Multi-degree-of-freedom Research Articles

A novel spherical ultrasonic motor with wire stators and measuring torque and preload via a new method.

The present study introduces a multi-degree-of-freedom (MDOF) ultrasonic motor, which is capable of driving a spherical rotor using spiral wire stators and a piezoelectric stack actuator. Wire stators and piezoelectric stack actuators enable the proposed motor to be smaller and simpler, lower in power consumption, and have different modes at different frequencies. In this motor, two wire stators are used to drive the spherical rotor and rotate it in different directions. The eigenfrequency and frequency domain analyses were carried out using the finite element method (FEM) to evaluate the MDOF capability of the motor in different vibration modes. It has been demonstrated that the piezoelectric stack actuator can provide MDOF motions through its vibration modes. The resonant frequency obtained by the frequency domain approach agreed with the impedance analyzer test. Rotational speed, torque, and preload force were experimentally investigated. Using shear stress caused by viscous fluid in contact with the spherical rotor, a new torque calculation method was developed. Based on the buoyancy force exerted on the immersed rotor, the preload force was measured. The experimental results indicated that the maximum rotational speed of the spherical rotor was 306rpm, and the maximum torque was 4.7 μNm.

Improved model for parametric optimization of tuned mass damper-inerter for wind-induced vibration control of high-rise building

When analyzing the wind-induced response of multi-degree-of-freedom (MDOF) structures controlled by a tuned mass damper-inerter (TMDI), a generalized single-degree-of-freedom (GSDOF) model, which represents the first-order mode is used to simplify the calculation. However, neglecting the contributions of higher modes may lead to considerable errors during the evaluation and performance of the controlling effect of TMDI, respectively, which is a threat to structural safety and functionality. Herein, an improved simplified model is derived to consider higher modes and preserve the calculation efficiency of GSDOF by introducing entries into the frequency response function (FRF) of the GSDOF model, which represents higher mode contributions weighted using equivalent coefficients. The analytical solutions of the coefficients are further derived using customized maximum tolerable errors on an H2 and H∞ norm of the FRF within the concerned frequency interval. Using a real high-rise building, the accuracy and computational efficiency of the previous simplified and improved models are quantified using different TMDI parameter combinations. The multi-objective parametric optimization of the TMDI is performed to identify a set of Pareto-optimal TMDIs, and the control performances of the representative TMDIs is designed based on both assessed models. The results show that the changes in inertance and frequency ratios greatly influence the accuracy of both simplified models. Compared with the precise and previous simplified models, the improved model presented in this study not only guarantees the accurate calculation of the standard deviation of the structural responses but also maintains the calculation efficiency.

A polynomial extrapolation-based wavelet-Galerkin method for dynamic response reconstruction

In this work we present a single scale wavelet-Galerkin method (WGM) for obtaining the linear dynamic response of single degree of freedom (SDOF) and multi-degree of freedom (MDOF) systems, the equation of motion is discretized using a polynomial extrapolation-based time stepping scheme. The aim of the study is to investigate the accuracy of the dynamic response resulting from the application of the proposed method and to explore the Daubechies wavelet types that can be used for unconditional stability. In our work we solve only for the scaling function coefficients of the displacement response, the scaling function coefficients of the velocity and the acceleration responses are obtained from the solved scaling function coefficients of the displacement function and the pertaining connection coefficients. The classical central differences method (CCDM) is used to generate consistent values of the velocity and the acceleration response to replace the distorted ones at the edges of the time interval. Stability analysis shows that the method using D6 wavelets is unconditionally stable for the practical range of the product of the time step and the frequency of vibration. An application of a SDOF system with initial conditions shows that for D6 wavelets the calculated responses at an adequate approximation level correspond well with those obtained using Newmark’s average acceleration method (AAM). The method is also applied to a MDOF system without performing a modal analysis, the resulting dynamic response is found to be accurate enough to be compared to that of the mode superposition method used by the STAAD pro program.

