Nonlinear Inerter Research Articles

A force-restricted inerter damper for enhancing the resilience of seismically isolated structures

An inerter is a mechanical device that generates a resisting force proportional to the relative acceleration between its two terminals. Several inerter-based dampers have been developed and studied to protect critical structures from the damaging effects of strong earthquake events. However, under high-frequency excitations, conventional inerter-based dampers may generate high resisting forces, which can result in excessive stresses in the supporting members and degrade the performance of the isolation systems. To overcome this issue, a novel force-restricted inerter damper (FRID) is proposed in this study for use in base-isolated structures. A simplified mechanical model of the proposed FRID was developed, which consists of a parallel layout of a viscous damping element and a nonlinear inerter element with a friction force restriction mechanism. The nonlinear hysteretic behavior of the FRID is discussed with an emphasis on the frequency dependence. Time- and frequency-domain methods were developed to evaluate the nonlinear dynamic response of the FRID-controlled structure. The performance of the FRID was investigated and compared with that of commonly used fluid viscous dampers (FVDs) and viscous mass dampers, when incorporated into base-isolated structures under short- and long-period ground motions. Parametric studies were conducted to investigate the influence of the FRID’s characteristic parameters on the seismic performance of controlled structures. The analysis demonstrated that the viscous mass damper and FRID provided superior control than the FVD on the displacement of a base-isolated structure, and the FRID is more effective than the viscous mass damper in reducing the control force and structural acceleration. This confirms that the proposed FRID is a promising, high-performance, and cost-effective device for enhancing the resilience of seismically isolated structures.

Dynamics and isolation performance of a vibration isolator with a yoke-type nonlinear inerter

Previous studies have shown that nonlinear inerters can achieve superior vibration suppression compared to linear inerters, such as broadening the effective frequency band of the vibration isolator. However, nonlinear inerters are typically implemented by incorporating linear inerters into nonlinear configurations, resulting in indirect configurations and extra connections. This study introduces a direct and simple way to realize a yoke-type nonlinear inerter by employing the Scotch yoke mechanism, which is named the Scotch yoke inerter (SYI). The primary contributions of this paper are introducing a concept about the physical realization of a nonlinear inerter capable of providing both apparent mass and nonlinear inertial effects and investigating the dynamic responses and isolation performances of a vibration isolator enhanced by the proposed nonlinear inerter. The working mechanism for how the proposed SYI generates the nonlinear inertia is introduced and a simple configuration that facilities the application of this nonlinear inerter is proposed. The mechanical model of the SYI is built to describe its inertial behavior using the Euler-Lagrange method. Then, the SYI is incorporated into a vibration isolator to improve its performances. The averaging method is adopted to obtain the analytical responses and dynamic characteristics of the isolator with SYI subjected to force excitation. The stability of this nonlinear isolator is analyzed, and numerical integration using the fourth-order Runge-Kutta method is employed to verify the analytical results. The isolation performance evaluation of the isolator with SYI is conducted through three indices including the peak dynamic displacement, peak force transmissibility and effective isolation frequency band. The mechanical behavior indicates that the SYI can successfully generate the apparent mass effect of an inerter and nonlinear inertial behavior. The analytical responses agree well with the numerical results for different parameters of the isolator with SYI, which verifies the analytical solutions. The use of SYI in the vibration isolator can bend the backbone curve to the low frequencies, which indicates the softening characteristic of the frequency response. The isolator with SYI demonstrates beneficial performances in terms of force transmissibility and effective isolation frequency band. It is concluded that the proposed SYI can be seen as an alternative nonlinear inerter and is beneficial for improving the performance of the vibration isolator.

Vibration Isolation Performance Enhancement Using Hybrid Nonlinear Inerter and Negative Stiffness Based on Linkage Mechanism

Vibration Isolation Performance Enhancement Using Hybrid Nonlinear Inerter and Negative Stiffness Based on Linkage Mechanism

Experimental seismic performance assessment and numerical modelling of nonlinear inerter vibration absorber (IVA)‐equipped base isolated structures tested on shaking table

