Inerter System Research Articles

Response control of chimneys using tuned mass damper, multi-tuned mass damper and tuned mass inerter system

Growing industry and shifting environmental regulations have made chimneys taller and more flexible, thus making them susceptible to wind forces. Consequently, it becomes necessary to analyze the chimney for undesired wind force causing vortex induced vibration (VIV) and to enhance their performance by the implementation of appropriate countermeasures. In this study, three passive control devices, namely, tuned mass inerter system (TMIS), tuned mass damper (TMD) and multi-tuned mass damper (MTMD), are used to control the VIV of high-rise chimneys. The TMIS comprises a mass element, spring, damper, and inerter subsystem. The MTMD is distributed over the top one-third height of the chimney. The three control devices control the response of the chimneys under random vortex induced forces, and their relative performances are evaluated. The modal spectral analysis and Genetic Algorithm are employed to establish a method for optimizing the damper-structure system for VIV control. The response analysis duly considers the effect of the nonlinear aero-elastic effect. The novelty of the paper lies in the application of TMIS for chimney subjected to vortex induced vibration and comparing its results with other traditional dampers (TMD and MTMD) for the three chimneys of height 120 m, 210 m, and 360 m of varying diameter, taken as illustrative examples. In addition, the study examines the impact of different mass ratios and the mass of the inerter on chimneys. For the three chimneys considered, it is observed that the performance of the TMD is best among the three control techniques adopted. For the tallest chimney (360 m), all three control devices display an optimum mass ratio for which the response reduction is maximum. The performance of the TMIS improves with the increased height of the chimney.

Mitigating seismic effects on frame structures with inerter system

Mitigating seismic effects on frame structures with inerter system

Development of a semi-active MR inerter for seismic protection of civil structures

Civil engineering structures are susceptible to collapsing when exposed to severe vibrations. Therefore, it is essential to protect them from undesirable vibrations triggered by natural calamities like earthquakes or strong winds. This paper proposes an innovative semi-active Magnetorheological (MR) inerter system with a compact structure for seismic protection. The inerter system consists of four rubber bearings and the semi-active MR inerter. The inertance of the semi-active MR inerter can be switched according to different working scenarios. This unique operating principle enhances the adaptability of the system. To assess the performance of the proposed inerter system, a scaled three-storey building was constructed following scaling laws. Four scaled earthquake signals with different dominant frequencies were used as ground motion excitations. An inertance switch controller based on short-time Fourier transformation (STFT) methodology was built to determine the desired inertance of the inerter. Both the simulation and experimental results indicated that the proposed semi-active MR inerter system provides superior vibration mitigation capacity over the passive inerter systems. Specifically, the employment of the semi-active MR inerter effectively reduces the acceleration responses of the structures under different seismic excitations.

Optimal Layout of Suspension System Employing Mechatronic Inerter for Comfort Enhancement Based on Structure-Immittance Approach

<div>The usage of the inerter and its studies has greatly developed in recent years as it offers better performance compared to passive systems and has lower cost and power consumption than active and semi-active systems. This article focuses on studying a half-vehicle model to obtain the optimal layout of the mechatronic inerter, spring, and damper suspension system (ISD) for comfort enhancement with the aid of the structure-immittance approach, ensuring structural simplicity.</div> <div>The mechatronic inerter, which consists of a single capacitance, resistance, and inductance, is added to a half-vehicle model composed of an inerter, spring, and damper. All possible layouts are studied to achieve the optimal design layout. Evaluation criteria such as the performance index, system peak-to-peak value, and settling time are utilized to assess body acceleration, thereby improving passenger comfort. Furthermore, the system’s impact on dynamic tire load and suspension working space under diverse road conditions is analyzed. Theoretical analyses conducted using MATLAB/Simulink demonstrate that the novel mechatronic ISD layout significantly enhances body acceleration performance compared to conventional passive systems, switchable hydraulic ISD systems, and fuzzy logic-controlled three-setting switchable dampers.</div>

Topology optimization analysis of a frame-core tube structure using a cable-bracing-self-balanced inerter system

