•Identification of nonlinear damping.•Study of nonlinear damping for geometrically nonlinear vibrations.•Comparison of numerical and experimental results.•Three different damping mechanisms.
Three ...different dissipation models have been used to identify the increase of damping with the vibration amplitude for a rubber rectangular plate. For this purpose, a square rubber plate made of silicone with fixed edges has been tested and its linear and nonlinear responses have been measured by laser Doppler vibrometers. First, a reduced-order model, using energy based approach and global discretization, has been constructed, taking into account geometric imperfections; the linear viscous damping at each excitation level in the nonlinear regime has been identified from the experimental data. This numerical model with linear viscous damping has been widely validated and constitutes the basis for comparison with subsequent damping identifications. Then, three different single degree of freedom models have been fitted to the same experimental data; each model has a different damping description. Specifically, the models are based on a modified Duffing oscillators with linear, quadratic and cubic stiffness and: (i) a linear viscous damping; (ii) a nonlinear viscoelastic dissipation described by the loss factor; (iii) a standard linear solid viscoelastic model with nonlinear springs. The dissipation identified by the different models is discussed and confirms the major nonlinear nature of damping as a function of the vibration amplitude.
Widely used in civil, mechanical and automotive engineering since the early 1980s, multilayer rubber bearings have been used as seismic isolation devices for buildings in highly seismic areas in ...many countries. Their appeal in these applications comes from their ability to provide a component with high stiffness in one direction with high flexibility in one or more orthogonal directions. This combination of vertical stiffness with horizontal flexibility, achieved by reinforcing the rubber by thin steel shims perpendicular to the vertical load, enables them to be used as seismic and vibration isolators for machinery, buildings and bridges.Mechanics of Rubber Bearingsfor Seismic and Vibration Isolationcollates the most important information on the mechanics of multilayer rubber bearings. It explores a unique and comprehensive combination of relevant topics, covering all prerequisite fundamental theory and providing a number of closed-form solutions to various boundary value problems as well as a comprehensive historical overview on the use of isolation.Many of the results presented in the book are new and are essential for a proper understanding of the behavior of these bearings and for the design and analysis of vibration or seismic isolation systems. The advantages afforded by adopting these natural rubber systems is clearly explained to designers and users of this technology, bringing into focus the design and specification of bearings for buildings, bridges and industrial structures.This comprehensive book:includes state of the art, as yet unpublished research along with all required fundamental concepts;is authored by world-leading experts with over 40 years of combined experience on seismic isolation and the behavior of multilayer rubber bearings;is accompanied by a website at www.wiley.com/go/kellyThe concise approach of Mechanics of Rubber Bearingsfor Seismic and Vibration Isolationforms an invaluable resource for graduate students and researchers/practitioners in structural and mechanical engineering departments, in particular those working in seismic and vibration isolation.
Long stay cables in cable-stayed bridges have low and close-spaced modal frequencies and are subjected to multimode vibrations, e.g., rain–wind vibrations and vortex-induced vibrations. Many types of ...dampers used in practice for cable vibration control can be described using a linear hysteretic damping model, e.g., high-damping rubber dampers and viscous-shear dampers. Such dampers are able to provide frequency-independent damping effects while the maximal achievable damping is limited due to their intrinsic stiffness effect. Therefore, this study investigates dampers with linear hysteretic damping enhanced by inerters for cable vibration control. A general inerter damper, consisting of a spring with complex stiffness and an inerter in parallel which is then connected to another inerter in series, is attached to a cable for dynamic analyses. Complex modal analysis is performed to appreciate cable damping. The optimal damping effect is discussed with reference to dynamic properties of the damper with respect to frequency, with comparison to the system of a cable with an inerter damper with viscous damping. It is found that two inerters, respectively in parallel and in series with a damper of linear hysteretic damping, can achieve a large improvement on multimode damping of a cable. The inertance of the inerter in series with the damper needs to be large for optimal performance while a small inertance of the other inerter is preferable. Furthermore, a case study based on a cable attached with a viscous-shear damper on the Sutong Bridge is conducted to show the feasibility of the inerter dampers.
•Inerter dampers with linear hysteretic damping (IDHs) for cable vibration control.•Parametric studies on optimum multimode cable damping provided by an IDH.•IDHs compared with inerter dampers with viscous damping for cable vibration control.•A case study of using inerters in a cable–damper system of the Sutong Bridge.
