Particle dampers that use soft/hard particles are attracting attention as a solution to problems such as oil leakage of oil dampers and the temperature dependence of their characteristics. Particle dampers effectively attenuate vibration using the friction and inelastic normal collisions generated between particles or between particles and walls. Here, the effects of the packing fraction of particles, the vibration frequency, and hardness of the material on the damper force characteristics of a separated dual-chamber single-rod type damper with elastomer particle assemblages were investigated experimentally. The maximal damper force and its hysteresis increased with the packing fraction, the vibration frequency, and the Young’s modulus of the particle material. Numerical simulations using the discrete element method (DEM) were performed to confirm the behavior of the elastomer particles when they were packed in both chambers. The compressive force distribution and velocity vector diagram of particles in the simulations showed that friction and compression between particles due to particle movement, friction between particles and the chamber walls, and the viscosity of the elastomer particles caused a large hysteresis in the damper force. The maximum damper force is affected by the viscoelastic component force and the friction force in the same proportion, and the hysteresis is dominated by the friction force. The simulation results were confirmed to be in good agreement, both qualitatively and quantitatively, with the experimentally measured damper force characteristics.

Air damper dynamic vibration absorber (DVA) is modeled using Maxwell transformed element and coulomb element. This damper serves to minimize vibration at resonant and operation of constant speed machine. Its stiffness and damping factor are transformed from Maxwell to Voigt arrangement. Meanwhile, viscous equivalent Coulomb damping is expressed by absolute relative motion. System transmissibility contours are plotted by min–max approach. Its optimal parameters are determined using this approach. Contour operation minimization is obtained from minimum system transmissibility. Moreover, exact solution of fixed points and optimal natural frequency ratio are obtained by a modified fixed point theory. Optimal design curve is derived by Coulomb damping derivative and maximum condition. Operational vibration level is minimized by 7% at the operation minimization using minimum condition. On the experimental side, test platform of the air damper is constructed using linear slide block system. Computational model of the air damper is established by its physical details and experimental data. Linear relationship is obtained between viscous and Coulomb damping angles. Modified fixed points are validated by frequency response function resonant peaks. Experimental vibration level is minimized by 5%, which being close to the minimization result. The model is validated within 5% accuracy by its optimal experimental curve.

It has been shown that shunting electromagnetic devices with electrical networks can be used to damp vibrations. These absorbers have however limitations that restrict the control performance, i.e., the total damping of the system and robustness versus parameter variations. On the other hand, the electromagnetic devices are widely used in active control techniques as an actuator. The major difficulty that arises in practical implementation of these techniques is the power consumption required for conditioners and control units. In this study, robust hybrid control system is designed to combine the passive electromagnetic shunt damper with an active control in order to improve the performance with low power consumption. Two different active control laws, based on an active voltage source and an active current source, are proposed and compared. The control law of the active voltage source is the direct velocity feedback. However, the control law of the active current source is a revisited direct velocity feedback. The method of maximum damping, i.e., maximizing the exponential time-decay rate of the response subjected to the external impulse forcing function, is employed to optimize the parameters of the passive and the hybrid control systems. The advantage of using the hybrid control configuration in comparison with purely active control system is also investigated in terms of the power consumption. Besides these assets, it is demonstrated that the hybrid control system can tolerate a much higher level of uncertainty than the purely passive control systems.