This paper describes the role of the cable-bracing-self-balanced inerter system (CBSBIS) for vibration control of frame-core tube structures and focuses on the efficiency improvements of the inerter system brought by the topology optimization corresponding to the cable-bracing schemes. Different cable-bracing schemes are proposed to explore the installation efficiency applied to frame-core tube structures. According to the characteristics of the bending deformation, the simplified discrete model of a frame-core tube structure with the CBSBIS is established, and an optimal design method based on the modal control is proposed from the perspective of the convenience of design. According to the results of parameter analysis and numerical cases, the vertical bracing scheme is more effective in utilizing the overall bending deformation of the frame-core tube structure, particularly through the outriggers, which amplify the displacement driving the CBSBIS. Meanwhile, the damping effect of controlling multiple modes of the structure is demonstrably superior to that of controlling a single mode. Compared with the traditional damped outrigger and tuned mass damper, the CBSBIS provide a better solution for the control of structures which means that the CBSBIS has a significant improvement in the control of the structure's harmful inter-story drift ratio and acceleration response.

Seismic response of structures with friction pendulum inerter system (FPIS) under near-fault earthquakes

Near-fault ground motions with high acceleration peaks and long-period velocity pulses pose a serious threat to the reliability of engineering structures. To reduce the displacement of isolation layer and improve the seismic performance of superstructure under the near-fault ground motions, a composite isolation system, which is composed of friction pendulum system (FPS) and inerter system, namely FPIS, was used in this paper. Based on D’Alembert’s principle, the nonlinear motion equations of a base-isolated structure with FPIS were established. The damping effect of two different mechanical layouts of FPIS subsystems, i.e, series-parallel inerter system-I-FPS(SPIS-I-FPS) or series-parallel inerter system-II-FPS(SPIS-II-FPS), were investigated in this study. The strong nonlinearity of FPIS was considered, and the inerter system parameters were designed based on the principle of maximum damping enhancement. The fourth-order Runge-Kutta approach was used to solve the dynamic response of a multi-degree-of-freedom system under seismic excitations. The effectiveness of FPIS was verified by comparing the isolation layer displacement and the acceleration of superstructure calculated by MATLAB with the friction pendulum system and viscous damper (FPS-VD). The nonlinear time history analysis results indicate that within a certain additional damping range, the SPIS-I-FPS subsystem performs effectively than SPIS-II-FPS in reducing the superstructure acceleration and isolation layer displacement. To increase the energy dissipation efficiency of structures, it is recommended to increase the design parameters of the inerter system and control the friction coefficient of FPS within the range of 0.05∼0.10.

Seismic response prediction and parameters estimation of the frame structure equipped with the base isolation-fluid inerter system (FS-BIFI) based on the PI-LSTM model

This paper introduces a novel approach, the physics-informed long short-term memory (PI-LSTM) model, to address the forward and inverse problems of the frame structure equipped with the base isolation-fluid inerter system (FS-BIFI). Validation of the PI-LSTM model's effectiveness is demonstrated through a numerical case study of a single-story FS-BIFI. Employing this approach, the PI-LSTM model accurately predicted displacement and acceleration responses of a three-story FS-BIFI. Moreover, it conducts an evaluation of unknown damping-related parameters (β1, β2) and a stiffness-related parameter (μ) of the fluid inerter mounted on the FS-BIFI. The model demonstrates a robust confidence value of 96.68% in predicting response error values within the range of [− 10%, 10%]. Notably, the relative errors in estimating unknown parameters (β1, β2, μ) stand at 12.760%, 8.857%, and 3.750%, respectively. The results show that the PI-LSTM model has great potential for response prediction and parameter inversion of complex structural systems.

System Identification of a Structure Equipped with a Cable-Bracing Inerter System Using Adaptive Extended Kalman Filter

