Maximum Displacement Amplitude Research Articles

Parametric Dynamic Simulation and Bayesian Design Optimization of a Front-Loading Washing Machine

Abstract Objective This paper presents the dynamic modeling and design optimization of a fully parametrized front-loading washing machine. Methods A thorough mathematical analysis is performed to capture the effect of nine design variables (including rotation speed, spring stiffness, weight balancer mass density, damping coefficient, spring and damper angles) on vibrational characteristics of the washing machine. The parametric simulation reveals a complex relationship between the vibrational dynamics and design variables, entailing a computationally efficient optimization approach. A Bayesian Optimization (BO) framework is developed, in which a Gaussian process model and Genetic Algorithm (GA) are utilized along with carefully selected acquisition functions to enable adaptive sampling and search for optimal design values. The objective function is to minimize the maximum amplitude of the tub displacement inside the washing machine body. Two case studies are performed to consider a different number of design variables and choices of various infill methods. Results Results show that the fully parametrized front-loading washing machine model is applicable for parametric simulation and design optimization. The proposed BO is able to successfully find a set of design variable values corresponding to the lowest maximum displacement for vibration reduction. A comparison analysis is also carried out to exhibit the difference in optimization convergence and computational cost caused by the choice of acquisition functions. Conclusion It is shown that the fully parametrized washing machine model yields a lower maximum displacement than the model with fewer design variables. Of the two acquisition functions studied for optimization, the Expected Improvement function converges more rapidly than the Lower Bound criterion.

Vibration controlling effect of tuned liquid column damper (TLCD) on support structural platform (SSP)

A bidirectional fluid-structure coupling model between tuned liquid column damper (TLCD) and support structural platform (SSP) was developed to study effects of TLCD-SSP mass ratio and tuning ratio on reducing SSP vibration. Laboratory experiments of TLCD interaction with SSP were conducted to validate TLCD-SSP coupling model. Good agreements between numerical results and experimental data are obtained. TLCD/SSP mass ratio increases from 1% to 3%, the maximum amplitude of SSP upper displacement decreases from 43.77% to 78.32%, and the upper acceleration damping rate increases from 43.26% to 77.88%. There is a phase differences between dynamic water pressure offered by sloshing inside TLCD and upper displacement curves, and the damping energy dissipation effect is maximized when the hysteresis phase difference reaches π/2. The larger mass ratio is more effective in suppressing the structural vibration. But it also brings about a fundamental frequency drift. It is advised that the mass ratio of water in TLCD to SSP should be 1.5%, the total mass of water and shell of TLCD should be about 2.5% of the mass of SSP, and the intrinsic frequencies of TLCD and SSP should be tuned the same so that the vibration controlling performance of TLCD can be improved maximally.

Resonant-type Luneburg lens for broadband low-frequency focusing

In this paper, a novel structural Luneburg lens with local resonators is proposed. This lens allows the realization of subwavelength focusing in low-frequency range. The lens is achieved by graded refractive index from the lens's centre to the outer surface. Numerical simulations are conducted to obtain data on wave propagation waveform, maximum displacement amplitude, and full width at half-maximum (FWHM) of the lens's focal region. The results show that a broadband frequency range can be achieved for subwavelength focusing. This provides a straightforward and adaptable method for designing the structural Luneburg lens for numerous applications.

Propagation Features of Diurnal Internal Tides West of the Luzon Strait Revealed by a Large PIES Array

