16 th World Conference on Earthquake, 16WCEE 2017 Santiago Chile, January 9th to 13th 2017 Paper N° 4010 Registration Code: S-Y1450185613 DYNAMIC ANALYSIS MODEL OF VISCOELASTIC DAMPERS CONSIDERING TEMPERATURE-RISE AND HEAT CONVECTION UNDER LONG DURATION LOADING K. Kasai (1) , D. Sato (2) , and D. Osabel (3) (1) Professor, Tokyo Institute of Technology, Japan, kasai.k.ac@m.titech.ac.jp (2) Assoc. Professor, Tokyo Institute of Technology, Japan, sato.d.aa@m.titech.ac.jp (3) Graduate Student, Tokyo Institute of Technology, Japan, osabel.d.aa@m.titech.ac.jp Abstract Viscoelastic dampers dissipate energy through shear deformation of the viscoelastic materials; generating heat within the material causing it to soften. Therefore, under long duration excitation such as long period and duration earthquake, as well as wind loading, heat conduction and convection can occur and control the rise of temperature. The writers previously proposed two analytical methods simulating these effects and frequency sensitivities. First method combines three- dimensional heat transfer analysis and static analysis using common finite element model of the damper to estimate its dynamic properties referring to inclination and fatness of the hysteresis loop. The properties are estimated for every cycle considering transient state, or only a cycle which represents steady state cycle. The second method combines one- dimensional heat transfer analysis and viscoelastic constitutive rule using fractional time-derivatives of stress and strain, and it calculates step-by-step the force-deformation time histories of the damper. The present paper applies the above two methods to investigate the dampers of different proportions causing changes in heat generation, conduction, and convection. The paper also proposes a modified algorithm for calculating fractional time-derivatives of stress and strain, i.e., an approximate method using uniform shear strain distribution at every step. The analytically obtained deformed shape of the viscoelastic material is almost a straight-line, suggesting to idealize a uniform shear strain distribution. This modified algorithm is sufficiently accurate and hold advantage over the original algorithm in calculation time. The analysis models in this study accurately predict the real behavior of a viscoelastic damper when subjected to long duration loadings. Keywords: viscoelastic damper; fractional derivative; long duration loading, temperature rise, heat transfer 1. Introduction 1.1 Viscoelastic Dampers Among the widely-used devices to control structural vibration, viscoelastic (VE) dampers (e.g. Fig. 1a) are recognized to have significant advantage. They can be used not only for wind but also for earthquake excitations. These devices work by dissipating energy through shear deformation of the VE material. In the process of energy dissipation, heat is generated within the VE material; softening it and affecting its dynamic mechanical properties. For long duration excitations, significant heat conduction and convection can occur and control the temperature-rise. 1.2 Short Duration and Long Duration Models Fig. 1a shows a VE damper subjected to dynamic loading, where F d (t) and u d (t) are time-varying damper force and deformation, respectively. Heat is generated within the VE material causing the damper dynamic properties such as storage stiffness K' d and loss stiffness K" d (Fig. 1b) to decrease. The proposed short duration model (Fig. 2) by Kasai et al [1, 2] showed the effect of temperature-rise due to the dissipated energy, and it considers uniform temperature θ and shear strain γ within the VE material. This has been found to be accurate for a short