An innovative cable-bracing inerter system (CBIS) has been proposed and shown to be effective in mitigating the structural response under dynamic excitation. The CBIS comprises an inerter element, an eddy current damping element, and a pair of tension-only cables that can transfer the story drift to rotating flywheels. To further investigate the characteristics of the CBIS, a system identification approach based on an adaptive extended Kalman filter (AEKF) and a recursive least-squares (RLS) algorithm is proposed. Depending on the CBIS model’s availability, the proposed approach uses two strategies: the AEKF identifies the parameters of the structure and the CBIS when the model is specific; alternatively, when the model is unspecific, the KF combined with an RLS algorithm identifies the restoring force generated by the CBIS as an unknown fictitious input. In addition, the AEKF incorporates a time-variant fading factor to track the target adaptively. The proposed approach is validated through free vibration and shaking table tests, demonstrating the accuracy in identifying structural parameters and restoring force provided by the CBIS. The identification process involves two stages: initially, the AEKF identifies the parameters of the bare structure without the CBIS, followed by a dual strategy using either AEKF or KF-RLS for identifying the parameters of the CBIS or its restoring force, respectively. The findings also verify the feasibility and validity of the mechanical model and operating principle of the CBIS, thereby contributing to the advancement and application of the CBIS in future studies.

Study on vortex-induced vibration mitigation of parallel bridges by multi-tuned mass damper inerter

This study proposes a novel Multi-Tuned Mass Damper Inerter (MTMDI) system for mitigating the vortex-induced vibration (VIV) responses of parallel bridges. In the proposed system, two individual bridges are linked using two Tuned Mass Damper Inerters (TMDIs). A model of parallel bridges with MTMDI under vortex-induced force is constructed, and two additional schemes wherein each bridge is equipped with a TMDI and a Tuned Mass Damper (TMD) separately are considered. The VIV responses of the parallel bridges are estimated through full bridge aeroelastic model wind tunnel tests. The performance of the MTMDI system with the optimal parameters obtained by the multi-objective optimization technique is compared with the performance of the other aforementioned two schemes. The results indicate that the optimal MTMDI system with smaller attached mass and inertance effectively mitigates the vertical VIV responses when applied to the parallel bridges. The frequency response functions and displacement time histories further demonstrate the effectiveness of the MTMDI system as an attractive alternative to the other schemes. Finally, the sensitivity of performance against variations in each parameter in the MTMDI system is discussed.

Vibration control of adjacent structures equipped with inerter-based dampers considering nonlinearities: Analytical and experimental studies

Inerter-based dampers (IBDs) have been demonstrated to be effective in reducing structural vibration due to the mass amplification and energy dissipation enhancement effects of inerters. However, previous studies adopted mostly an idealized linear inerter model, and the influences of inerter nonlinearities on the effectiveness of IBDs, especially in seismic-induced vibrations of adjacent structures, have yet to be fully studied. To address this research gap, a new nonlinear model is proposed to characterize the inerter nonlinearities, with the nonlinear parameters identified and validated through the mechanical performance tests. An analytical model is then established for the adjacent structures equipped with an inerter device, validating its accuracy by comparing results with shaking table tests. Finally, the influences of inerter nonlinearities on three classical IBDs, namely tuned inerter damper (TID), tuned viscous mass damper (TVMD), and spring dashpot inerter system (SDIS), in reducing the seismic responses of adjacent structures are systematically investigated. The experimental and analytical results demonstrate that inerter nonlinearities significantly affect the relative displacement between adjacent structures, and the friction is the dominant inerter nonlinearity, with the elastic effect being generally negligible. Furthermore, the influences of nonlinearities on TVMD and TID control effectiveness are contingent upon external excitations.

Optimum design and performance evaluation of inerter‐based dampers for seismic protection of adjacent bridges

Pounding between adjacent bridge structures was frequently observed in previous major seismic events. This paper proposes using inerter-based dampers (IBDs) to preclude pounding damage between adjacent bridges, and comprehensively investigates their optimum designs and control performances. Specifically, four classical IBDs are investigated, including tuned inerter damper (TID), tuned mass damper inerter (TMDI), tuned viscous mass damper (TVMD), and spring dashpot inerter system (SDIS). Analytical models of adjacent bridges equipped with these IBDs are developed, and corresponding equations of motion are derived. Three control objectives are defined, and the numerical search method is utilized to determine the optimum design parameters of IBDs for each control objective. In addition, sensitivity analysis is performed to demonstrate the robustness of IBDs against the uncertainties from their actual design parameters. Finally, the control effectiveness of IBDs under various excitations, including the white noise and natural seismic events, are investigated and compared with each other. The results show that the introduction of IBDs could reduce not only the relative displacement between the adjacent bridges but also the displacement and acceleration responses of each individual bridge; the TVMD and SDIS are more effective than the TID and TMDI with the same inertance, but the TID and TMDI can achieve optimal performance with smaller damping ratio. In addition, the control forces of the optimal TID and TMDI are smaller than those of the TVMD and SDIS with the same inertance ratio.

