio. As the nonlinearity progresses, the spring constant rapidly deteriorates and the damping substantially increases. Increments of damping of the lightly damped linear SDOF system are more than that of the moderately damped one. A comparison of the response of the equivalently linearized system to that of the corresponding linear system reveals the capability for growth in the nonlinear response. The nonlinear response predicable by either method is identified by values of the ensemble ductility ratio and damping ratio of the linear SDOF system. In addition, in a range of the ensemble ductility ratio where the bulk of the engineered structures are included, neither method can properly evaluate the nonlinear response. Although the results presented herein give the mean nature of the nonlinear response and phase and amplitude characteristics of accelerograms make the nonlinear response vary around the mean, uniform application of either displacement method or energy method to approximating the nonlinear response may be reconsidered.

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