# Energy-Based Prediction of the Displacement of DCFP Bearings
###### Abstract  
Isolation systems are currently being widely applied for earthquake resistance. During the design stage for such systems, the displacement response and input energy of the isolation layer are two of the main concerns. The prediction of these values is also of vital importance during the early stages of the structural design. In this study, the simple prediction method of double concave friction pendulum (DCFP) bearings is proposed, which can relate the response displacement of the isolation layer to the ground velocity through energy transfer with sufficient accuracy. Two friction models (the precise and simplified model) and a constant friction coefficient of double concave friction pendulum (DCFP) bearings are comprehensively validated by full-scale sinusoidal dynamic tests under various conditions. In addition, a response analysis, based on previous studies, was conducted using the friction models under selected unidirectional earthquake excitations, and the accuracy of using the simplified model in the response analysis was verified. Based on the response analysis data, this article verifies and optimizes the proposed prediction method by parameterizing the characteristics of earthquakes and combining the energy balance in order to gain a deeper understanding of the design of the isolation systems. seismic isolation; double concave friction pendulum bearing; full-scale dynamic test; friction dependencies; prediction method; response displacement; input energy; isolation system design 202028 July 202028 July 202028 July 202028 July 202028 July 202028 July 20  
The clear force-displacement relationship of friction pendulum bearings (FPBs) makes numerical analysis one of the best ways in which to study and predict their performance. The main focus is on the calculation of the friction force. This is because the friction coefficient's dependence on pressure, velocity and temperature is the most important characteristic for the performance of a FPB (Friction Pendulum Bearing). Therefore, the lubricant material used in an FPB and the characteristics of this material are very important. [PERSON] et al. (2012) proposed an experimental methodology for the characterization of self-lubricating materials based on pressure, velocity, external temperature and displacement through small-scale specimens [1]. In addition to external temperature, particular attention was paid to the temperature increase on the sliding surface caused by friction heating because this increase in temperature had a significant influence on the behavior of the FPB during an earthquake event. Moreover, the measurement of this temperature increase is very difficult to perform during dynamic excitation. To confront this difficulty, [PERSON] et al. (2013) proposed a friction model that takes into account the vertical load, velocity and cycling effect (degradation of friction characteristics due to the repetition of cycles and consequent temperature rise) by performing 1D prototype dynamic tests on single concave friction pendulum (SCFP) bearings [2]. [PERSON] et al. (2014) proposed a 3D finite element model (FEM) of an SCFP bearing to estimate friction heating, and the estimated temperature was validated with experimental data measured by thermocouples embedded in the concave sliding plate [3]. Following this work, some studies proposed simplified temperature simulation methods. [PERSON] et al. (2015) proposed a simplified model to calculate the representative temperature of the sliding surface in thermal calculations (Method 2 in the article) and considered pressure, velocity and temperature dependency. The analysis results were verified by 2D prototype dynamic tests of the SCFP bearings [4]. The distributions of the maximum displacement under 30 sets of ground motions in the original model (Method 1 in the article) and the simplified model were compared, and a relatively small difference was found between the models; thus, the simplified model could be applied instead of the original model.