PENGARUH INTERAKSI TANAH-STRUKTUR PADA TANAH LUNAK TERHADAP DILATASI DARI DUA BANGUNAN TINGGI AKIBAT GEMPA

Earthquakes that occur in buildings can lead to collision force with the next building if the initial gap between the two buildings is not sufficient for its free vibration responses. Collisions can cause amplification of the internal forces in the structural elements and the collision force on the contact zone is usually not considered in the initial design so that it can lead to damage and collapse of buildings. This study aime to determine the effect of Soil-Structure Interaction in the dilatation of two structures in soft soil with consideration of the collision to the next building. The structure is modeled as a structural system with multi degree of freedom (MDOF). The upper structure is considered linear elastic model and does not have damping as well as the lower structure (foundation). The collision can only occur on the floor level of the two buildings in which the contact zone is modeled as an elastic element. The rheological model for Soil-Structure Interaction are taken as a horizontal spring and a rotational spring. Structural dynamic equations was solved by using the Houbolt integration method. The resolution of numerical program was solved by the Matlab software. The results of study showed that soil-strucutre interaction increases the relative displacement under the condition of initial distance (gap) between the two buildings was reduced.

Data set from shaking table tests of a slender MDOF structure with base-rocking mechanisms

Numerical models of seismic-resistant structures are typically validated by comparing numerically predicted key seismic response parameters to those obtained from benchmark shake table experiments. However, studies have shown that for structures rocking on rigid foundations, the seismic response can be unrepeatable in experiments and deterministically unpredictable by numerical models. Therefore, researchers have proposed to validate rigid rocking models using statistical approaches, yet no experimental study has examined whether the same observations apply to slender multi-degree-of-freedom (MDOF) free-rocking structures or controlled rocking structures with positive post-rocking stiffness and dedicated energy dissipation. This data paper describes the now publicly available data obtained from a series of 254 shaking table tests of a slender MDOF tower structure with two base-rocking mechanisms, which can be used to examine the predictability of the seismic response of an MDOF rocking structure and to statistically validate different approaches aiming to model tall and slender structures that utilize base-rocking mechanisms to mitigate the dynamic response due to higher-mode effects.

Adaptive linear quadratic regulator for optimal structural control based on wavelet transform and genetic algorithm

PurposeIn real life, excitations are highly non-stationary in frequency and amplitude, which easily induces resonant vibration to structural responses. Conventional control algorithms in this case cannot guarantee cost-effective control effort and efficient structural response alleviation. To this end, this paper proposes a novel adaptive linear quadratic regulator (LQR) by integrating wavelet transform and genetic algorithm (GA).Design/methodology/approachIn each time interval, multiresolution analysis of real-time structural responses returns filtered time signals dominated by different frequency bands. Minimization of cost function in each frequency band obtains control law and gain matrix that depend on temporal-frequency band, so suppressing resonance-induced filtered response signal can be directly achieved by regulating gain matrix in the temporal-frequency band, leading to emphasizing cost-function weights on control and state. To efficiently subdivide gain matrices in resonant and normal frequency bands, the cost-function weights are optimized by a developed procedure associated to genetic algorithm. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structures subjected to near- and far-fault ground motions are studied.FindingsResonant band requires a larger control force than non-resonant band to decay resonance-induced peak responses. The time-varying cost-function weights generate control force more cost-effective than time-invariant ones. The scheme outperforms existing control algorithms and attains the trade-off between response suppression and control force under non-stationary excitations.Originality/valueProposed control law allocates control force amounts depending upon resonant or non-resonant band in each time interval. Cost-function weights and wavelet decomposition level are formulated in an elegant manner. Genetic algorithm-based optimization cost-efficiently results in minimizing structural responses.

Blast-resistant design approach for RC bridge piers

Piers are the critical components to support the superstructure of bridge, but susceptible to the intentional and accidental explosions due to its easy accessibility. The blast-induced damage to the pier may cause the entire bridge to collapse, resulting in huge casualties and economy loss, and thus it is necessary to perform the blast-resistant design for the bridge pier. At present, the analytical model and blast-resistant design approach for blast-loaded reinforced concrete (RC) pier considering both the direct shear and flexural responses were studied. Firstly, six shots of field ground explosion test on 1/5-scale circular and square RC columns were carried out, in which the TNT charges with the scaled distances of 0.86–1.22 m/kg1/3 were adopted. Then, the corresponding numerical simulations incorporating the newly developed Structured Arbitrary Lagrangian Eulerian (SALE) solver were conducted, and the validity of finite element (FE) analysis approach was verified by comparing the experimental incident and reflected overpressure-time histories acting on the periphery of pier with deviations for most measuring points less than 20%. Afterwards, total 176 explosion scenarios were numerically simulated, and a blast loading distribution model on the pier for ground explosions was proposed, which considers the pier cross-section shapes (circular and square) and pier diameter/edge length (0.2–1.6 m), the scaled distances of explosive charge (0.3–2.3 m/kg1/3), as well as the blast wave reflection and diffraction by the pier. Furthermore, a Timoshenko beam-based multi-degree of freedom (MDOF) analytical model was established, and validated by both the existing explosion tests on RC columns and refined numerical simulations of blast-loaded bridge piers with corresponding deviations no more than 5%. Finally, a blast-resistant design procedure incorporating the above-proposed blast loading distribution and MDOF models was given, providing a reliable and efficient blast-resistant evaluation and design tool for bridge piers.