The multi-degrees-of-freedom (MDOF) tuned mass damper (TMD) has proven its ability to suppress multiple modes of interest, and it possesses less mounting space than multiple single degree-of-freedom TMDs of equal damping mass. However, it is challenging to implement the exact design of MDOF TMDs having expected vibration modes. The conceptual design of MDOF TMD containing visualized DOFs is first presented by the graphical approach, and the visualization of the quantitative relationship between the freedoms and constraints of TMD is attained. Then, dynamics modeling is analytically formulated by incorporating experimental data, and optimization of MDOF TMD considering background modes is performed. Two scenarios of MDOF TMD (i.e., 2DOFs TMD and 3DOFs TMD) are simulated. Vibration suppression of single dominant mode and multiple modes are achieved, corresponding to the case when the primary structure is subjected to wide and narrow band harmonic excitations, respectively. Afterward, a TMD with one rotational and two translational (1R2 T) DOFs is designed by embodying the geometric constraint patterns by flexible beams, and changeable elastic elements are incorporated. Experiments show that the first, second, and third bending modes of the cantilever beam are suppressed by 80.0%, 67.5%, and 61.2%, respectively, by the 3DOFs TMD for multiple modes suppression.

Annular tuned liquid dampers (TLDs) may be installed in slender structures with limited floor space, in which people and utilities must pass through the core, such as a wind turbine or observation tower. This study investigates an annular-shaped TLD equipped with damping screens. A linearized equivalent mechanical model capable of capturing the fundamental sloshing mode response of an annular TLD is presented. An experimental shake table testing program is completed to assess the performance of the model. Thirty-six frequency sweep tests consisting of various TLD configurations, excitation amplitudes, and excitation directions are completed. Good agreement is observed between the linearized equivalent mechanical model and experimental wave heights, sloshing forces, and energy dissipated per cycle that have been filtered to include only the fundamental sloshing mode response. The model is also observed to be in good agreement with experimental data for different excitation directions. The model is coupled to a generalized structure to investigate the response of a structure equipped with an annular TLD. The annular TLD is found to reduce the response of a generalized offshore wind turbine structure undergoing harmonic force excitation. The annular TLD provides performance comparable to an optimal linear tuned mass damper (TMD) with the same properties for a range of force excitation amplitudes.

Articular cartilage is a thin layer of a solid matrix swollen by fluid, and it protects joints from damage via poroviscoelastic damping. Our previous experimental and simulation studies showed that cartilage-like poroviscoelastic damping could widen the range of damping methods in a low-frequency range (<100 Hz). Thus, the current study aimed to realize cartilage-like damping capacity by single- and two-indenter–foam poroviscoelastic dampers in a low-frequency range. Multiple single-indenter–foam dampers were designed by combining foam sheets with different pore diameters and indenters with different radii. Their damping capacity was investigated by dynamic mechanical analysis in a frequency range of 0.5–100 Hz. Single-indenter–foam dampers delivered peak damping frequencies that depended on the foam’s pore diameter and characteristic diffusion length (contact radii). Those dampers maximize the damping capacity at the desired frequency (narrowband performance). A mechanical model combined with simple scaling laws was shown to relate poroelasticity to the peak damping frequencies reasonably well. Finally, combinations of single-indenter–foam dampers were optimized to obtain a two-indenter–foam damper that delivered nearly rate-independent damping capacity within 0.5–100 Hz (broadband performance). These findings suggested that cartilage-like poroviscoelastic dampers can be an effective mean of passive damping for narrowband and broadband applications.

Eigen-decomposition remains one of the most invaluable tools for signal processing algorithms. Although traditional algorithms based on QR decomposition, Jacobi rotations and block Lanczos tridiagonalization have been proposed to decompose a matrix into its eigenspace, associated computational expense typically hinders their implementation in a real-time framework. In this paper, we study recursive eigen perturbation (EP) of the symmetric eigenvalue problem of higher order (greater than one). Through a higher order perturbation approach, we improve the recently established first-order eigen perturbation (FOP) technique by creating a stabilization process for adapting to ill-conditioned matrices with close eigenvalues. Six algorithms were investigated in this regard: first-order, second-order, third-order, and their stabilized versions. The developed methods were validated and assessed on multiple structural health monitoring (SHM) problems. These were first tested on a five degrees-of-freedom (DOF) linear building model for accurate estimation of mode shapes in an automated framework. The separation of closely spaced modes was then demonstrated on a 3DOF + tuned mass damper (TMD) problem. Practical utility of the methods was probed on the Phase-I ASCE-SHM benchmark problem. The results obtained for real-time mode identification establishes the robustness of the proposed methods for a range of engineering applications.

