Multi-degree-of-freedom Research Articles

Whole-Body Teleoperation Control of Dual-Arm Robot Using Sensor Fusion.

As human-robot interaction and teleoperation technologies advance, anthropomorphic control of humanoid arms has garnered increasing attention. However, accurately translating sensor-detected arm motions to the multi-degree freedom of a humanoid robotic arm is challenging, primarily due to occlusion issues with single-sensor setups, which reduce recognition accuracy. To overcome this problem, we propose a human-like arm control strategy based on multi-sensor fusion. We defined the finger bending angle to represent finger posture and employed a depth camera to capture arm movement. Consequently, we developed an arm movement tracking system and achieved anthropomorphic control of the imitation human arm. Finally, we verified our proposed method's effectiveness through a series of experiments, evaluating the system's robustness and real-time performance. The experimental results show that this control strategy can control the motion of the humanoid arm stably, and maintain a high recognition accuracy in the face of complex situations such as occlusion.

Optimisation of the Parameters of a Vibration Damper Installed on a Historic Bridge

Abstract The paper presents theoretical analyses of renovating a historical bridge in order to decrease stresses. The installation of additional equipment, including a vibration absorber, is relatively easy to perform if such a need is indicated by the current bridge diagnostics or the monitoring of the structure’s vibrations. Moreover, absorbers could be mounted in such a way as not to alter the appearance of the historic structure. The authors focused on the problem of optimising the cooperation between a dynamic vibration absorber (DVA) and a structure under dynamic load moving with constant velocity. A simple degree of freedom (SDOF) system – as a model of the absorber and a multi-degree of freedom (MDOF) system – as the primary structure, were adopted in the calculations. Every force is regarded as a random variable, as well as interarrivals of moving forces. Two different situations and solutions were presented. The first case is when the stream of moving forces with a constant velocity is modelled as the filtered Poisson process. The second one when one of the forces is located in the point of the beam in which the response of the beam has the maximum value.

A high-fidelity model for nonlinear self-excited oscillations in rotary drilling systems

This paper presents an integrated model to analyze self-excited axial and torsional vibrations in rotary drilling systems using realistic PDC bits. The model combines a multi-degree-of-freedom (MDOF) drillstring representation with a detailed PDC bit–rock interaction model, accounting for cutter layouts and rock properties. The bit–rock interaction is described by rate-independent laws for reactive force and torque, encompassing cutting and frictional contact at the cutter face and wear flat. The regenerative rock cutting introduces state-dependent delays (up to 100) due to complex cutter layout of the bit, while the unilateral nature of frictional contact is formulated as a nonlinear boundary condition. The state-dependent delays are transformed into constant angular offsets prescribed by the bit design by introducing a bit trajectory function whose evolution is governed by a partial differential equation (PDE), which is coupled with the drillstring dynamics described by ordinary differential equations (ODEs). The Galerkin method with Chebyshev polynomials transforms the set of coupled PDE–ODEs into a system of ODEs. This approach bypasses the need to search for multiple delays at each time step, allowing implementation of this integrated rock-bit-drillstring model. Simulation results replicate field observed torque-on-bit (TOB) effects including velocity-weakening and hysteresis due to torsional stick–slips, attributing them to cutting depth variation rather than downhole friction. Preliminary findings regarding the influence of bit design on torsional stick–slips align with field drilling practices. The results of parametric study correspond to field test observations, enabling analysis of bit design, drillstring configuration, and drilling parameters on self-excited torsional stick–slips.

An efficient framework for structural seismic collapse capacity assessment based on an equivalent SDOF system

Assessing the structural collapse capacity efficiently and accurately is a key issue in earthquake engineering. Here, an efficient framework for structural seismic collapse capacity assessment based on an accurate equivalent single-degree-of-freedom (ESDOF) system is proposed. The corresponding ESDOF system is calibrated by matching the cyclic static pushover (SPO) curves of a more complex multi-degree-of-freedom (MDOF) system (e.g., high-fidelity finite element models) through a meta-heuristic optimization method. In this way, both the backbone curve and hysteretic characteristics (the stiffness and strength deterioration, and pinching behavior) of the complex MDOF system are considered in the corresponding ESDOF system. Then, incremental dynamic analysis (IDA) is carried out to assess the structural seismic collapse capacity using the ESDOF system instead of the corresponding MDOF system to improve the computational efficiency. The efficiency and accuracy of the proposed framework have been validated through three case studies, including a bare reinforced concrete (RC) frame, a steel frame, and an infilled wall RC frame. These results affirm that the proposed framework can accurately and efficiently assess the collapse capacity of low-rise bare and infilled RC frame structures, as well as steel frame structures.

