Chapter 18 Nonlinear Damping in Floor Vibrations Serviceability: Verification on a Laboratory Structure OnurAvci Abstract Damping is a critical parameter in dynamics of structures which has been proven to be dependent on the amplitude of the applied force on the structure. This is known as nonlinear damping or amplitude-dependent damping. While the nonlinear characteristics of damping have been studied thoroughly for earthquake and wind loading excitations; it has not been comprehensively studied for floor vibration serviceability applications. This paper focuses on a laboratory structure in an attempt to shed some light on obtaining and verifying the modal damping ratio with experimental and analytical studies. Finite element models were built and updated per static and dynamic tests conducted in laboratory environment. The nonlinear damping behavior of the laboratory structure is verified for different amplitudes of sinusoidal excitations. Keywords Floor vibrations • Serviceability • Damping • Nonlinear damping • Amplitude dependent damping 18.1 Introduction Damping is a critical parameter in structural dynamics. Dealing with damping has been a challenge for floor vibrations researchers as the acceleration predictions are very sensitive to damping ratio values. While the nonlinear nature of damping is extensively researched for seismic and wind excitations [1–13], it is not studied in great detail for floor vibrations applications. Damping has been reported to have a material and non-material components. Material damping is due to the energy dissipation capacities of the structural materials. Non-material damping on the other hand, is due to the surroundings of the vibrating structure. Material damping has three components: Coulomb damping, viscous damping and radiation damping. This paper focuses on the amplitude depending characteristics of damping based on the experiments conducted on a laboratory footbridge structure. The structure was studied extensively with static and dynamic tests; 3D finite element (FE) models were created. There has been numerous static and dynamics tests conducted on the structure, all of which were used to fine-tune the three-dimensional finite element model for various bottom chord extension configurations [14–21]. This paper is presenting the results of a study on the nonlinear damping behavior of the structure. 18.2 Experimental Modal Testing on the Laboratory Structure The laboratory structure dimensions are 2.2 m by 9.2 m. The cold-formed deck is 38 mm deep and concrete slab depth is 114 mm resulting in a total slab depth of 152 mm. The slab is supported on two parallel 30 K7 9.2 m joist members at 1.2 m on center (Fig. 18.1). Vibration testing is done for two different bottom chord extension configurations to determine the modal parameters (natural frequencies, mode shapes and modal damping ratios). Stage 1 is the configuration for bottom chords being extended to the supports and Stage 2 is the configuration for the bottom chords extensions are removed from the structural system. Individual FRF results, MEScope curve fitting approximations and FE model predictions are presented in Table 18.1 [15]. According to Table 18.1, removing the bottom chord extensions from the system (Stage 2) results in a 14% decrease in the natural frequency of the first bending mode (the frequency dropped from 8.08 Hz to 6.95 Hz). Stage 1 natural frequency O. Avci ( ) Department of Civil and Architectural Engineering, Qatar University, Doha, Qatar e-mail: oavci@vt.edu © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_18 139
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