Design of Optimal Passive Tuned Mass Damper with Static Output Feedback and Updating Iterative Procedure

In this study, the optimal design issue of a passive tuned mass damper (TMD) was transformed into the nonsparse control gain matrix optimization problem, and a general passive TMD optimization design method to minimize structural mean square responses or impulse response is therefore proposed. The proposed optimization procedure combines the static output feedback (also known as direct output feedback) algorithm and the updating iterative procedure. The proposed method can be applied to variant design scenario, whether the main structure is single-degree-of-freedom (SDOF) or multidegree-of-freedom (MDOF) structures, undamped or damped structures, subjected to wind disturbances or earthquake excitations. In addition, the proposed method is capable to consider the excitation shaping filter, so the design results are more suitable for practical application. The design procedure of the proposed method is presented, and all the required weighting matrices are introduced and derived in detail. Firstly, the SDOF structures are used as the main structure to demonstrate the correctness of the proposed method. The numerical simulation results verify that the obtained optimal design parameters of TMD were found identical to some cases which contain the analytic solution. The accuracy and feasibility of the proposed design method are confirmed. Finally, a passive TMD is optimally designed for a 5-story MDOF structure subjected to Kanai–Tajimi spectrum comparable earthquakes and a 60-story high-rise MDOF structure subjected to Davenport spectrum comparable wind loads for demonstration.

Simplified Estimation Method of Plastic Energy Dissipation for MDOF Systems Using Force Analogy Method

Plastic energy dissipation is a key factor in the response of inelastic structures subjected to seismic input, and is often regarded as a primary source of structural damage due to the inelastic deformation of structural components. Accurately predicting a structure’s plastic energy dissipation is essential for efficient energy-based design and seismic assessment. While a single-degree-of-freedom (SDOF) system provides a simple and effective method for estimating plastic energy dissipation, few studies have explored the use of nonlinear analysis methods or equivalent SDOF systems for this purpose. Based on the principle-of-force-analogy method, firstly, the formulas of plastic energy dissipation of a multi-degree-of-freedom (MDOF) system and its equivalent SDOF system were established. Secondly, two estimation methods of plastic energy dissipation of MDOF systems were proposed. Finally, numerical simulations were performed on several multi-story and high-rise structures with varying heights and spans to compare the plastic energy dissipation of MDOF systems and the equivalent SDOF systems of different modes. The simulation results demonstrate that the proposed methods and formulas accurately estimate plastic energy dissipation in multi-story and high-rise structures, while also requiring fewer calculations and less storage.

Energy-based procedures for seismic fragility analysis of mainshock-damaged buildings

In recent decades, significant research efforts have been devoted to developing fragility and vulnerability models for mainshock-damaged buildings, i.e., depending on the attained damage state after a mainshock ground motion (state-dependent fragility/vulnerability relationships). Displacement-based peak quantities, such as the maximum interstory drift ratio, are widely adopted in fragility analysis to define both engineering demands and structural capacities at the global and/or local levels. However, when considering ground-motion sequences, the use of peak quantities may lead to statistical inconsistencies (e.g., fragility curves’ crossings) due to inadequate consideration of damage accumulation. In this context, energy-based engineering demand parameters (EDPs), explicitly accounting for cumulative damage, can help address this issue. This paper provides an overview of recent findings on the development of aftershock-fragility models of mainshock-damaged buildings. Particular focus is given to state-of-the-art frameworks for fragility analyses based on cumulative damage parameters. Moreover, a literature review on damage indices and energy-based concepts and approaches in earthquake engineering is reported to better understand the main advantages of the mostly adopted energy-based parameters, as well as their limitations. Different refinement levels of seismic response analyses to derive fragility relationships of mainshock-damaged buildings are also discussed. Finally, the benefits of adopting energy-based EDPs rather than, or in addition to, peak quantities in state-dependent fragility analyses are demonstrated on a reinforced concrete frame building. Specifically, a refined lumped plasticity modeling approach is adopted, and sequential cloud-based time-history analyses of a Multi-Degree-of-Freedom (MDoF) model are carried out. The results highlight that energy-based approaches for fragility analysis effectively capture damage accumulation during earthquake sequences without inconsistencies in the obtained statistical models. On the other hand, estimating global or local structural capacity in terms of cumulative EDPs is still challenging. Further experimental data are needed to better calibrate the quantification of energy-based damaged states.