Abstract Energetic internal tides (ITs) are generated from the Luzon Strait (LS) and propagate westward into the South China Sea (SCS). Owing to the lack of large-scale synchronous measurements, the propagation features and seasonal variations of diurnal ITs remain unclear. From 2018 to 2019, mode-1 diurnal ITs west of the LS were continuously observed using a large-scale moored array of 27 pressure-recording inverted echo sounders (PIESs) and a thermistor chain. Measurements confirmed that diurnal ITs radiate from the LS with a north–south asymmetrical pattern, with the most energetic channel located in the middle and south of the LS. The total energy radiated into the SCS across 120°E is 2.67 GW for the K1 ITs and 1.54 GW for the O1 ITs, approximately 2 times larger than those inferred from satellite observations. K1 dominates among the diurnal ITs, with its maximum isopycnal displacement (amplitude) and energy input to the SCS being the strongest in summer (i.e., 16.3 m and 2.81 GW, respectively). The propagation speed of K1 is higher in summer and autumn along the main channel (i.e., 4.33and 4.36 m s−1, respectively). Seasonal stratification and circulation play important roles in the seasonal variation of amplitude and propagation speed of the K1 ITs. The seasonal variability of diurnal-band ITs, which includes all diurnal constituents, is location-dependent and primarily results from the superposition of the K1 and P1 ITs. In particular, vertical displacement is strong in summer and winter along the main channel of the K1 and P1 ITs. The seasonal amplitude of K1 can modulate this seasonal feature. Significance Statement Internal tides (ITs) are internal waves at tidal frequencies. The Luzon Strait (LS) is one of the most energetic sites to generate large-amplitude ITs. The ITs propagate into the South China Sea (SCS), interact with mesoscale eddies, large-scale circulations, etc., and influence local hydrodynamics as well as ecosystem and sediment transport. This motivated an observation plan to investigate the ITs at the western entrance of the LS. From June 2018 to August 2019, an array of 28 PIESs was deployed in the northeastern SCS, almost covering the western entrance of the LS, to investigate the propagation properties of ITs including their amplitude, phase speed, wavelength, propagation direction, and energy fluxes and their annual and seasonal variations. Here, we primarily focus on the mode-1 diurnal ITs. The new insights enrich our understanding of IT dynamics and seasonal variations and support further improvements in numerical simulations.

Design of fixture for ultrasonic assisted gas tungsten arc welding using an integrated approach

Abstract The welding fixture greatly impacts the weld quality matrixes. In this work, the welding fixture for ultrasonic-assisted gas tungsten arc welding to reduce the hot cracking behaviour in weldments was designed using the finite element analysis approach. A three-level, five-factor central composite design-based response surface methodology analysis was followed to vary the dimensions of the fixture for the modal and harmonic analysis of the fixture using Ansys software. The optimum fixture dimensions to achieve maximum displacement amplitude and minimum von-Mises stress have been optimized using a genetic algorithm approach. The model predictions for maximum displacement amplitude and minimum von-Mises stress were compared to the experimental findings at optimal conditions. A strong consensus between the model prediction by genetic algorithm and experimental findings indicates the correctness of the developed model.

Experimental–Numerical Analysis on the Cable Vibration Behavior of a Long-Span Rail-Cum-Road Cable-Stayed Bridge under the Action of High-Speed Trains

Rail-cum-road cable-stayed bridges are widely used to span rivers, bays, and valleys. It is vital to understand the vibration behavior of the cables, which are the crucial load-bearing components of a cable-stayed bridge, as it is the leading cause of cable fatigue. First, a numerical model of cable vibration under double-end excitation was derived by neglecting the bending stiffness and was verified through a cable’s multi-segment bar finite element model, and a numerical solution program was compiled based on MATLAB R2022a software. Then, a finite element model (FEM) was established according to the design documents of a long-span rail-cum-road cable-stayed bridge. Finally, the dynamic response of the cable under the train loads was analyzed based on the FEM and numerical model. The study shows that the numerical model can accurately simulate the cable with a relative error of less than 1% for its first four frequencies compared with the FEM; the maximum displacement amplitude appears at the longest cable near the middle of the main span; the vibration frequency of the cable is approximate to the cable end excitation frequency within a 1% discrepancy; and the vibration amplitude at the center of the cable is approximately twice that of the excitation amplitude at the end of the cable.

Rod-Shaped Linear Inertial Type Piezoelectric Actuator

This article presents a numerical and experimental investigation of a novel rod-shaped linear piezoelectric actuator that consists of a square cross-section-shaped rod with eight piezo ceramic plates and a cylindrical guidance rail. The rod has a hollow cut made with an offset from the longitudinal axis of the symmetry. A cylindrical guidance rail is placed on one side of the rod, while T-shaped clamping is formed on the opposite side. The slider is mounted on the rail and is moved along it. The actuator is compact, making it possible to mount it directly on a printed circuit board (PCB) or in another device with limited mounting space, restricted mass, or actuator footprint. The operation of the actuator is based on the excitation of the first longitudinal vibration mode of the rod that induces in-plane bending vibration of the nodal zone of the rod due to a hollowed cut asymmetrically placed in the central part of the actuator. The actuator is driven by two sawtooth waveform electric signals with the phase difference of π that allows exciting longitudinal deformations of the rod and controls the reverse motion of the slider. The results of numerical investigations confirmed the operation principle of the actuator at the frequency of 59.72 kHz. The maximum displacement amplitude of the guidance rail in the longitudinal direction reaches up to 152.9 μm while the voltage of 200 Vp-p was applied. An experimental investigation of the actuator was made, and a maximum linear speed of 45.6 mm/s and thrust force of 115.4 mN was achieved.

