Forced Response Research Articles

Study on Collision Dynamics Similarity of Thickness Distortion Model of Train Five-Hole Thin-Walled Structure

Full-scale train collision tests are rarely carried out because of high cost, but small-scale model tests have good economy and repeatability, providing a new research method for train crashworthiness design. The metal thin-walled tube is a commonly used energy-absorbing structure for trains. Its collision characteristics directly affect the impact resistance and collision behavior evolution process of trains. This paper studies the collision dynamics similarity of the small-scale model of a five-hole thin-walled energy-absorbing structure at the end of a high-speed train. Firstly, the dynamic mechanical behavior and governing equations of high-speed train collision were analyzed, and the applicable similarity criterion was derived by similarity transformation to develop a similarity scale model. According to the simulation, the energy absorption, peak force and other key responses of the full-scale prototype collision were analyzed. Then, the applicability of the thickness distortion scale model of the five-hole energy-absorbing structure in the high-speed train was proved by equation analysis and error analysis. The impact dynamic responses of the complete similarity model and the distortion similarity model were discussed. A correction program with collision deceleration as the dependent variable was proposed for the distortion similarity model, and the fitting relationship between the distortion factor and the correction factor was obtained. The results calculated by the proposed method prove that the peak force-deformation-energy absorption error of the thickness distortion similarity model in predicting the dynamic responses of the prototype collision is less than 8%, which means the thickness distortion scale model has good accuracy in the prediction of full-scale prototype collision dynamics responses.

Grip force control under sudden change of friction.

A task as simple as holding a cup between your fingers generates complex motor commands to finely regulate the forces applied by muscles. These fine force adjustments ensure the stability and integrity of the object by preventing it from slipping out of grip during manipulation and by reacting to perturbations. To do so, our sensorimotor system constantly monitors tactile and proprioceptive information about the force object exerts on fingertips and the friction of the surfaces to determine the optimal gripforce. While the literature describes the transient responses, humans can generate to react to perturbations in load force, it is yet to be determined if humans can also react to abrupt changes in friction while already holding an object. Only recently technology using imperceivable ultrasonic vibrations became available to modulate friction in real time to investigate thisquestion. In this study, we used an object with an integrated friction modulation device suspended in a pulley system controlling the load. With this device, we explored the rapid adaptation of the sensorimotor system to changes in friction alone and in combination with changes in load. When load force and friction changed simultaneously, the grip force response was regulated based on the grip safety requirements. Participants increased their grip force in response to decrease in friction. However, they did not adjust their grip force when the friction increased, which is expected based on our biomechanical model of friction sensingmechanisms. KEY POINTS: Simple tasks like pouring water into a glass mobilize intricate interactions between fingertip sensory inputs and motor commands to account for the weight change and friction. It has been investigated how humans react to force perturbations when holding an object, but very little is known about how frictional changes are sensed and acted upon while holding an object, for example, due to sweating or condensation. We engineered a unique experimental object that utilizes imperceivable ultrasonic vibrations to change the frictional properties of the surface in a few milliseconds. This apparatus enabled us to study how human subjects react to change of friction when gripping or holding an object. We showed that humans adjust the strength of their grasp when forces in the direction of gravity either increase or decrease; however, frictional change evokes adjustments only when friction decreases.

MULTI-AEROELASTIC PHENOMENA MODELLING PART I: THE DEVELOPMENT OF WHOLE LPC MODEL FOR CIVIL TURBOFAN ENGINE

Abstract Aeroelastic phenomena in the low pressure compression (LPC) system of civil turbofan engines can cause a significant high cycle fatigue (HCF) risk to LPC components. Currently, the mechanical integrity risk to the LPC components is assessed by performing multiple, discrete aeromechanical simulations, which require large resources and incur high time cost. Therefore, the development of a comprehensive modelling simulation approach is necessary to assess multiple phenomena and components simultaneously that can provide accurate results within design timescales. This paper presents the methodology for generating a common, system level model for investigating multiple aeroelastic phenomena in fan and outlet guide vanes (OGVs). The development of a high fidelity, full annulus CFD model of the whole low pressure compression system is described. Time accurate unsteady CFD simulations are then conducted at multiple flight conditions. These information-rich simulation models are interrogated to extract various parameters of interest to assess multiple aeroelastic phenomena such as, 1EO fan forced response, fan alternating passage divergence (APD) forced response, OGV buffet, and OGV resonant forced response etc. In the second part of this paper, the application of this modelling methodology is demonstrated to evaluate and to better understand the efficacy of OGV asymmetric cyclic patterns.