Mechanism study on the effect of floor rotation angle on supported tuned mass damper system of high-rise structure

The bending deformation of the super high-rise structures will cause floor rotation angle, and thus affect the vibration reduction effect of the supported tuned mass damper (TMD) system. This paper proposes a motion equation of the TMD control system with the effect of floor rotation angle. Firstly, a finite element model of the supported TMD control system was established by ETABS. Secondly, the formation and floor rotation angle parameters of the structure were obtained by ETABS modal analysis. Then, the structures ETABS model is simplified into a multi-degree-of-freedom (MDOF) model based on the dynamic characteristics of the structure. This paper also presents an evaluation index of the effect of floor rotation angle on the supported TMD system and a supported TMD control system is selected as a simulation example. The relationship between the floor rotation angle coefficient and the TMD parameters is later parametric analyzed. Finally, experiments were designed to verify the effect of floor rotation angle on the supported TMD control system. The experimental results show that the relationship between the rotation angle of the first formation floor and the generalized displacement of the first formation of the assumed structure is close to linear. Therefore, the effect of floor rotation angle of the structure is highly recommended to be considered as an important factor for the design of the supported TMD control system for super high-rise structures.

The Data Assimilation Approach in a Multilayered Uncertainty Space

The simultaneous consideration of a numerical model and of different observations can be achieved using data-assimilation methods. In this contribution, the ensemble Kalman filter (EnKF) is applied to obtain the system-state development and also an estimation of unknown model parameters. An extension of the Kalman filter used is presented for the case of uncertain model parameters, which should not or cannot be estimated due to a lack of necessary measurements. It is shown that incorrectly assumed probability density functions for present uncertainties adversely affect the model parameter to be estimated. Therefore, the problem is embedded in a multilayered uncertainty space consisting of the stochastic space, the interval space, and the fuzzy space. Then, we propose classifying all present uncertainties into aleatory and epistemic ones. Aleatorically uncertain parameters can be used directly within the EnKF without an increase in computational costs and without the necessity of additional methods for the output evaluation. Epistemically uncertain parameters cannot be integrated into the classical EnKF procedure, so a multilayered uncertainty space is defined, leading to inevitable higher computational costs. Various possibilities for uncertainty quantification based on probability and possibility theory are shown, and the influence on the results is analyzed in an academic example. Here, uncertainties in the initial conditions are of less importance compared to uncertainties in system parameters that continuously influence the system state and the model parameter estimation. Finally, the proposed extension using a multilayered uncertainty space is applied on a multi-degree-of-freedom (MDOF) laboratory structure: a beam made of stainless steel with synthetic data or real measured data of vertical accelerations. Young’s modulus as a model parameter can be estimated in a reasonable range, independently of the measurement data generation.

Wind-induced vibration control of tall buildings by designing the overhead fire water tanks as compliant deep tank dampers-inerter

Building codes often mandate the installation of overhead fire water tanks (OFWTs) on multi-storeyed buildings. The present study proposes a cost-effective solution by utilizing these OFWTs as tuned liquid dampers (TLDs) in tall buildings to improve serviceability under wind-induced excitation. However, designing OFWTs as TLDs is often hindered by the deep nature of the OFWTs and practical constraints in dimensioning the tank as per the tuning requirement. To alleviate these hindrances, the OFWT is designed as a compliant deep tank damper-inerter (CDTDI). A compliant damper system is achieved by connecting the tank with the building through spring and dashpot elements. This allows relative motion of the whole tank with respect to the building. Further, an inerter is employed to improve the efficiency of the compliant damper. Three example buildings, 20-, 30-, and 40-storeyed, are considered and modeled as multi-degrees-of-freedom (MDOF) systems. The CDTDI-MDOF structural system’s motion equations are formulated. An excitation-independent, genetic algorithm-based single-objective optimization is performed to estimate the optimum CDTDI parameters. Sequentially, the 2nd-order or H2 and infinity or H∞ norms of the transfer function of the roof displacement are chosen as objective function. The efficacy of the CDTDI is examined by subjecting the structure to 10 simulated wind excitations. The results reveal the proficiency of the CDTDI in controlling the multiple modes of the structure, alongside providing significant damping. The CDTDI induces up to 25 and 21 % reduction, respectively, in the peak roof displacement and peak roof acceleration of the example buildings. Further, CDTDI with parameters obtained through H∞ optimization is found to be relatively better performing.