Impact response analysis of vibration system with inerter

This research investigates using an inerter system to control the impact-induced vibration response of a single degree of freedom(SDOF) and two degrees of freedom(TDOF) vibration system. An analytic model of the SDOF system with an inerter is first derived, and simulation is performed to compare the inerter performance in suppressing the maximum acceleration response under shock load. Next, a more complex TDOF vibration model with an inerter is derived, and the effectiveness of the inerter in reducing the large acceleration amplitude is evaluated. The energy analysis is conducted to investigate the energy transfer mechanism during impact. The simulation study shows that one can significantly decrease the maximum acceleration response with an appropriate selection of the inerter parameters. For the SDOF vibration system with an inerter, response reduction is greatly influenced by the system’s natural frequency. In the TDOF vibration system, the maximum acceleration response attenuation is caused by two factors. For a large inerter radius, the acceleration response reduction is mainly influenced by energy transfer between unsprung and inerter mass. However, for a big inerter mass, attenuation of the acceleration response is caused by decreasing the system’s natural frequency. It is observed from the simulation that the maximum acceleration response can be reduced up to 35% by adjusting the inerter radius of gyration. Furthermore, the optimum condition for reducing the acceleration response occurs when the inerter mass is half the unsprung mass ( m i = 0.5 m u). An experimental study is conducted to validate the simulation results.

A novel mean square formulation of stochastic nonlinear dynamic systems based on Adomian decomposition

An Adomian decomposition based mathematical framework to derive the mean square responses of nonlinear structural systems subjected to stochastic excitation is presented. The exact mean square response estimation of certain class of nonlinear stochastic systems is achieved using Fokker–Planck–Kolmogorov (FPK) equations resulting in analytical expressions or using Monte Carlo simulations. However, for most of the nonlinear systems, the response estimation using Monte Carlo simulations is computationally expensive, and, also, obtaining solution of FPK equation is mathematically exhaustive owing to the requirement to solve a stochastic partial differential equation. In this context, the present work proposes an Adomian decomposition based formalism to derive semi-analytical expressions for the second order response statistics. Further, a derivative matching based moment approximation technique is employed to reduce the higher order moments in nonlinear systems into functions of lower order moments without resorting to any sort of linearization. Three case studies consisting of Duffing oscillator with negative stiffness, Rayleigh Van-der Pol oscillator and a Pendulum tuned mass damper inerter system with linear auxiliary spring–damper arrangement subjected to white noise excitation are undertaken. The accuracy of the closed form expressions derived using the proposed framework is established by comparing the mean square responses of the systems with the exact solutions. The results demonstrate the robustness of the proposed framework for accurate statistical analysis of nonlinear systems under stochastic excitation.

Vibration control of beams under moving loads using tuned mass inerter systems

Traditional tuned mass dampers (TMDs) have been proven efficient for the moving-load-induced vibration control of beams. However, a large tuned mass is required in TMDs to adjust the structural dynamic characteristics and achieve the demanded performance targets, which leads to additional dynamic effects and inconvenience of installation. The tuned mass inerter system (TMIS) is an ungrounded lightweight passive control device, which contains a suspended mass, a parallel-connected tuned spring and an inerter-based subsystem. In this study, the application and optimization of TMISs on vibration suppression of multi-span beam models under moving load series are investigated. Using the Bubnov-Galerkin integration method, the modal-superposition generalized system for specified modes of a beam with TMIS under successive moving load series is established. Then, a design strategy for TMISs is proposed to achieve the structural target performance demand by decreasing the moving load-induced resonant responses and attached tuned mass. In the optimization algorithm, the tuned mass ratio is taken as the optimal objective, and the limited dynamic response amplitude under different speed parameters is the constraint condition. A single-span simply supported beam with the TMIS under a moving load series is analyzed. The designed TMISs are tuned to the dominating mode with the maximum mass participate factor of the main structures. TMISs show good vibration mitigation compared to TMDs with equal tuned mass. Meanwhile, under the premise of identical structural performance demands, TMISs require less tuned mass than TMDs and achieve a lightweight control effect. The corresponding dynamic amplitude vs speed curves and time history response curves of beams with TMISs and TMDs are also depicted through comparative analyses. The vertical deflection and acceleration responses apparently decrease, and the resonance is mitigated due to the designed TMISs. The sensitivity analysis results indicate that TMISs attached to beams are insensitive to the perturbance of their parameters and the input moving load excitations; thus, TMIS proves to be a robust tuning system.