Impact of sacroiliac interosseous ligament tension and laxity on lumbar spine biomechanics under vertical vibration: a finite element study

Objective To investigate the impact of tension and laxity in the sacroiliac interosseous ligament on lumbar spine displacement and force response in vibration environments. Methods A finite element model of the lumbar-pelvis, previously crafted and rigorously validated, was used to simulate ligament tension and laxity by adjusting the elastic modulus of the SIL under a sinusoidal vertical load of ±40 N at 5 Hz. Comparisons of lumbar spine horizontal and axial displacements as well as annulus fibrous stress, nucleus pulposus pressure, and facet joint force were performed, respectively. Results With the elastic modulus of the SIL varying by +50, −50, and −90%, the maximum vibration amplitude changed by +20.00, −175.00, and −627.27% for lumbar horizontal displacement, +30.00, −157.14, and −627.22% for lumbar axial displacements, +5.88, −19.35, and −245.16% for annulus fibrous stress, +10.00, −25.00, and −157.14% for nucleus pulposus pressure, as well as +6.54, −20.13, and −255.37% for facet joint force, respectively. Conclusion In contrast to static environments, large laxity of the SILs not only diminishes lumbar spine stability in vibrational settings but also significantly amplifies dynamic loads, thereby heightening the risk of lumbar spine vibratory injuries and low back pain disorders.

A robust hybrid estimation method for local bearing defect size based on analytical model and morphological analysis.

This paper presents a robust hybrid method using an analytical model and morphological analysis for estimating defect sizes on bearings, addressing inaccuracies in traditional peak-based approaches. First, a spatial contact analytical model is developed to analyze roller movement through defects. Numerical results indicate that radial defect sizes significantly impact dual-impulse intervals for accurate estimation, while axial size has minimal effect. An analysis of contact deformation, force, and vibration response reveals that the defect entry aligns before the first low-frequency peak, and the exit aligns after the first high-frequency peak, preceding the second low-frequency peak. Finally, testing of the derived model on four samples, incorporating vibration characteristics and geometry, achieves a minimum estimation error of 0.03%, demonstrating high accuracy and practical value.

C60 fullerene helps restore muscle soleus contraction dynamics after achillotomy-induced atrophy

Background. The search for new means that would effectively influence the pathological consequences of muscle immobilization is an urgent priority request of modern biomedicine. Previously, the positive effect of water-soluble C60 fullerenes, as strong antioxidants, was established on the background of muscle ischemia, mechanical muscle injury, and other muscle dysfunctions. These carbon nanoparticles have been shown to reliably protect muscle tissue from damage caused by oxidative stress. Materials and Methods. The biomechanical parameters of muscle soleus contraction of rats were studied by simulating non-functioning hind limbs using a clinical model – a rupture of the Achilles tendon (achillotomy). Muscle contraction parameters, namely the maximum contraction force and muscle force impulse, were determined on the 15th, 30th, and 45th days after initiation of atrophy using tensometry. As a therapeutic nanoagent, daily oral administration of C60 fullerene aqueous solution at a dose of 1 mg/kg was used throughout the experiment. Results. Previous registration of muscle soleus contraction force when applying 1 Hz stimulation lasting 1800 s with three pools revealed a decrease in maximal force responses after 15, 30, and 45 days of atrophy. The 45th day after atrophy is considered to be the limit for the fastest recovery of the muscle after immobilization, the further process takes place over several months. In all the tests performed, the therapeutic admini­stration of water-soluble C60 fullerenes (dose 1 mg/kg) an increase in biomechanical parameters was recorded (maximum force of contraction – the change in the form of the “stimulation – force contraction” dependence is a consequence of the development of the pathological process in muscle and the muscle force impulse, which allows assessing the performance of the muscular system after a long-term immobilization), by approximately 29–49±2 % for the maximum contraction force and by 21–37±2 % for the muscle force impulse compared to the atrophy group for 15, 30 and 45 days. Conclusions. The obtained results indicate the prospects of using water-soluble C60 fullerenes, which can alleviate pathological conditions in the muscular system that arise from skeletal muscle atrophy due to immobilization.