Design and optimization of roof-top fire water tanks as compliant deep tank dampers-inerter for seismic protection of multi-storeyed buildings

Water tanks are installed on the roofs of high-rise buildings for services and to fight fire outbreaks. These tanks are often considered unsuitable for design as tuned liquid dampers (TLDs) and have higher depth ratios than that required in conventional TLDs due to practical constraints in dimensioning the tank as per the tuning requirement. The present work aims at alleviating these hindrances and utilizing deep water storage tanks as effective passive damping devices for the host building. In this paper, a water storage tank for firefighting, situated on the roof of a building, is designed as a compliant deep tank damper inerter (CDTDI) in controlling the response of the host building subjected to seismic excitations. The tank is flexibly connected to the building through spring and damping elements to act as a compliant damper system. Further, the tuning effect, mass, and damping enhancement potential of an inerter element are employed to improve the volumetric efficiency of the compliant damper system. Two example buildings, 10- and 20-storey, are taken up and modeled as multi-degree-of-freedom (MDOF) systems whose masses are lumped at storey levels. The coupled dynamic equations of motion of the CDTDI-MDOF structural system are formed and solved in the time domain using the Newmark-β method. An external excitation-dependent, multi-objective Grey Wolf optimization is performed to estimate the optimum CDTDI parameters by subjecting the buildings to 100 recorded seismic ground excitations. The average values of the peak roof displacement, the maximum inter-storey drift ratio, and the peak floor acceleration are considered objective functions of the optimization. The results reveal the proficiency of the CDTDI in controlling the multiple modes of the structure. Further, the optimally designed CDTDI provides significant damping and stability to the structure, which is evident from the energy plots.

Dynamic coupling of multi-degrees of freedom constrained-layer vibration neutralizers: A new methodology

Dynamic neutralizers, also known as dynamic absorbers, are efficient means of mitigating vibrations in structures. They have been particularly effective in addressing broad-band passive vibration control in structures with high modal density through the use of multi-degrees of freedom (MDoF) and viscoelastic materials (VEMs). Therefore, sandwich-type or constrained-layer beams can offer great potential when used as MDoF control devices. However, there is limited literature exploring these structures as auxiliary systems, with coupling typically assumed to be single-point and limited to only translational degrees of freedom (DoFs). In this context, this article presents a methodology to determine the dynamic behavior of a compound system, coupling the displacement and rotation DoFs between a metal structure–referred to as the primary system–and a MDoF auxiliary system. The coupling is achieved by utilizing an equivalent dynamic stiffness obtained at the base of the auxiliary system through ANSYS finite-element software, providing a robust and comprehensive approach. A Matlab code transfers the auxiliary system's geometry and properties to ANSYS, where the dynamic stiffness at the base is determined and subsequently coupled to the primary system. A MDoF auxiliary system of the constrained-layer type with VEM was studied, and both single-point and distributed coupling were analyzed. The auxiliary system was attached to a cantilever metal beam for numerical and experimental validation. The proposed generalized equivalent dynamic stiffness model accurately estimates the response of the compound system, offering a 25% reduction in response computation time compared to the finite-element model of the complete compound system. This methodology enables the accurate representation of compound system dynamics while minimizing computational time, making it valuable for the optimal design of a set of MDoF viscoelastic dynamic neutralizers.

Seismic Behavior of Colliding Buildings, Incorporating Soil-structure Interaction and Accounting for Variability in Structural Parameters, Soil Parameters, and Seismic Action

Pounding between buildings that are not sufficiently separated has been observed several times during earthquakes. This destructive impact may severely damage the structure and lead to its collapse. Although it is impossible to completely eliminate such losses, measures can be taken to minimize them. This article investigates the effect of the variability of structural parameters, soil parameters, and seismic action on the seismic response of two colliding buildings, taking the soil-structure interaction (SSI) into account. Two adjacent structures closely separated, modeled as inelastic lumped mass systems with different structural characteristics, were considered in this study. Both structures were modeled in the analysis using multi-degree-of-freedom (MDOF) systems, and the pounding was simulated using the modified linear viscoelastic model. The analysis was conducted in two cases: probabilistic analysis and deterministic analysis. Probability curves were established to analyze the effect of the variability of the parameters on the responses of the two colliding buildings. The comparison between the two analyses indicates that the probabilistic analysis is more precise than the deterministic analysis. It has been indicated that taking into account the variability of structural parameters, soil parameters, and seismic action is efficient in determining the realistic behavior of colliding buildings. Additionally, pounding is more critical in the case of buildings founded on very soft soil, followed by those on soft soil, then on hard soil, and finally on rocky soil.