SWINGO: Conceptualisation, modelling, and control of a swinging omnidirectional wave energy converter

The vast majority of existing wave energy converter (WEC) technologies are designed to absorb wave power through a single mode of motion, often constraining the device on the remaining degrees-of-freedom (DoF) or neglecting their effects on the system dynamics and resulting power production. This paper introduces a novel multi DoF WEC designed to harvest wave power through the mechanical coupling of a gyropendulum system, parametrically excited by a moored floater. The gyropendulum mechanism is a hybrid technology that can incorporate, in a single body, the properties of both pendulum and gyroscope mechanics, ensuring effective energy harvesting in virtually every operational condition, i.e. making it suitable for multidirectional sea wave scatters. The gyropendulum versatility is enhanced during intermediate wave directions, in which both pitch and roll rotation are induced on the floater, prompting both gyroscopic effects, and the elasticity reaction forces on the mechanism. Relaying on such properties, the swinging omnidirectional (SWINGO) device can absorb wave power independently from the excited DoF, and therefore guaranteeing energy extraction independently of the incoming wave direction. System analysis and dynamic properties of the SWINGO system are computed by performing sensitivity studies, through the variation of both geometric properties and control conditions of the gyropendulum mechanism. For these purposes, we apply impedance-matching theory to explore the dynamic characteristics of the system under controlled conditions, and its performance in terms of power, making explicit emphasis in its main characteristics.

Influence of biomechanical compliance on control performance of a magnetorheological sliding seat system

We investigate the feasibility of a sliding seat with a magnetorheological (MR) energy absorber (MREA) to minimize loads transmitted to a payload in a ground vehicle for frontal impact speeds ranging as high as 7 m/s (15.7 mph). The crash pulse for a given impact speed was assumed to be a rectangular deceleration pulse having a prescribed magnitude and duration. The control objective is to bring the seat system to rest using the available stroke, while accommodating changes in impact velocity and occupant mass ranging from a 5th percentile female to a 95th percentile male. The seat system was first treated as a single-degree-of-freedom (SDOF) rigid occupant (RO) model, and two control algorithms are developed: (1) constant Bingham number control and (2) constant force control. To explore the effects of occupant compliance on the adaptive seat system performance, a multi-degree-of-freedom (MDOF) compliant occupant (CO) model was integrated with the seat mass and the same control algorithms were used. Simulation results showed that the designed adaptive controllers successfully controlled load-stroke profiles to bring the seat system to rest in the available stroke and reduced occupant decelerations. Analysis showed extensive coupling between the seat structures and occupant biodynamic response.

Validation of an Analytical Model for the Acoustic Impedance Eduction of Multicavity Resonant Liners by a High-Fidelity Large Eddy Simulation Approach

Abstract The massive growth of the air traffic during the last years is leading to stricter limitations on the noise emission levels radiated from aircraft engines. To face this issue, the installation of acoustic liners on the intake duct and the exhaust nozzles is a common strategy adopted to properly abate noise emissions coming from the fan, the compressor, the turbine, and the jet. In this context, the aim of the present article is to use high-fidelity large Eddy simulation (LES) to validate a multi-degree-of-freedom (MDOF) extension of the single-degree-of-freedom (SDOF) and double-degree-of-freedom (DDOF) analytical model provided by Hersh for impedance eduction of acoustic liners. First, the results of the original Hersh model are compared with LES calculations performed with the openfoam suite on a single-orifice and single-cavity layout (SDOF). Then the extension of the Hersh model to multicavity (MDOF) geometries by using a recursive formulation is presented. Finally, high-fidelity simulations are carried out for single-orifice and multicavity (MDOF) configurations to validate the method extension and to understand how resonant coupling and acoustic impedance are affected by multicavity resonant elements. The excellent agreement between the high-fidelity results and the analytical predictions for the single-cavity pattern confirms that the Hersh model is a useful formulation for a preliminary design of a SDOF acoustic liner. The model extension to MDOF configurations enables the designers to broaden the design space, and thus, a validated analytical method is strictly necessary to perform sensitivity studies to the multicavity geometrical parameters (i.e., facesheet thickness, cavities depth, porosity). Basically, a multicavity configuration makes the liner element resonate at different frequencies, leading to multiple absorption peaks in the audible range. In this way, the acoustic performance of the liner is extended to a wider frequency range, overcoming the limitations of a traditional SDOF configuration.