Diffraction of plane P waves by a circular-arc canyon in an unsaturated poroelastic half-space

Based on the theory of unsaturated porous elastic medium, the diffraction around the circular-arc canyon in unsaturated half-space under the incidence of plane P wave is studied by using the Fourier-Bessel series expansion method of wave function. Through numerical examples, the influence of parameters such as incident wave frequency, incident angle, arc depth-width ratio and saturation on the surface displacement amplitude in unsaturated half-space circular-arc canyon is analyzed. The results show that the saturation has a significant effect on the variation of surface displacement amplitude, and the influence law of saturated and unsaturated site soils on the variation of surface displacement amplitude is very different under different depth-to-width ratio and incident frequency. In the case of different depth-width ratios of unsaturated half-space circular-arc canyon, the displacement amplitude change of semi-circular canyon (h/a = 1) is more sensitive to the change of saturation than that of shallow circular canyon (h/a = 0.5). When the incident frequency is low, the maximum displacement amplitude of the half-space circular-arc-canyon in both saturated and unsaturated cases increases with the increase of the incident angle. It is worth noting that when the saturation Sr = 0.99, i.e., when the soil is close to saturation, the maximum surface displacement amplitude caused by unsaturated depressed terrain (Sr = 0.8) is greater than that caused by the saturated soil case as the incidence angle increases.

Fundamental study on rapid detection of the insufficient lateral resistance of ballasted railway tracks by dynamic loading

To resume trains operation as soon as possible after disasters, it is necessary to quickly find out locations of ballasted railway with insufficient lateral ballast resistance. In this study, a new method was proposed to evaluate the lateral ballast resistance using dynamic lateral excitation. The dynamic method was performed on 1/9-scale ballasted railway models with ballast densities of 1.5 and 1.6 g/cm3. The simple harmonic excitation was generated from a pair of 20g flywheels, and the accelerations of the vibrator and the central sleeper were recorded by sensors attached on the central sleeper and the vibrator, respectively. Based on the obtained data sets, maximum accelerations as well as the maximum amplitudes of the lateral displacements of the vibrator and the central sleeper were analysed. It was found that the maximum accelerations of the vibrator were higher than those of the central sleepers. This was also true for the maximum amplitude of the lateral displacements. The ratio of the maximum amplitude of the lateral displacement of the central sleeper to that of the vibrator was evaluated. It was found that the amplitude ratio of the track model with the ballast density of 1.5 g/cm3 was higher than that with the ballast density of 1.6 g/cm3. This implies that the difference in the lateral ballast resistance owing to the difference in the ballast density may be detected based on the evaluation of the amplitude ratio.

Dynamic response amplification of resonant microelectromechanical structures utilizing multi-mode excitation

This work presents an analytical and experimental study to enhance the dynamic response of the higher-order vibration modes of resonant microstructures. The detection of higher order vibration modes is usually very difficult due to their low amplitude response, which gets buried in noise. Higher input voltages can be used to enhance the response; however, it is highly energy demanding, can result in electronics problems, and may lead to pull-in of the lower participating modes. In this paper, we present a multi-mode excitation (MME) technique to enhance the vibration response of the higher order modes of an electrostatically actuated micro cantilever beam. First, we derive the dynamic equations of motion of the micro resonator accounting for two electrostatic excitation sources. Then, we apply the Galerkin method to analyze the dynamics of the system analytically. We investigate the effect of using various dynamic AC combinations on the involved modes to yield optimal conditions of the amplitude magnification. Then, an experimental investigation is conducted based on a micro resonator made of polyimide. The results showed that, compared to the single mode excitation (SME), the MME can significantly raise the level of the response above noise and amplify the displacement amplitude to yield a higher signal-to-noise ratio. The maximum displacement amplitude can be amplified multiple times as determined by the AC loads. Hence, the improved displacement amplitude with the proposed technique makes it promising for future signal processing technologies and for realizing high-sensitivity sensors.