Full-body Human Motion Reconstruction with Sparse Joint Tracking Using Flexible Sensors

Human motion tracking is a fundamental building block for various applications including computer animation, human-computer interaction, healthcare, and so on. To reduce the burden of wearing multiple sensors, human motion prediction from sparse sensor inputs has become a hot topic in human motion tracking. However, such predictions are non-trivial as (i) the widely adopted data-driven approaches can easily collapse to average poses, and (ii) the predicted motions contain unnatural jitters. In this work, we address the aforementioned issues by proposing a novel framework which can accurately predict the human joint moving angles from the signals of only four flexible sensors, thereby achieving the tracking of human joints in multi-degrees of freedom. Specifically, we mitigate the collapse to average poses by implementing the model with a Bi-LSTM neural network that makes full use of short-time sequence information; we reduce jitters by adding a median pooling layer to the network, which smooths consecutive motions. Although being bio-compatible and ideal for improving the wearing experience, the flexible sensors are prone to aging which increases prediction errors. Observing that the aging of flexible sensors usually results in drifts of their resistance ranges, we further propose a novel dynamic calibration technique to rescale sensor ranges, which further improves the prediction accuracy. Experimental results show that our method achieves a low and stable tracking error of 4.51 degrees across different motion types with only four sensors.

MLPER: A Machine Learning-Based Prediction Model for Building Earthquake Response Using Ambient Vibration Measurements

Deep neural networks (DNNs) have gained prominence in addressing regression problems, offering versatile architectural designs that cater to various applications. In the field of earthquake engineering, seismic response prediction is a critical area of study. Simplified models such as single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems have traditionally provided valuable insights into structural behavior, known for their computational efficiency facilitating faster simulations. However, these models have notable limitations in capturing the nuanced nonlinear behavior of structures and the spatial variability of ground motions. This study focuses on leveraging ambient vibration (AV) measurements of buildings, combined with earthquake (EQ) time-history data, to create a predictive model using a neural network (NN) in image format. The primary objective is to predict a specific building’s earthquake response accurately. The training dataset consists of 1197 MDOF 2D shear models, generating a total of 32,319 training samples. To evaluate the performance of the proposed model, termed MLPER (machine learning-based prediction of building structures’ earthquake response), several metrics are employed. These include the mean absolute percentage error (MAPE) and the mean deviation angle (MDA) for comparisons in the time domain. Additionally, we assess magnitude-squared coherence values and phase differences (Δφ) for comparisons in the frequency domain. This study underscores the potential of the MLPER as a reliable tool for predicting building earthquake responses, addressing the limitations of simplified models. By integrating AV measurements and EQ time-history data into a neural network framework, the MLPER offers a promising avenue for enhancing our understanding of structural behavior during seismic events, ultimately contributing to improved earthquake resilience in building design and engineering.

Development of a 3-DOF rotary piezoelectric actuator with compact structure

Piezoelectric actuators have been widely applied in precision electromechanical equipment due to their high resolution, fast response, and flexible structure. However, existing rotary piezoelectric actuators still face the contradiction between the structure miniaturization and the multi degrees of freedom (MDOF) motion output. Therefore, a novel rotary piezoelectric actuator is developed to achieve characteristics of compact structure and 3-DOF motions in this study, in which an orthogonal axis support system for a spherical rotor is adopted. And a stick-slip combined direct excitation scheme is designed to obtain large working range and microradian-resolution outputs. The configuration and motion principle are designed and illustrated in detail. The statics model is established for structural optimization design and parameters determination. The actuator prototype is fabricated and tested, a compact structure is achieved with an overall size of 72 mm in diameter and 80 mm in height. 3-DOF full circle rotary motion outputs around axes X, Y and Z are achieved, the corresponding maximum rotary speeds are 0.423, 0.438, and 0.975 rad/s, and the corresponding resolutions are 4.14, 4.28 and 2.32 μrad, respectively. Moreover, the prototype has successfully completed the imaging application of multi objects in large working range. The experimental results preliminarily demonstrate the potential application of the 3-DOF rotary piezoelectric actuator in the field requiring large working range and microradian-resolution.