Space restrictions at the top of tall buildings may necessitate using tuned sloshing dampers (TSD) tanks with large rectangular penetrations to accommodate the structural core of the tower. A finite element model is employed to predict the natural sloshing frequencies and mode shapes of liquid sloshing in a rectangular tank with a rectangular core. Equivalent mechanical properties are determined to predict the sloshing response. Frequency response predictions of wave heights, sloshing forces, and energy-dissipation per cycle agree with results from shake table testing conducted on a rectangular tank with a rectangular core. Energy dissipation due to flow around the core adds considerable damping to the liquid and is proportional to the response velocity-squared. Nonlinear coupling among sloshing modes results in multiple peaks in the frequency response plots near the fundamental resonant frequency. An interior core with a broad dimension in one direction substantially reduces the fundamental sloshing frequency and equivalent mechanical mass in the perpendicular direction; however, the fundamental sloshing frequency and equivalent mechanical mass in the parallel direction are only influenced marginally. Large rectangular cores reduce the proportion of the total water mass that is effective in controlling tower motion. A TSD with a rectangular penetrating core may enable a TSD option to be considered for the control of a tall building in cases where a traditional rectangular TSD is infeasible.

Underplatform dampers are used to limit the resonant vibration of turbine blades. In recent years, various strategies have been implemented to maximize their damping capability. Curved-flat dampers are preferred to ensure a predictable bilateral contact, while a pre-optimization procedure was developed to exclude all those cross-sectional shapes that will bring the damper to roll and thus limit the amount of dissipated energy. The pre-optimization bases its predictions on the assumption that the effective width of the flat contact interface corresponds to the nominal one. It is shown here that this hypothesis cannot be relied upon: the energy dissipated by two nominally identical dampers, machined according to the usual industrial standards, may differ by a factor up to three due to the morphology of the flat-to-flat contact interface. Five dampers have been tested on two dedicated test rigs, available in the AERMEC laboratory, specially designed to reveal the details of the damper behavior during operation. Their contact interfaces are scanned by means of a profilometer. In each case, the mechanics, the kinematics, and the effectiveness of the dampers in terms of cycle shape and dissipated energy are correlated to the morphology of the specific contact surface. To complete the picture, a state-of-the-art numerical simulation tool is used to show how this tribo-mechanic phenomenon, in turn, influences the damper effect on the dynamic response of the turbine.

A numerical methodology is described to study the influence of the contact location and contact condition of friction damper in aircraft engines. A simplified beam model is used to represent the blade for the preliminary design stage. The frictional damper is numerically analyzed based on two parameters, contact angle and vertical position of the platform. The nonlinear modal analysis is used to investigate the nonlinear dynamic behavior and damping performances of the system. The harmonic balanced method with the continuation technique is used to compute the nonlinear modes for a large range of energy levels. By using such a modeling strategy, the modal damping ratio, resonant amplitude, and resonant frequency are directly and efficiently computed for a range of design parameters. Monte Carlo simulations together with Latin hypercube sampling is then used to assess the robustness of the frictional damper, whose contact parameters involve much uncertainties due to manufacturing tolerance and also wear effects. The influences of those two parameters are obtained, and the best performances of the frictional damper can be achieved when the contact angle is around 25 deg–30 deg. The vertical position of the platform is highly mode dependent, and other design considerations need to be accounted. The results have proved that the uncertainties that involved contact surfaces do not have significant effects on the performance of frictional damper.