Multi-modal seismic control design for multi-storey buildings using cross-layer installed cable-bracing inerter systems: Part 1 theoretical treatment

Many attempts have been made to improve the performance of buildings subjected to ground motions with a novel mechanic element, known as an inerter, thereby giving buildings more stability. Recently, a characteristic of the inerter system on controlling the target mode, called the target mode control effect, has been discovered. Considering the prospects of target mode control effect on controlling those buildings affected by multi-modal responses, in this study, cross-layer installed cable-bracing inerter systems (CICBISs) will be used for the multi-modal seismic control. For releasing the end torsion constraints demand of the ball-screw inerter and simplifying the CICBIS's realization, a self-balanced inerter is proposed. A multi-modal seismic control design strategy is proposed to determine the optimal parameters of CICBISs. The equivalent mass with a physical meaning of the multi-storey building with a CICBIS is proposed to quantify the control efficiency of the CICBIS's placement and determine the installation placement of CICBISs directly. A 20-story benchmark building is used to validate the design strategy. The results show that the CICBISs tuned to multi-modes through applying the proposed design strategy can simultaneously focus on controlling multiple target modes. Moreover, it is proved that under the same constraint on each device's control force, the designed CICBISs obtain a higher efficiency on suppressing seismic responses than those CICBISs for single-modal seismic control we proposed in the past and cross-three-layer installed tuned viscous mass dampers. Further sections of the study, including device tests on a self-balanced inerter's prototype and shake table tests on corresponding CIBCIS, will be offered in the following companion paper: Part 2 Experimental treatment.

Random response analysis of nonlinear structures with inerter system

Most researches on inerter focused on the mechanism or deterministic vibration analysis, and some studies lied in the random vibration of linear structures. However, many structures exhibit the nonlinear characteristics under a large excitation, and the effects of inerter system on additional properties and probabilistic distribution of random response of nonlinear structure under random excitation have rarely been considered at present. Based on the enhancement effect of inerter system on nonlinear structure, the influence of various components of inerter system on the response suppression of nonlinear structure is investigated from the probability level, and a developed response analysis method suitable for inerter system is proposed in this paper. The stochastic differential equation of nonlinear structure with inerter is established in this work, in which both the nonlinear structure without hysteresis and the hysteretic structure are considered. The probability density function of structural response is obtained by the exponential polynomial closure (EPC) method combined with the state-space-split technique. In terms of nonstationary random excitation, a scheme of equivalent stationary excitation is proposed to split the state space vector. Meanwhile, the EPC method is developed through the reduction of undetermined coefficients in the probabilistic solution, which significantly improves the efficiency. Numerical results show that the response suppression effectiveness of inerter system is robust to nonlinear structures, and the inerter system mainly provides additional damping for the primary structure, thereby achieving the vibration mitigation. However, an excessively rigid inertia system may lead to a negative additional stiffness for the primary structure and inhibit the vibration mitigation.

Vibration Reduction Mechanism of a Novel Enhanced Particle Inerter Device

This work proposes an enhanced particle inerter device (EPID) capable of significantly enhancing the vibration control effect (VCE) of a conventional particle tuned mass damper (PTMD). EPID, an inerter is coupled to the PTMD device, that is, the inerter is attached to the damper cavity on one end and to the ground on the other, mainly using its mass amplification effect. To accomplish the goal, the EPID’s mechanical model is established first. Then, the system’s governing equation is derived based on the single degree of freedom (SDOF) system, and the EPID’s effectiveness is verified via inputting seismic excitation. Finally, the parameter analysis and multi-objective optimization design are carried out for EPID, and the superiority of the proposed multi-objective optimization design method compared with the traditional design method is verified. The results indicate that EPID can effectively minimize the main structure’s displacement and acceleration response. In particular, under the El Centro wave’s excitation, the vibration reduction rate of the dynamic responses (peak response and root mean square response) is close to 50%, which is over 35% increasing compared to PTMD, and its VCE is better for excitation band changes. At the same time, it is found that the lower the damper’s auxiliary mass ratio, the more obvious the enhancement of the inerter system’s VCE is, which brings about the lightweight design of the high-control effect of PTMD.