AbstractIn recent years, inerter vibration absorbers (IVAs), such as the tuned mass damper inerter (TMDI), attracted much attention in the literature for reducing seismic displacement demands of base isolated structures (BISs). Several theoretical studies reported reduced BIS seismic demands with increasing inertance endowed by a grounded inerter element, but adopted mostly idealized linear dynamical models. Herein, the potential of TMDI‐configured IVAs for seismic response reduction of BISs modelled as single‐mass structures is assessed under the combined effects of nonlinear inerter and structural behavior. To this aim, experimental data from a shaking table testing campaign are considered utilizing a custom‐built flywheel rack‐and‐pinion grounded inerter prototype with variable inertance, along with high damping rubber bearings in the isolation layer and in the BIS‐to‐absorber link. White noise excitation and an ensemble of six ground motions (GMs) with different frequency content are used in the tests for which bearings exhibit softening nonlinear behavior. Experimental results demonstrate improvement of BIS nonlinear seismic response in terms of displacement and base shear with increasing inertance for nonlinear and nonoptimally tuned IVAs. It is found though that the considered IVAs may be detrimental to BIS acceleration response depending on the GMs time‐varying frequency content signatures as captured by the continuous wavelet transform spectrogram. Finally, it is concluded that representing the inerter device by a simplified linear dissipative model as opposed to a nonlinear model with friction and gear backlash suffices to trace the BIS response with acceptable accuracy and, thus, can be used for optimal seismic TMDI design.

A review of the mechanical inerter: historical context, physical realisations and nonlinear applications

In this paper, a review of the nonlinear aspects of the mechanical inerter will be presented. The historical context goes back to the development of isolators and absorbers in the first half of the twentieth century. Both mechanical and fluid-based nonlinear inerter devices were developed in the mid- and late twentieth century. However, interest in the inerter really accelerated in the early 2000s following the work of Smith [87], who coined the term ‘inerter’ in the context of a force–current analogy between electrical and mechanical networks. Following the historical context, both fluid and mechanical inerter devices will be reviewed. Then, the application of nonlinear inerter-based isolators and absorbers is discussed. These include different types of nonlinear energy sinks, nonlinear inerter isolators and geometrically nonlinear inerter devices, many relying on concepts such as quasi-zero-stiffness springs. Finally, rocking structures with inerters attached are considered, before conclusions and some future directions for research are presented.

Enhanced vibration isolation performance of quasi-zero-stiffness isolator by introducing tunable nonlinear inerter

The concept of quasi-zero-stiffness (QZS) vibration isolator was proposed inrecent decades aiming at improving the low-frequency isolation performance in a passive manner. However, large excitation and small damping usually cause the transmissibility curve to bend seriously to the right, which greatly reduces the effective isolation region. This paper focuses on enhancing the QZS isolator by introducing tunable nonlinear inerter (TNI). After formulating the dynamic equation, the response is analytically calculated, the stability is analyzed, and numerical simulations are conducted. By comparing the isolation performances of the QZS isolator and the QZS-TNI isolator, it is shown that adding the inerter can considerably suppress the bending trend of the transmissibility curve, thereby resulting in a much wider frequency range of isolation as well as a lower peak transmissibility.

A nonlinear stiffness and nonlinear inertial vibration isolator

A nonlinear stiffness and nonlinear inertial vibration isolator is proposed in this article. It consists of an inerter, a damper, and spring elements. The nonlinear stiffness characteristic is achieved through a negative stiffness structure based on the diamond-shaped structure that generates nonlinear displacement terms. The nonlinear inertial characteristic is implemented via a geometrical nonlinear inerter that produces a nonlinear acceleration term and a nonlinear quadratic velocity term. An averaging method is developed to analyze approximately the dynamic response. The isolation performance is evaluated using four performance criteria: dynamic displacement peak, force transmissibility peak, isolation frequency band, and high-frequency force transmissibility. The effects of the nonlinear inertial characteristic on the dynamic response and isolation performance are examined. The results show that the backbone curve of the nonlinear stiffness and nonlinear inertial vibration isolator has two changing trends: bending first to the right and then to the left and bending directly to the left. The corresponding frequency response curve displays linear, hardening, and softening characteristics. The isolation performance of the nonlinear stiffness and nonlinear inertial vibration isolator is compared with that of the nonlinear stiffness and nonlinear stiffness and linear inertial ones. It could achieve a smaller force transmissibility peak, lower resonant frequency, and larger isolation frequency band than the nonlinear stiffness one and could have smaller dynamic displacement peak and smaller high-frequency force transmissibility than the nonlinear stiffness and linear inertial one. The proposed nonlinear stiffness and nonlinear inertial vibration isolator achieves a better integrated isolation performance among the three vibration isolators.

Experimental study and numerical modeling of nonlinear dynamic response of SDOF system equipped with tuned mass damper inerter (TMDI) tested on shaking table under harmonic excitation