Simplified Nonlinear Dynamic Analysis by Hexagonal Collapse Surface Model of Steel Frame Structure

AbstractBased on the need for effective evaluation of multistorey structures response to seismic loading, this research includes the study of simplified nonlinear dynamic analysis (SNDA) by hexagonal collapse surface model. Existing conventional analysis methods such as FEMA440, restrict the extended use of Nonlinear Static Procedure (NSP) and Nonlinear Dynamic Procedure (NDP) by using the equivalent one‐degree‐of‐freedom (SDOF) model on multi‐degree‐of‐freedom (MDOF) structure. A large error known as Multiple‐Degree‐of Freedom Effects occurs in the elastoplastic behavior. To overcome the limitations of this analysis technique, the understanding of it in the entire structural system due to the influence of the higher‐order vibration modes are investigated, in addition to distinguish the elastoplastic behavior of a structure more precisely. Based on the important collapse mechanisms that are probable to occur during earthquake response, the development of a simplified dynamic analysis technique in which higher‐order vibration mode components were extracted to construct the plastic collapse safety region of a structure. Simplified nonlinear dynamic analysis (SNDA) aims to develop such method whereby multiple vibration mode components are properly considered. Primary and secondary mode of vibrations are generally examined with multiple load patterns corresponding to the condition whereby several independent variables reach maximum concurrently. The formation of hexagonal plastic collapse surface from the probability limit analysis based on proportional load results was discussed. The target for this study is to investigate the competency of this simplified analysis approach in seismic response of structure evaluating techniques.

A two-step method to locate multiple local nonlinearities

Nonlinear localization is an important component of structural nonlinear identification. Its accuracy is of great significance for damage localization, health monitoring, and performance prediction of structural systems. In this paper, a two-step localization method is proposed for the nonlinear localization of multi-degree-of-freedom (MDOF) systems with multiple local nonlinearities. The approach achieves accurate nonlinear localization in two steps. In the first step, subset nonlinearity detection is performed to initially narrow down the nonlinear localization range. This effectively reduces the dimensionality of the candidate nonlinear basis functions in the second step. In the second step, candidate nonlinear basis functions are used to further confirm the doubtful connections. The accuracy and effectiveness of the method are verified by two numerical examples of a one-dimensional chain-type structure and a two-dimensional structure. In addition, an experimental study is conducted on a floor structure with two local nonlinearities to verify the effectiveness of the proposed method. Results show that the proposed method has good accuracy in a noisy environment and it requires only the input and output data of the system under a wide-band excitation.

MDOF stochastic stability analysis and applications to a coupled rotating shaft system

Stochastic stability analysis and generalization of moment Lyapunov exponents of multi-degree-of-freedom (MDOF) systems under white noise excitation were carried out using the transformation method and the perturbation method. Such systems represent coupled dynamic models exposed to stochastic disturbances and they are very common in engineering practice. The analysis of individual parts of a mechanical system does not give a clear picture of its real behavior as a whole, so the consideration of dynamic couplings is of great importance. This study proposes a generalized set of new transformations for MDOF systems that are necessary for obtaining Itô’s equations needed for further consideration of stochastic stability. The eigenvalue problem for moment Lyapunov exponents is derived and then solved by the method of perturbation. The generalized procedure is applied in an example of a rotating coupled shaft system whose dynamic behavior should be analyzed with at least four generalized coordinates. Similar models have so far been analyzed with limitations on SDOF and 2DOF systems that do not fully correspond to realistic models. The methodology demonstrated in the study could be applied more broadly, as it has the potential to analyze the dynamic stability of even more intricate or diverse systems whose dynamics have not been previously studied.

Visualization of regional seismic response based on oblique photography and point cloud data

Efficient and realistic visualization of regional seismic response is of great significance for risk education and emergency response. This study proposes an efficient visualization framework for seismic response of regional buildings, which consists of three parts: (1) oblique photography-based three-dimensional (3D) point cloud modelling of regional buildings; (2) time-history response analysis of regional buildings; and (3) hybrid processing for dynamic visualization. Specifically, the unmanned aerial vehicle (UAV) is adopted for oblique photography. The building coordinate extraction with the least square method and point cloud data segmentation with the clustering algorithm are implemented for the pre-processing. The simplified multi-degree-of-freedom (MDOF) model is developed for the time-history displacement analysis of buildings. Then, the MDOF model is used to match the point cloud model of the buildings for visualization. Preset rendering parameters and dynamic geometrical updating are used to further improve the visualization quality. Taking the Southeast University Jiulonghu campus in Nanjing, China for example, a case study is conducted to validate the feasibility of the developed framework.