A Time-Domain Approach for Accurate Spectral Source Estimation with Application to Ridgecrest, California, Earthquakes

ABSTRACTWe determine the seismic moment and corner frequency of earthquakes using narrowband, time-domain measurements of the maximum shear-wave displacement amplitude. Each S wave is passed through a set of one-octave band-pass filters between 0.25 and 32 Hz to measure the peak amplitude on the horizontal components. Following the development of Richter (1935) local magnitude scale, we derive a functional form of maximum amplitude versus distance, but separately for each frequency band, and use them to estimate wave attenuation as a function of frequency and distance. Attenuation is a strong function of frequency, approximately proportional to 1/f, with path averaged Q increasing (attenuation decreasing) with propagation distance. We use these empirical attenuation curves to correct the time-domain peak amplitudes to a reference distance of 10 km to recover the source spectrum. We find that the spectral shape is consistent with the Brune model, showing a well-defined plateau at low frequency and a decay at high frequency proportional to ω−2. We use the median spectrum for stations at distances up to 120 km for each event to measure the moment and corner frequency. This time-domain method provides a reliable and efficient way to accurately measure earthquake source parameters.

Quantified analysis of facial movement: A reference for clinical applications.

Most techniques for evaluating unilateral impairments in facial movement yield subjective measurements. The objective of the present study was to define a reference dataset and develop a visualization tool for clinical assessments. In this prospective study, a motion capture system was used to quantify facial movements in 30 healthy adults and 2 patients. We analyzed the displacements of 105 reflective markers placed on the participant's face during five movements (M1-M5). For each marker, the primary endpoint was the maximum amplitude of displacement from the static position (M0) in an analysis of variance. The measurement precision was 0.1 mm. Significant displacements of markers were identified for M1-M5, and displacement patterns were defined. The patients and age-matched healthy participants were compared with regard to the amplitude of displacement. We created a new type of radar plot to visually represent the diagnosis and facilitate effective communication between medical professionals. In proof-of-concept experiments, we collected quantitative data on patients with facial palsy and created a patient-specific radar plot. Our new protocol for clinical facial motion capture ("quantified analysis of facial movement," QAFM) was accurate and should thus facilitate the long-term clinical follow-up of patients with facial palsy. To take account of the limitations affecting the comparison with the healthy side, we created a dataset of healthy facial movements; our method might therefore be applicable to other conditions in which movements on one or both sides of the face are impaired. The patient-specific radar plot enables clinicians to read and understand the results rapidly.

Electrical properties of the base film heterosystem Al/ITO/polyimide/Al2O3 for capacitive converter

On the basis of the conducted structural studies of thin films, a structural and technological solution was developed and a thin film capacitive transducer was created for acoustic monitoring of metal products by a capacitive method. It was determined that along with the crystalline structure of the layers, it is also necessary to control the surface electrical resistance of the conductive ITO layer, the values of which determine the possibility of using such a structure as a coating of a capacitive converter without significant losses of the useful signal, and the dielectric permeability of the Al2O3 layer, which significantly affects the value of the useful signal With the help of the four-probe method, it was established that the surface electrical resistance (R□) of ITO layers under optimal deposition conditions is equal to 8–15 Ohm/□. The study of electric power Hall results indicate that the obtained value of specific electrical resistance is determined by the concentration of the main charge carriers from about 8.3·1020 cm–3 and the mobility of the main charge carriers at the level of 44 cm2/(V·s). The results of studies of dielectric properties indicate an increase in the value of the dielectric constant of the polyimide/Al2O3 structure, which is 8.5–11.5 relative to units, relative to the polyimide film (3–3.9 relative units) by approximately 3 times at frequencies of the exciting signal in the range of 10 Hz–10 MHz. This fact confirms the assumption about the possibility of increasing the dielectric constant of the interlayer due to the application of a thin layer of Al2O3 on the polyimide film. To confirm the possibility of increasing the sensitivity of the method due to the use of a capacitive transducer based on the Al/ITO/polyimide/Al2O3 structure, in comparison with classical transducers, a series of aluminium samples was studied at an oscillation frequency of 2.5 MHz. The value of the received signal when using a thin-film converter increases by 7.6 times compared to a classic converter, which correlates well with the measurements of dielectric permeability of dielectric layers and taking into account the decrease in the thickness of the dielectric layer. Thus, the increase in the sensitivity of the capacitive method in the case of using thin-film capacitive converters based on the Al/ITO/polyimide/Al2O3 structure is experimentally confirmed. The maximum amplitude of the acoustic displacement occurs at the edge of the plate, so studies were conducted on electrodes with cutouts, which made it possible to increase the acoustic signal twice for a large internal cutout.