Aerosol-Induced Changes in Atmospheric and Oceanic Heat Transports in the CESM2 Large Ensemble

Abstract The total poleward energy transport (PET) is set by the top of atmosphere radiation flux and is therefore sensitive to any process which can alter those fluxes, particularly in the shortwave. One example is the direct and indirect effects of anthropogenic aerosols, which increase the local reflection of solar radiation back into space. The historic emission of sulfur dioxide, which peaked in the northern midlatitudes during the 1980s, has been proposed as a primary contributor to historic anomalies in cross-equatorial energy transport, as well as related processes such as a shift in the tropical rainband. In this study, we analyze simulations from the Community Earth System Model, version 2 (CESM2), large ensemble and single-forcing projects to better understand the forced response of PET to historical forcings. First, analysis of the single-forcing project reveals that the position of the intertropical convergence zone (ITCZ) responds in a nonlinear manner to greenhouse gas forcing in CESM2. This type of nonlinearity has been found previously in the context of the aerosol-only simulations in the CESM2 single-forcing project but may be the first identification of a similar effect in the greenhouse gas–only simulations. Second, through analysis of the full CESM2 large ensemble simulations, we find that anomalous heat transport occurred in both the atmosphere (through the mean meridional circulation and atmospheric eddies) and the oceans (through the Atlantic and Indo-Pacific sectors) due to a variety of related processes including the Hadley cells, the midlatitude storm tracks, the Atlantic meridional overturning circulation (AMOC), and the Pacific wind-driven subtropical gyre. Significance Statement In this study, we investigate how the Earth system changed the transport of energy from the tropics to the poles in response to historic pollution. We analyze a large number of climate model simulations of the recent past (1850 to present) and find that historic emissions of sulfur dioxide caused the model to transport more energy in the form of stronger ocean currents, stronger storms, and stronger prevailing winds. This is because the modeled currents in the Atlantic were too sensitive to historic pollution and transported too much warm water northward.

Fast flutter and forced response analyses using a cubic-B-spline-based time collocation method

Fast flutter and forced response analyses using a cubic-B-spline-based time collocation method

Emergence of biphasic versus monotonic response of actin retrograde flow and cell traction force with varying substrate rigidity.

The transmission of cytoskeletal forces to the extracellular matrix through focal adhesion complexes is essential for a multitude of biological processes, such as cell migration, cell differentiation, tissue development, and cancer progression, among others. During migration, focal adhesions arrest the actin retrograde flow towards the cell interior, allowing the cell front to move forward. Here, we address a puzzling observation of the existence of two distinct phenomena: a biphasic vs a monotonic relationship of the retrograde flow and cell traction force with substrate rigidity. In the former, maximum traction force and minimum retrograde flow velocity are observed at an intermediate optimal substrate stiffness; while in the latter, the actin retrograde flow decreases and traction force increases with increasing substrate stiffness. We propose a theoretical model for cell-matrix adhesions at the leading edge of a migrating cell, incorporating a novel approach in force loading rate sensitive binding and reinforcement of focal adhesions assembly and the subsequent force-induced slowing down of actin flow. Our model exhibits both biphasic and monotonic responses of the retrograde flow and cell traction force with increasing substrate rigidity, owing to the cell's ability to sense and adapt to the fast-growing forces. Furthermore, our analysis shows how competition between different timescales regulated by loading rate sensitivity influences the biphasic versus monotonic behavior and the emergence of optimal substrate rigidity in the biphasic scenario. We also elucidate how the viscoelastic properties of the substrate regulate these nonlinear responses and predict the loss of cell sensitivity to variation in substrate rigidity when adhesions are subjected to high forces.