In this paper, nonlinear vibrations of fiber-reinforced composite cylindrical shells (FRCCSs) with bolted joint boundary conditions are studied both theoretically and experimentally, where the ...nonlinear amplitude-dependent material property of fiber-reinforce composites (FRCs) and partial bolt loosening boundary conditions are taken into account. By representing the nonlinear material property via Jones-Nelson theory, Love shell theory is used to calculate the elastic strain energy of shells. The bolt loosening boundary conditions are achieved using artificial spring-damper technique. The Rayleigh-Ritz method is employed to derive the equations of motion for FRCCSs, from which the natural frequencies, damping ratios, and forced response can be obtained. Then, a series of vibration tests are carried out on a FRCCS specimen to validate the modeling approach proposed here. Based on the validated model, vibrations of FRCCS structures accounting for amplitude dependence of FRCs with different partial bolt loosening boundary conditions are investigated. It is found that increasing bolt loosening degree and loose bolt number leads to decrement of natural frequencies, and increment of modal damping ratios and resonant response amplitudes due to the coupling effect of declined boundary stiffness and increased boundary damping at bolted constraint edges. As the excitation level rises, the amplitude-dependent characteristics of natural frequencies and damping parameters of FRCCSs gradually become weak, while the increasing rates of resonant response amplitudes show an upward trend.
Linear electromagnetic shunt damping (L-EMSD) has been investigated deeply for vibration control in previous studies. This paper proposes nonlinear electromagnetic shunt damping (N-EMSD) for ...vibration isolation enhancement of linear vibration isolators (LVIs), which has not been discussed in existing literature. N-EMSD composes of a pair of the permanent magnets (PMs) and a pair of the coils, where the two coils are wound in opposite direction and connected in series. The nonlinear electromagnetic coupling coefficient is derived. The coupling governing equations of a LVI with N-EMSD are established and the amplitude-frequency relationship is theoretically derived using the harmonic balance method (HBM). Both the simulations and experiments are carried out to verify the nonlinear damping characteristic of N-EMSD. The results demonstrate that the LVI with N-EMSD can effectively reduce the vibration in the resonance region without affecting the vibration isolation performance in the isolation region compared with the traditional L-EMSD. It is also found in both simulation and experiment for the two coils configuration that the frequency of the induced voltage is twice the frequency of the displacement. Furthermore, the transmissibility of the LVI with N-EMSD reduces with the increase of the input amplitude in the resonance region, which demonstrates the nonlinearity of N-EMSD. The natural frequency slightly decreases with the decrease of the peak transmissibility. This paper extends the electromagnetic shunt damping (EMSD) technique from linear to nonlinear fields and provides a guideline to design nonlinear damping.
•Nonlinear electromagnetic shunt damping (N-EMSD) is proposed and modeled.•The linear and nonlinear electromagnetic coupling coefficients are discussed.•The voltage frequency of the coils is two times of the displacement frequency.•A linear vibration isolator with N-EMSD is analyzed via the harmonic balance method.•N-EMSD can achieve nonlinear damping to improve vibration isolation performance.
In recent seismic analyses, it is considered that the structural damping ratio should be treated as independent of frequency, for safety side estimation. Therefore, frequency‐insensitive damping is ...required for realistic seismic simulations. This paper investigates the performance of various sparse matrix damping models (extended Raleigh, capped viscous and uniform damping) in the inelastic seismic analysis of a 35‐story moment‐frame steel building. These sparse matrix damping models were compared with Rayleigh, tangent Rayleigh, and Wilson‐Penzien (modal) damping models to provide insight into damping models suitable for large‐scale inelastic response history analysis (RHA). First, the necessity of frequency‐insensitive damping in large‐scale analysis is illustrated via numerical simulations. Then, the vibration characteristics with simultaneous inputs of horizontal and vertical ground motion are analyzed using the abovementioned damping schemes, and their results are compared. The comparisons are analyzed by focusing on horizontal displacement/acceleration, story drift angle, beam‐end ductility factor, the amplitude due to beam vibration, and the associated vertical acceleration. Finally, the computation speeds are compared. As a result, it is shown that although these sparse matrix damping models are practically useful, they are not yet sufficient and present challenges.
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