This paper considers a novel shaking table testing campaign to assess the tuned mass-damper-inerter (TMDI) vibrations suppression attributes in harmonically excited structures under the combined effect of nonlinear structural response and nonlinear inerter device behavior deviating from the ideal linear inerter element developing acceleration-dependent force proportional to the inertance constant. Physical specimens of TMDI-equipped single-degree-of-freedom (SDOF) structure are considered featuring a custom-built rack-and-pinion flywheel inerter device with nonlinear behavior due to friction and backlash effects to connect the TMDI secondary mass to the ground. Damping and elastic properties are endowed to the SDOF structure and to the TMDI via high damping rubber bearings (HDRBs) exhibiting softening nonlinear elastic behaviour. Comprehensive experimental data in time and frequency domains are presented for 9 specimens with different sets of secondary mass and inertance subject to sine-sweep excitations for three different amplitudes. The data demonstrate that the main practical advantage of the TMDI established in the literature for linear structures and ideal inerter elements (i.e., improved vibration suppression through increasing inertance without increasing secondary mass leading to lightweight vibration absorbers) is maintained for nonlinear structures and inerter devices. Moreover, a comparison of experimental data with data derived from two different nonlinear parametric numerical models capturing faithfully the HDRBs response, one using a nonlinear mechanical model to represent the inerter device and the other using an ideal linear inerter element instead, demonstrate that displacement, acceleration and base shear response of the SDOF structure is insignificantly influenced by the nonlinear attributes of the inerter device. This outcome paves the way for developing simplified, thus practically meritorious, optimal TMDI tuning approaches adopting the ideal inerter element assumption to model physical inerter devices.

Active nonlinear inerter damper for vibration mitigation of Duffing oscillators

In this paper, a nonlinear active damping strategy based on force feedback is proposed. The proposed device is composed of a pair of collocated actuator and force sensor. The control law is formed by feeding back the output of the force sensor, through one single, one double integrator and another double integrator of its cube. An equivalent mechanical network which consists of a dashpot, an inerter and a cube root inerter is developed to enable a straightforward interpretation of the physics behind. Closed-form expressions for the optimal feedback gains are derived. Numerical validations are performed to demonstrate the proposed control strategy.

An investigation of the dynamic performance of lateral inerter-based vibration isolator with geometrical nonlinearity

Inerter, which is defined as a two-terminal mechanical element, has the characteristic that the force generated at its two terminals is proportional to the relative acceleration of the two ends. In this paper, a vibration isolator with lateral inerters is proposed and the effect of this geometrical nonlinear inerter on its dynamic performance is investigated. The force of the inerters in the moving direction of the mass and the acceleration term in the dynamic equation are nonlinear. The dynamic response is obtained using the averaging method and further checked by the numerical results, the stability analysis is also considered. The critical surface of the structural parameters which leads to no jump phenomenon and the jump frequencies when jump phenomenon occurs are determined by the Sylvester resultant method. The isolation performance of the lateral inerter-based vibration isolator is evaluated using four performance indexes: maximum dynamic displacement, maximum transmissibility, isolation frequency band and transmissibility in the higher isolation frequency band, and is compared with the parallel and series-connected inerter-based vibration isolators, as well as the linear vibration isolator. The results show that when the force amplitude is small, compared with the linear vibration isolator, the lateral inerter-based vibration isolator proposed in this paper can have a smaller maximum force transmissibility and larger isolation frequency band; the force transmissibility in the higher isolation frequency band is the same, which has the corresponding advantages of the parallel and series-connected inerter-based vibration isolators, respectively.

On the dynamics of a vibration isolator with geometrically nonlinear inerter

The inerter is a two-terminal mechanical element that produces forces directly proportional to the relative acceleration between these terminals. The linear behaviour of this element has already been described in the literature. In this work, the nonlinear effects of the geometrical arrangement of the inerter are investigated in terms of vibration isolation and compared to the traditional arrangement. The analysis comprises the use of harmonic-balanced method applied to the exact equation, as well as approximations for low amplitude and high amplitude. Numerical analysis is used to complement the investigation. Comparison with classic vibration isolators shows possible benefits for high frequency regimes. The effects from the geometrical nonlinearity vanish when the amplitude of motion is large.

Ride Evaluation of Vehicle Suspension Employing Non-Linear Inerter

Inerter is a recent element in suspension systems with the property that the generated force is proportional to the relative acceleration between its two terminals, which is similar to the way a spring reacts to relative displacement and a damper to relative velocity. This paper presents the analysis of a non-linear inerter working in parallel to passive spring and damper of a vehicle suspension to evaluate its effect on vehicles ride. The non-linear inerter was theoretically capable of switching between on and off states depending on whether or not the suspension deflection was beyond a specified free play. In the study, this behavior was represented mathematically as control law which depended on the relative displacement between the sprung and unsprung masses. A mathematical quarter vehicle model incorporating the non-linear inerter was simulated in MATLAB/Simulink to determine the vehicle responses due to road input in the form of step profile for different combinations of free play and inerters on-state proportionality constant called the inertance. Results showed improvements in vehicle ride comfort, as demonstrated by the lower root-mean-squared sprung mass accelerations compared to the ordinary passive suspension with only spring and damper. Additionally, implementation of non-linear inerter gave lower percentage overshoot to step input, indicating better transient response than ordinary passive suspension.