Frequency domain transfer function based multimodal design method for seismic mitigation of building structures

Multiple tuned mass dampers (MTMD) are widely used to mitigate structural seismic response. With the emergence of more and more high-rise buildings, various MTMD design methods applicable to multi degree of freedom (MDOF) model have been developed. However, the existing MTMD design methods for MDOF models often involve complex optimization algorithms. In order to simplify the MTMD design while effectively reducing the seismic response of the structure, this paper proposes an explicit frequency domain transfer function, theoretically showing the mechanism of decomposing the seismic mitigation of MDOF model into simultaneous seismic mitigation of multiple modes, and developed a theoretical design method of MTMD, so that the dynamic parameters and position of each TMD can be directly obtained based on the developed explicit design formula. A benchmark model was used as an example to verify the seismic mitigation performance. It is shown that the developed multimodal control MTMD design method achieves 22.25% reduction rate of acceleration and 18.5% reduction rate of displacement with 3% mass ratio.

Structure Design of Multi-DOF Motor with Stator Permanent Magnet based on Flux Switching

This paper aims at the problems of no core in the stator coil of a compact multi-degree-of-freedom (M-DOF) motor, i.e., small output torque and low power density. In order to increase the output torque, a stator permanent magnet spherical motor based on flux switching is proposed. Firstly, the principle of flux switching is introduced. The basic structure of the new motor is preliminarily designed, and the motion mechanism is analysed for spin motion and tilt motion respectively. Then the minimum model of a novel motor is established in ANSYS by using the virtual displacement method. The key parameters such as the ratio of stator pole tooth to permanent magnet size, different stator pole tooth end structures, different pole tooth surface shapes, different pole sizes, permanent magnet thickness, different magnetisation methods and different ampere-turn numbers are optimised within a reasonable parameter range. The simulation results are analysed and discussed, and the optimal results for each key parameter are thus given. Finally, considering the arrangement of the stator and rotor poles, the rationality of the three-DOF motion was verified by means of two energising strategies, spin motion and tilt motion, verified the reasonableness of the above optimal parameters and thus determined the structural parameters of the new spherical motor to accomplish the three-DOF motion and the maximum torque range. The simulation results show that the electromagnetic torque varies approximately linearly over a range of ampere-turns for the same position of the rotor pole teeth. It provides an opportunity for the M-DOF motor design of a high torque output and power density.

Experimental investigation of wind effects on a 282-meter-high tower with complex aerodynamic shapes based on a rigid model and multi-degree-of-freedom aeroelastic model

Slender and flexible high-rise structures are very sensitive to large wind-induced vibration phenomena such as vortex-induced vibration and galloping under strong winds. However, pressure measurements on rigid models cannot consider coupling aeroelastic effects, and single-degree-of-freedom aeroelastic model wind tunnel tests can only consider the contribution of the first-order linear mode. For wind-sensitive structures with complex aerodynamic shapes, the effect of higher-order modes on the wind-induced response may not be ignored. In this study, a series of multi-degree-of-freedom (MDOF) aeroelastic model wind tunnel tests and pressure measurements of a rigid model were conducted to comparatively investigate the wind effects of a 282-meter-high tower with complex aerodynamic shapes. A detailed analysis of the aeroelastic effects on the high-rise tower is presented, and the effects of the structural damping ratio, wind speed, and wind direction are also discussed. The results show that the variation trends of the peak acceleration responses are generally consistent, while in those wind-sensitive directions (165-degree wind direction), the peak acceleration responses of the MDOF model are almost 1.5 times larger than those of the rigid model, indicating that the aeroelastic effects are remarkable. The corresponding response spectral peak values of the MDOF model are significantly larger than those of the rigid model by a factor of more than 3 and the correlations of responses in the two orthogonal directions also increase greatly by 43.5%. However, the “set-back” aerodynamic shape (180-degree wind direction) can considerably weaken aeroelastic effects and the peak acceleration responses are close to those of the rigid model. The generalized aerodynamic force spectrum also shows broadband features, implying its superior aerodynamic performance. The comfort assessments for different structural damping ratios are conducted based on various codes and criteria, suggesting that the structural damping ratio should be larger than 3%. The equivalent static wind loads on the upper floors are notably affected by aeroelastic effects while the lower floors are relatively insensitive. This study provides a detailed perspective of the aeroelastic effect for slender tower, and hence facilitates the wind-resistant design of flexible structures.