Multi-objective trajectory optimization of the 2-redundancy planar feeding manipulator based on pseudo-attractor and radial basis function neural network

The establishment and solution of the inverse kinematic model is the key to improve the efficiency of trajectory optimization. To improve the trajectory smoothness and reduce energy consumption of multi-degree-of-freedom (MDOF) robots, this article presents the time-, jitter-, and energy-optimal trajectory optimization method based on pseudo-attractor and radial basis function neural network. Based on the geometric method, the forward kinematic model of MDOF robots is firstly established. The diversity of inverse kinematic solutions is reduced by determining redundant joints. Combined with the attractor theory, the time-adaptive allocation strategy can automatically endow time information with path points. On this basis, the 7-time polynomial interpolation method is used to fit discrete trajectory points and generate the initial trajectory without singularity points. Affected by the pseudo-attractor, radial basis function neural network is transformed into the improved radial basis function neural network (I-RBFNN) to optimize the initial trajectory. The 2-redundancy planar feeding manipulator (2-RPFM) is introduced to verify the effectiveness of the proposed method. Experiment and simulation results show that the proposed method is available in generating high-performance trajectories, which is beneficial to improve the production efficiency of the auto-body-out-panel stamping line.

Multi-degree-of-freedom kinetic model and its applications in simulation of three-dimensional nonequilibrium flows

A multi-degree-of-freedom (MDOF) kinetic model is developed to simulate three-dimensional nonequilibrium flows. By modifying collision term of Boltzmann model equation, a multi-scale molecular collision mechanism with translational, rotational and vibrational degrees of freedom is indicated by three coupled relaxation processes. Molecular vibration is modeled by harmonic oscillator. As a result, the degree of freedom of vibration may be directly related to temperature. Internal energy of various degrees of freedom are computed based on the equipartition theorem, and equilibrium distribution functions for each relaxation step are calculated. The present MDOF kinetic model is beneficial for assessing multi-scale evolutions of internal energy and molecular inelastic collisions. Several three-dimensional flow cases, including lid-driven cavity flow and hypersonic flows around a blunt cone at varying angles of attack, are simulated using the current MDOF technique. All numerical results were consistent with the reference data. It was shown that the proposed MDOF kinetic model well explains the vibration–rotation-translation energy exchange of polyatomic molecules in high-temperature gas, and that the current computational technique is a useful engineering tool for nonequilibrium aerodynamic research.

On the optimal design and placement of Tuned-Mass-Damper-Inerter for Multi-Degree-Of-Freedom structures

Even if Tuned-Mass-Damper-Inerter (TMDI) design for Multi-Degree-Of-Freedom (MDOF) structures is a topic largely addressed in the current literature, some aspects still deserving insight emerge from a literature review. The state of the art presented in the paper highlights that Inerter-Vibration-Absorber (IVA) design is typically conducted based on simplified models (e.g. generalized 2-Degree-Of-Freedom (2-DOF) models) or sophisticated ones but a comparison between the two approaches is rarely made. Moreover, the device placement along the structure is not often addressed in the design formulation; nevertheless, a proper location greatly influences the absorber performance and its physical dimensions. The paper aims to be a comprehensive study that investigates in a unique formulation the optimal design together with the optimal placement of a TMDI in a MDOF structure and aims to make a comparison between the use of a 2-DOF model and a complete MDOF model for its optimal design and placement. The overall design methodology and performance evaluation is formulated considering a stationary white noise input. An exemplificative literature case study of a 10-DOF structure is utilized to apply the design procedure, evaluate the performance and make the comparisons. It is demonstrated that a reduced order model is useful for a first estimate of the TMDI design parameters but some, especially the damping coefficient, need improvement adopting more refined models. Structural performance is well cached with reduced order models, especially for those quantities that mainly depend on the first natural mode. An optimal placement, tradeoff between structural performances and absorber physical dimensions, is proposed. TMDI effectiveness is assessed also considering non-stationary input with natural earthquakes and comparisons with conventional and non-conventional Tuned-Mass-Damper (TMD) are conducted.