Vortex-induced vibration of a circular cylinder with nonlinear restoring forces at low-Reynolds number

The numerical simulation of two-dimensional flows around an elastically-mounted circular cylinder on a linear/quadratic spring configuration at low-Reynolds number (Re) is conducted in order to study the vortex-induced vibration (VIV) of the system. The extent of Re used in this study range from 50 to 150 inclusive. The data obtained from the numerical simulations are used to investigate the impact of the nonlinearity in the spring configuration on the VIV response of the dynamical system. The equivalent natural frequency for a circular cylinder supported elastically on a linear/quadratic spring is derived and found to depend on the square root of the maximum amplitude of the transverse displacement. The range of Re associated with the initial branch of the response is increased (extended) and the upper and lower branches are suppressed (almost disappearing when the hardening nonlinearity is sufficiently strong) for an elastically-mounted cylinder on a linear/quadratic spring configuration compared to that for the same cylinder supported elastically on a linear spring. The detailed characteristics (e.g., vortex shedding modes, amplitude and oscillation frequency of the transverse displacement, etc.) of the lock-in range and the transition out of this range for the VIV system as a function of increasing Re is studied using power spectrum, phase portrait and dynamical mode decomposition analysis. The information obtained from the analysis is synthesized in order to investigate the different physical mechanisms and phenomena appearing in the VIV system and how these are linked to the underlying vortex shedding and amplitude response regimes (initial branch, upper branch, desynchronization branch) of the dynamics of the fixed (stationary) and elastically-mounted cylinder.

Modeling Acoustic Emission due to an Internal Point Source in Circular Cylindrical Structures

In a previous paper [Appl. Sci. 2022, 12, 5272], we developed the first mathematical model for acoustic emission from an internal point source in a transversely isotropic cylinder. The point source, as an internal defect, is the most fundamental source generating AE in homogeneous media; it is represented by a spatiotemporal concentrated force and generates three scalar potentials for compressional, and horizontally and vertically polarized shear waves. The mathematical formulas for the displacements were derived by introducing the concentrated force-incorporated potentials into the Navier–Lamé equation. Since the publication of that paper, we detected some errors. In this paper, we correct the errors and extend the analytical modeling to a cylindrical shell structure. For acoustic emission in general circular cylindrical structures, we derived solutions by applying the boundary conditions at inner and outer surfaces of the structures. Under these conditions, we solve the radial, tangential, and axial displacement fields. Analytical simulations of the acoustic emission were carried out at several point source locations for circular cylindrical geometries. We show that the maximum amplitude of the axial displacement is dependent on the point source position and 2π-aperiodicity of the cylindrical geometry. Our mathematical formulas are very useful for characterizing AE features generated from an internal defect source in cylindrical geometries.

Design optimization of block horn for ultrasonic joining application using RSM–FEA–GA integration approach

This study investigates the design optimization of block horn used in ultrasonic insertion application. Ultrasonic insertion is the process of joining a metal insert with thermoplastic component. As the performance of ultrasonically produced joint depends upon the uniformity of amplitude of vibration generated by horn, the uniformity of displacement amplitude can be improved by optimizing the block horn design. The horn is computationally designed and acoustically analysed by integrating finite element analysis (FEA) with response surface methodology (RSM). The polynomial model for displacement amplitude is developed using RSM. Further, the design of horn is optimized to improve the displacement amplitude by coupling the developed polynomial model with genetic algorithm (GA) as fitness function. The optimized design is acoustically analysed, the results show that the optimal design yields maximum displacement amplitude of 29.57 µm, and the maximum stress induced in the optimal design is 16.3 MPa, which is much lower than fatigue strength of horn material. As the heat developed at joint is quality indicator, the temperature obtained at joint is measured using data acquisition system (DAQ). The measured temperature is 138°C, which correlates well with displacement amplitude developed by optimal design of block horn. The results of this study revealed that the proposed RSM–FEA–GA integration approach managed to find the optimal combination of design variables, which yields maximum displacement amplitude and results good joint performance.