The electromagnetic coupling effect can generate electromagnetic damping to suppress disturbance, which can be utilized for vibration serviceability control in civil engineering structures. An electrodynamic actuator is used as a passive electromagnetic damper (EMD). Ideally, the EMD is assumed to be attached between the ground and the structure. The kinetic energy of the vibrating structure can be converted to electrical energy to activate the electromagnetic damping. To induce appropriate damping, the two terminals of the damper need to be closed and cascaded with a resonant shunt circuit as an electromagnetic shunt damper (EMSD). In this study, an resistance–inductance–capacitance (RLC) oscillating circuit is chosen. For determination of optimal circuit components and comparing against the tuned mass damper (TMD), existing H ∞ design formulae are applied. This work extends this with a detailed development of an H 2 robust optimization technique. The dynamic properties of a footbridge structure are then selected and used to verify the EMSD optimal design numerically. The vibration suppression performance is analytically equivalent to the dynamic characteristic of the TMD and has feasible installation and better damping enhancement. To further evaluate the potential application of the EMSD, multi-vibration mode manipulation via connecting multiple RLC resonant shunt circuits is adopted. The multiple RLC shunt circuit connecting to EMD is an alternative to the single mode control of a traditional TMD. Therefore, the EMSD can, in principle, effectively achieve suppression of single and multiple vibration modes.

The inerter is referred to as a two-terminal device that provides inertial forces proportional to the relative accelerations between its two terminals. It has been widely applied in vibration control due to its mass amplification effect. In this paper, a new inerter-based damper is proposed to take advantage of the mass amplification effect, which consists of the classic rack-pinion inerter in conjunction with a torsional tuned mass damper. Unlike any other topologies of inerter-based dampers, the torsional mass damper is connected to the pinion of the inerter via a rotational spring and viscous damper. As a result, the weight of the torsional mass damper can be significantly reduced. The proposed damper is applied to single-degree-of-freedom primary structures and a two degrees-of-freedom structure, and the H 2 optimization is conducted to obtain the optimum tuning ratio and damping ratio analytically. When comparing the proposed damper with its counterpart reported in the literature, the proposed damper achieves 20–70% improvement when their weights are identical.

A pendulum-type tuned mass damper (TMD)-tuned sloshing damper (TSD) system is proposed as a cost-effective device to reduce wind-induced structural motion. Lagrange's principle is employed to develop an equivalent mechanical model for the system. The sloshing liquid provides additional gravitational restoring force to the pendulum TMD but does not provide a corresponding increase to its inertia. As a result, the natural frequency of the pendulum TMD is increased due to the TSD degree-of-freedom. Shake table testing is conducted on several pendulum TMD-TSD systems that are subjected to harmonic base excitation at discrete frequencies near the natural frequency of the pendulum TMD. The modeled and experimental results are in reasonable agreement when the liquid is not shallow or the response amplitude is not large. The pendulum TMD-TSD is coupled to a linear structure, and it is demonstrated through an analytical study that the device provides performance that is comparable to a traditional TMD. The proposed system is advantageous because it does not require a viscous damping system that is often one of the most costly components of traditional TMDs.

In this work, exact closed-form solutions are derived for optimizing the resonant shunt circuits of electromagnetic shunt dampers (EMSDs), which use an electromagnetic transducer, and piezoelectric shunt dampers (PZSDs), which use a piezoelectric element, shunted with an electric circuit. Modeling of the EMSD and PZSD is unified by nondimensional parameters. The optimization criteria selected for the EMSD and PZSD are H ∞ -norm minimization, H 2 -norm minimization, and exponential time-decay rate maximization. The aim of this study is to derive for the first time the exact solutions that have not previously been investigated, including cases that consider the inherent damping of the primary system. This paper comprehensively summarizes the exact solutions based on the optimization criteria together with approximated solutions obtained by the fixed-point method, which is commonly used to optimize the dynamic vibration absorber (DVA).