A broadband metamaterial damper design based on synergetic coupling among multi-cells

This paper proposes a broadband damping method to achieve broadband vibration absorption by superposition of the working bands of several damping units. The device composes of several local resonant metamaterial dampers with gradient elastic wave band gaps via weak coupling. By integrating the units with band gaps in different frequency ranges in parallel, a linear superposition of the absorption bandwidth can be achieved. This property overcomes the shortcomings of the traditional dynamic vibration absorbers (DVAs) or metamaterial dampers with narrow working bands, and provides a solution for broadband low-frequency vibration attenuation. Compared to conventional multi-degree-of-freedom (MDOF) DVAs, this design belongs to a special metamaterial-based MDOF damper that could satisfy both low damping ratio and weak coupling conditions. As the working bandwidth of each sub-unit could be optimized by changing structural parameters and structural forms, the available design parameters are significantly increased. Moreover, the sizes of the damper device and each sub-unit are sub-wavelength, so the additional mass is greatly lower than that of the traditional DVA. The design method and device proposed in this paper are expected to be widely used in the broadband low-frequency vibration suppression of various types of machinery and equipment.

Construct Validity of a Novel Assessment System for Laparoscopic Suture Accuracy Based on Stereoscopy.

An accurate and objective measuring tool is lacking for laparoscopic suture accuracy assessment in simulation training. We designed and developed the suture accuracy testing system (SATS) and aimed to determine its construct validity in this study. Twenty laparoscopic experts and 20 novices were recruited to perform a suturing task in three sessions using traditional laparoscopic instruments (Tra. session), a handheld multi-degree-of-freedom (MDoF) laparoscopic instrument (MDoF session) and a surgical robot (Rob. session), respectively. The needle entry and exit errors were calculated using the SATS and compared between the two groups. No significant difference of the needle entry error was found in all comparisons. As for the needle exit error, the value of the novice group was significantly higher than that of the expert group in Tra. session (3.48 ± 0.61mm vs. 0.85 ± 0.14mm; p = 1.451e-11) and MDoF session (2.65 ± 0.41mm vs. 1.06 ± 0.17mm; p = 1.451e-11) but not in Rob. session (0.51 ± 0.12mm vs. 0.45 ± 0.08mm; p = 0.091). The SATS demonstrates construct validity. Surgeons' experience in conventional laparoscopic instruments could be transferred to the MDoF instrument. Surgical robot helps to improve suture accuracy and may bridge the experience gap between laparoscopic experts and novices in basic exercises.

Multi-Objective Design Optimization of Multiple Tuned Mass Dampers for Attenuation of Dynamic Aeroelastic Response of Aerospace Structures

This paper proposes a design procedure to determine the optimal configuration of multi-degrees of freedom (MDOF) multiple tuned mass dampers (MTMD) to mitigate the global dynamic aeroelastic response of aerospace structures. The computation of the aerodynamic excitations is performed considering two models of atmospheric disturbances, namely, the Power Spectral Density (PSD) modelled with the Davenport Spectrum (DS) and the Tuned Discrete Gust (TDG) with the one-minus cosine profile. In order to determine the optimum sets of MTMD, a Multi-objective design Optimization considering Genetic Algorithm (MOGA) is implemented, where the selected fitness functions for the analysis are the minimization of the total mass of the resonators as well as the concurrent minimization of the peak displacements of a specified structural node in all translational degrees of freedom. A case study is presented to demonstrate the proposed methodology, where the optimal sets of MTMD are determined for the concurrent minimization of the pointing error of a truss-like antenna structure as well as the mass of the considered MTMD. It is found that the placement of the MTMD in the primary reflector of the antenna structure provided a maximum reduction in the pointing error of 62.0% and 39.2%, considering the PSD and the TDG models, respectively. Finally, this paper presents an advanced framework to estimate optimal parameters of MTMD control devices under convoluted loading cases as an initial step towards the use of such passive systems in applications that commonly employ active or semi-active solutions.

ダイナミック・マスを用いたTMDに関する最適設計条件の導出及び振動実験による検証

This paper derives the optimal design conditions by the relational expression of natural period and propose the design method for the tuned mass damper (TMD) using a rotary inertial mass damper called DTMD. It shows the design example for the multi degree of freedom (MDOF) system, and confirms the damping effect of DTMD by the response analysis. In addition, it verifies the proposed theory and confirms the control effect on the actual structure by the vibration tests.