Non-linear dynamic behavior of T0 and T90 mesopelagic trawls based on the Hilbert–Huang transform

Although adopting the T90 mesh orientation on the trawl net can improve the selectivity of the trawl codend, it is unknown whether the T90 mesh orientation influences the dynamic behavior of the trawl system. Therefore, this study uses non-linear dynamic analysis to examine the effect of mesh orientations, mesh size, and twine diameter on the mesopelagic trawls' fluttering motions and hydrodynamic force responses. Three trawls are designed with different mesh orientations (T0 and T90), mesh sizes (40 mm and 60 mm), and twine diameters (0.96 mm and 1.11 mm) on the codend and codend extension sections of the trawl model based on Tauti's law. These trawls are tested in a flume tank under various flow velocities and catch sizes. A time-frequency analysis method based on the Hilbert–Huang transform is utilized to analyze each trawl's dynamic responses, including motions and drag force responses. The results are compared with those obtained through Fourier analysis using power spectral density. The results highlight that the oscillation amplitude of the surge motion of the T90 trawl is higher than that of the T0 trawl. In contrast, the T90 trawl's heave motion oscillation amplitude is smaller. The dominant frequency of the periodic high-energy coherent structures of the surge and heave motions are detected at a low frequency. The surge and heave motions of the T0 trawl have a greater response to the current components with lower frequencies than that of the T90 trawl. An increase in mesh size, a decrease in twine diameter, and a change in mesh orientation decrease the drag force. The inherent characteristic oscillations of the drag force response for the three trawl models are synchronized with the low-frequency characteristic of surge and heave motions. The gravity periods of the low-frequency mode components of drag force, surge motion, and heave motion for the T90 trawl are higher than those for the T0 trawls. In other words, the T90 trawl is more stable and selective than the T0 trawl. The findings of this study offer important information for comprehending and enhancing the selectivity of trawls in marine mesopelagic fisheries, particularly for exposing the effects of mesh orientation and design parameters on trawl performances.

Real-time prediction of structural responses in deep-water jacket platforms using Ada-STLNet: A comprehensive analysis with prototype monitoring data

Real-time prediction of the mechanical behaviors based on prototype monitoring data is crucial for ensuring the integrity and safety of deep-water jacket platforms. As complex nonlinear systems, these platforms’ response exhibit varying temporal trends, dynamic spatial correlations, and load dependencies. This makes accurate prediction of future axial force and bending moment responses a significant challenge. In this paper, a novel deep learning method called Adaptive Spatio-Temporal Load Network (Ada-STLNet) is proposed aiming to address the issue of multi-node axial force and bending moment response prediction of deep-water jacket platform. Our model utilizes an enhanced graph convolution (EGCN) and self-attention mechanism for efficient spatial correlation modeling in multi-node response, LSTM for long sequence temporal feature capture. It integrates spatial and temporal, along with load-aware modules to capture intricate patterns in structural responses. Additionally, a multi-gated coupling mechanism with two independent gating modules is designed to adaptively represent the complex dependencies of structural responses, ensuring model stability and robustness. Extensive experiments conducted on prototype structural monitoring data from a deep-water jacket platform in the South China Sea demonstrate that Ada-STLNet outperforms six traditional models, including HA, SVR, KNN, MLP, LSTM, and GRU, across various prediction steps. The proposed model exhibits superior accuracy, particularly in short-term predictions, achieving up to 62.80% improvement in MAE and 48.11% in RMSE for axial force predictions compared to the second-best model. Ablation studies confirm the effectiveness of each component within Ada-STLNet. This research highlights the potential of Ada-STLNet for reliable and accurate prediction of structural responses, contributing significantly to the field of marine engineering.

A high sensitivity, low cost and fully decoupled multi-axis capacitive tactile force sensor for robotic surgical systems.