Optimal design and seismic performance of base-isolated storage tanks using friction pendulum inerter systems

The inerter system has been proposed and proven to be effective to improve the seismic performance of base-isolated storage tanks. However, only rubber bearings modelled with linear spring and dashpot are investigated. Considering the special characteristics of the liquid storage tank (i.e., the variable weight), the friction pendulum system whose isolation period is independent on the structural weight is preferred in a base-isolated storage tank. In this study, the traditional friction pendulum system combined with an inerter system, called friction pendulum inerter system (FPIS), is proposed for performance improvement of the base-isolated tank under seismic excitations. A demand-oriented optimum design method in time-domain is proposed for determining the parameters of the inerter subsystem for the tank with FPIS to meet the expected target performance under a representative artificial seismic input. The nonlinear time history analyses are employed in the optimization process, which considers the strong nonlinearity and the states of the stick and slip motion of the FPIS. Optimization cases are illustrated to verify the effectiveness of the optimum design and check the seismic performances of storage tanks with FPISs by nonlinear time history analyses under seven selected seismic input excitations. The results show that the isolation displacements and liquid sloshing heights of storage tanks can be mitigated as expected. The seismic performances of storage tanks, especially the isolation displacements, can be effectively improved. The proposed FPIS is concluded feasible for seismic improvement of base-isolated tanks and the proposed optimum design method is effective.

Lever-type high-static-low-dynamic-stiffness vibration isolator with electromagnetic shunt damping

Owing to the ultra-low frequency vibration isolation performance without compromising static stiffness, high-static-low-dynamic-stiffness (HSLDS) vibration isolators (VIs) have advantages over linear vibration isolators. This paper presents a lever-type HSLDS vibration isolator (L-HSLDS-VI) by employing negative resistance electromagnetic shunt damping (EMSD) together with eddy current damping to eliminate the jump phenomenon and thus to improve the stability of L-HSLDS-VIs. The lever inerter system can amplify the mass effect to broaden the isolation band. The theoretical model of L-HSLDS-VIs with EMSD (L-HSLDS-VI-EMSD) was established. The effects of negative resistance and lever ratio on the vibration isolation performance of L-HSLDS-VI-EMSD were investigated analytically and experimentally. The L-HSLDS-VI can provide significant nonlinear stiffness, which can realize the quasi-zero stiffness (QZS), and thus broaden the isolation band. EMSD produces a considerable damping effect to enhance the vibration mitigation performance of L-HSLDS-VI. The combination of the EMSD and nonlinear ECD damping is an efficient approach to improve the vibration isolation performance to overcome the jump phenomenon. This paper utilizes the lever effect to amplify damping effects, which could provide a guideline to modify the performance of HSLDS-VIs.

Optimization of inerter system for seismic response control based on a modified genetic algorithm with differential crossover strategy

The damping enhancement effect of the inerter system means that its energy dissipation efficiency can be improved with respect to the traditional dampers. Energy dissipation efficiency have been considered as the optimal design principle of the inerter system, however, the solution for optimized key parameters is difficult because of the special mechanical behavior of the inerter. A modified float-point encoding genetic algorithm is proposed in this study to realize the optimal design of the inerter system with maximized energy dissipation efficiency effectively and robustly. A novel and simple crossover strategy termed differential crossover is proposed and applied in the classical genetic algorithm to optimize the inerter system more effectively. The differential crossover strategy means that a new individual is generated based on the difference between two randomly selected individuals in the population. The mathematical expression for the optimization problem of the inerter system corresponding to the maximum energy dissipation efficiency design principle is established. Following the performance-oriented design concept, performance demand is taken as the constrained condition of the optimization problem. Case design confirms that the modified genetic algorithm can successfully solve the optimization problem of the inerter system and perform a better solving ability over the original genetic algorithms.