Viscoelastic dampers are one of the most popular earthquake mitigation devices for building structures with a large number of applications in civil engineering. The seismic performance of viscoelastic dampers is greatly affected by viscoelastic materials. The present paper addresses the theoretical and experimental studies of the viscoelastic damper. The regular polyhedron chain network models for viscoelastic materials are proposed based on the molecular chain network microstructures and the temperature–frequency equivalent principle. Several dynamic property tests for the viscoelastic damper at different temperatures, frequencies, and displacements are carried out, and the proposed models are verified by comparing the numerical and experimental results. The comparisons show that the viscoelastic damper has perfect energy dissipation capacity, and the regular polyhedron chain network models can well describe the mechanical properties of the viscoelastic damper at different environmental temperatures and excitation frequencies.

A novel type of dynamic vibration absorber (DVA) is proposed, which consists of a tuned mass damper (TMD) and tuned sloshing damper (TSD) connected in series to the structure. The system enables the expensive viscous damping devices (VDDs) associated with traditional TMDs to be omitted from the design. A linearized equivalent mechanical model and a nonlinear multimodal model are developed to investigate the proposed system. A TMD–TSD is nonlinear due to the quadratic damping associated with liquid drag, which ensures the system performance is amplitude-dependent. Simple expressions for the optimal TSD–TMD mass ratio, tuning, and damping ratios are employed to design a TMD–TSD coupled to a single degree-of-freedom (SDOF) structure. Frequency response curves for the structure, TMD, and TSD degrees-of-freedom are created for several excitation amplitudes, and the nonlinear behavior of the system response is evident. The performance of the TMD–TSD is evaluated against traditional TMD and TSD systems—with the same total mass—by computing the effective damping produced by each system. The proposed system is found to provide a superior acceleration reduction performance and superior robustness against changes to the frequency of the primary structure. The proposed system is, therefore, an effective and affordable means to reduce the resonant response of tall buildings.

The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and precompression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.

Tuned mass dampers (TMDs) are typically introduced and calibrated as natural passive control devices for the vibration mitigation of the steady-state response of primary structures subjected to persistent excitations. Otherwise, this work investigates the optimum tuning of TMDs toward minimizing the transient structural response. Specifically, a single-degree-of-freedom (SDOF) system is considered as a primary structure, with added TMD, subjected to pulse-like excitations. First, the system is analytically analyzed, within the time domain, for unit impulse base displacement, through Laplace transform. Then, the tuning process is numerically explored by an optimization procedure focused on an average response index, to extract the optimum condition toward best TMD calibration. The efficiency of the proposed control device is then assessed and demonstrated through further post-tuning numerical tests, by considering as dynamic loadings: first, a time unit impulse base displacement, coherent with the source description above; second, different pulse-like excitations, to detect the effectiveness of the so-conceived TMD for generic ideal shock actions; third, a set of nonstationary earthquake excitations, to enquire the achievable level of seismic isolation. It is shown that this leads to a consistent passive TMD in such a transient excitation context, apt to mitigate the average response. Additionally, the present tuning forms a necessary optimum background for a possible upgrade to a hybrid TMD, with the potential addition of an active controller to the so-optimized TMD, to achieve even further control performance, once turned on, specifically for abating the peak response, too.

In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

The building structural vibration control by an active mass damper (AMD) with delayed acceleration feedback is studied. The control is designed with a multi-objective optimal approach. The stable region in a parameter space of the control gain and time delay is obtained by using the method of stability switch and the numerical code of NDDEBIFTOOL. The control objectives include the setting time, total power consumption, peak time, and the maximum power. The multi-objective optimization problem (MOP) for the control design is solved with the simple cell mapping (SCM) method. The Pareto set and Pareto front are found to consist of two clusters. The first cluster has negative feedback gains, i.e., the positive acceleration feedback. We have shown that a proper time delay can enhance the vibration suppression with controls from the first cluster. The second cluster has positive feedback gains and is located in the region which is sensitive to time delay. A small time delay will deteriorate the control performance in this cluster. Numerical simulations and experiments are carried out to demonstrate the analytical findings.