This paper presents the design of a multi-axis capacitive tactile force sensor with a fully decoupled output response for input normal and shear forces. A patterned elastomer is used as a dielectric layer between capacitive electrodes of the sensor that allows to achieve relatively higher sensitivity. The sensor is fabricated utilizing a low-cost rapid prototyping technique and is characterized for normal and shear forces in the range of 0 ~ 10 N and 0 ~ 3.1 N respectively. The achieved force sensitivity for the normal axis is 2.03%/N and for shear axes is 1.67%/N. The difference between the estimated force from the sensor and actual force applied is negligible, which demonstrates the accuracy of the sensor. The reliability of the sensor is analysed by performing hysteresis and repeatability tests. The hysteresis error is found to be 4.94% and 4.69% for normal and shear forces respectively. The repeatability error of the sensor is less than 5%, which shows the stability of the sensor. The high sensitivity, linear output response, high force measurement range, reliability and low cost make the proposed tactile sensor suitable for the force feedback in the robotic surgical systems.

Lessons Learned for Developing an Effective High-Speed Research Compressor Facility

Few universities in the world conduct experimental research on high-speed, high-power turbomachinery. The Purdue High-Speed Compressor Research Laboratory has a longstanding tradition of partnering with industry sponsors to perform high-TRL (technology readiness level) experiments on axial and radial compressors for aerospace applications. Early work in the laboratory with Professor Sanford Fleeter and Professor Patrick Lawless involved aeromechanics and the addition of a multistage axial compressor facility to support compressor performance studies. This work continues today under the guidance of Professor Nicole Key. While other universities may operate a single-stage transonic compressor or a low-speed multistage compressor, the Purdue 3-Stage (P3S) Axial Compressor Research Facility provides a unique environment to understand multistage effects at speeds where compressibility is important. Over the last two decades, several areas of important research within the gas-turbine engine industry have been explored: vane clocking, stall/surge inception, tip-leakage/stator-leakage (cavity leakage) flow characterization, and forced response, to name a few. This paper addresses the different configurations of the facility chronologically so that existing datasets can be matched with correct boundary conditions and provides an overview of the different upgrades in the facility as it has developed in preparation for the next generation of small-core compressor research.

A Dynamical Adjustment Approach to Estimating Forced and Internal Variability in the North Atlantic

Abstract Quantifying the relative contributions of external forcing and internal variability to North Atlantic sea surface temperature (NASST) has important implications for attributing and predicting climate changes around the North Atlantic basin. Many previous methods have approached this problem by estimating the externally forced signal directly, making assumptions about forced variability for which there is no consensus. In this work, the separation of variability is approached in a fundamentally different way that does not specify the forced response’s temporal evolution. We propose a dynamical adjustment method in which the internal, spatially uniform component of NASST is predicted based on patterns of NASST that are orthogonal to the spatially uniform pattern. When applied to preindustrial simulations, the dynamical adjustment demonstrates skill in reconstructing the NASST basin-mean variability. Applying the dynamical adjustment to historical simulations demonstrates skill in a majority of climate models although the skill is reduced relative to preindustrial simulations because external variability partly contaminates the predictors. The dynamical adjustment is compared to several other methods which directly estimate the externally forced signal. We find that dynamical adjustment performs similarly to these comparative methods despite the fundamentally different prediction method. However, methods based on different principles yield considerably different estimates of external and internal variability.

On the suitability of rigorous coupled-wave analysis for fast optical force simulations

Abstract Optical force responses underpin nanophotonic actuator design, which requires a large number of force simulations to optimize structures. Commonly used computation methods, such as the finite-difference time-domain method, and finite element methods, are resource intensive and require large amounts of calculation time when multiple structures need to be compared during optimization. This research demonstrates that performing optical force calculations on 2D-periodic structures using the rigorous coupled-wave analysis method is typically on the order of 10 times faster than other approaches and with sufficient accuracy to suit optical design purposes. Moreover, this speed increase is available on consumer grade laptops, avoiding the need for a high performance computing resource.