Energy extraction via Vortex-Induced Vibrations: The effect of spring bistability

We study Vortex-Induced Vibration (VIV) of an elastically mounted cylinder placed in uniform flow using numerical simulations based on Immersed Boundary Method and theoretical analysis. We characterize the effect of bistability in elastic potential on energy harvesting from fluid flow, in which the energy generator is modeled as structural damping. A non-dimensional distance of 2β separates the two minima of the bistable spring potential. An increase in the peak energy extraction efficiency and widening of lock-in range is observed for VIV with bistable springs compared to VIV with linear springs, especially for low values of β. We report peak efficiency of 10% for VIV with bistable springs, whereas the peak efficiency for VIV with linear spring is 4%. These results can be explained by the presence of an “Equilibrium Constraint (EC)”, between oscillation amplitude and structure frequency, obtained by balancing the rate of energy production and the rate of energy dissipation due to either structural damping or electrical generators. The EC-based theory predicts that the maximum displacement amplitude depends on damping parameter b∗=2π2m∗ξ/Ur as suggested by Klamo et al. (2005), where m∗ is the solid-to-fluid mass ratio, ξ is the damping ratio and Ur is the reduced velocity of the incident fluid flow. We briefly discuss the wake structures for bistable springs for different β and b∗. We also derive a theoretical expression for oscillation amplitude and energy extraction efficiency for VIV with bistable springs, which agrees well with data from high fidelity numerical simulations, carried out in the present work.

Structural Luneburg lens for broadband ultralong subwavelength focusing

In this paper, a novel gradient index (GRIN) structural lens based on the concept of generalized Luneburg lens (GLL) is proposed. This lens allows for the realization of double foci and localization of energy flow between the two focal spots, thereby achieving ultralong focusing. The double-foci GRIN lens consists of two concentric circular regions with varying thickness defined in a thin plate structure. The two concentric circular regions are designed to realize continuous change of refractive indices with different profiles. Numerical simulations and experimental studies are performed to obtain the maximum displacement amplitude, full length at half maximum (FLHM), and full width at half maximum (FWHM) of the focal region of the lens. The results demonstrate that ultralong subwavelength focusing can be achieved for a broadband frequency range. In addition, our results show that the FLHM and FWHM can be tailored through the design of the focal length of the GLL. This offers a simple and flexible approach of engineering the GLL focusing characteristics and energy distributions for many applications.

Small size 2-DOF piezoelectric platform for unlimited locomotion

The paper represents a numerical and experimental investigation of a 2-DOF piezoelectric positioning platform that can provide unlimited locomotion in the plane. The platform's operation principle is based on the excitation of the first bending mode of piezoelectric bimorph plates. A numerical investigation of the 2-DOF platform was performed, and it was found out that the suitable vibration mode of the bimorph plates occurs at 23.54 kHz Harmonic response analysis showed that the maximum displacement amplitude of the contact reached 561.12 μm or 2.67 μm/Vp-p while an excitation signal of 210 Vp-p was applied. The experimental study was performed and showed that maximum linear velocity of 44.45 mm/s or 0.212 mm/s/Vp-p were obtained while the load of 55.68g and applied and electrical signal of 210 Vp-p was used. In addition, at the same conditions output force of the platform was measured, and it was found that the platform is able to provide 44.16 mN of output force.

Parameter Optimization and Application for the Inerter-Based Tuned Type Dynamic Vibration Absorbers

As an acceleration-type mechanical element, inerter element has been widely used in the dynamic suppressing field. In this paper, a tuned mass damper with inerter (TMDI) is presented for vibration control and energy dissipation. To evaluate the effectiveness of the TMDI, the simplified model of TMDI coupled with a single-degree-of-freedom (SDOF) structure has been established. Numerical optimization has been conducted with the goal of minimizing the maximum transfer function amplitude of displacement for the damped primary structure. The control performance and robustness for TMDI has been evaluated with the SDOF system in the frequency and time domain, compared with the classical TMD device. Lately, multiple active TMDI (MATMDI) has been proposed as a vibration suppression strategy for a multi-story steel structure. The performances of passive and active control methods have been evaluated in the time domain via real earthquake excitations, and it has proven that the MATMDI is more effective at reducing the response of the structure and the stroke of devices. The results show that the proposed optimal TMDI system can sufficiently harvest vibrational energy and enhance the robustness of structure.