Quasinormal mode expansion in thin elastic plates

Elastic wave manipulation using large arrays of resonators is driving the need for advanced simulation and optimization methods. To address this we introduce and explore a robust framework for wave control: quasinormal modes (QNMs). Specifically, we consider the problem for thin elastic plates, where the Green's function formalism is well known and readily exploited to solve multiple scattering problems. By studying the associated nonlinear eigenvalue problem we derive a dispersive QNM expansion, providing a reduced-order model for efficient forced response computations which reveals physical insight into the resonant mode excitation. Furthermore, we derive eigenvalue sensitivities with respect to resonator parameters and apply a gradient-based optimization to design quasi-bound states in the continuum and position eigenfrequencies precisely in the complex plane. Scattering simulations validate our approach in structures such as graded line arrays and quasicrystals. Drawing on QNM concepts from electromagnetism we demonstrate significant advances in elastic metamaterials, highlighting their potential for tailored wave manipulation. Published by the American Physical Society 2024

Fan Non-Synchronous Forced Vibration Under Crosswind

Abstract In this paper, a new aeroelastic phenomena for fans, referred to as non-synchronous forced vibration (NSFV), is presented. This type of aeroelastic instability can occur at high crosswind conditions when the flow at the intake lip separates and the disturbances caused by flow separation become unsteady. The results show that in the presence of unsteady separation in the intake, the fan can experience non-synchronous frequency excitations, which can result in resonant response in modes that are not identified by the Campbell diagram. The findings are corroborated by aeroacoustic theories. To the best of authors knowledge, this is the first time that fan forced response due to unsteady distortion is studied and the findings can unlock some of unexplained and unexpected vibrations experienced by engines.

Observed Responses of Gravity Wave Momentum Fluxes to the Madden‒Julian Oscillation Around the Extratropical Mesopause Using Mohe Meteor Radar Observations

AbstractThe 12‐year continuous observation of gravity wave momentum fluxes (GWMFs) estimated by the Mohe meteor radar (53.5°N, 122.3°E) revealed prominent intraseasonal variability around the extratropical mesopause (82–94 km) during boreal winters. Composite analysis of the December‒January‒February (DJF) season according to the Madden‒Julian Oscillation (MJO) phases revealed that the zonal GWMFs notably increased in MJO Phase 4 (P4) by ∼2–4 m2/s2, and a Monte Carlo test was designed to examine the statistical significance. The response in zonal winds lags behind the GWMF response by two MJO phases (i.e., 1/2π), indicating a “force‒response” interaction between them. Additionally, time‐lagged composites revealed that strengthened westward GWMFs occurred ∼25–35 days after MJO P4, coincident with the MJO impact on the zonal winds in the stratosphere. The analysis results also suggested that the mechanism of MJO by which the MJO influences the stratospheric circulation might involve poleward propagating effects of stationary planetary waves with zonal wavenumber one. This work emphasizes the importance of GW intraseasonal variability, which impacts tropical sources from the troposphere to the extratropical mesopause.

Improving flexible actuating behaviors of gel-based artificial muscles through chamomile polysaccharide crosslinking

Abstract The flexible actuating behaviors of gel-based artificial muscles (GBAMs) are contingent upon the properties of their hydrogel actuating membranes. While the current preparation system for these membranes is deemed flawless, the electromechanical characteristics are constrained by the inherent properties of the material. The majority of raw materials used in this process are chemically synthesized; however, Chinese herbal polysaccharides offer a convenient, environmentally friendly, and non-toxic alternative, making them a prime candidate for actuating membrane preparation. The biological activities of chamomile polysaccharide (CP) include anti-inflammatory, lipid-lowering, sugar-lowering, and OH- clearance properties. Therefore, the actuating membrane of GBAM was prepared by crosslinking sodium alginate (SA) with CP. The findings indicated that at a crosslinking ratio of 4:5 for CP-SA, the electrically actuated force density and response speed reached 20.12 mN/g and 0.09 mN/g·s, respectively. Additionally, the working life extended to 781 seconds, tremor frequency decreased by 47.67%, and tremor amplitude was 19.55% of the control group. The elastic modulus was measured at 15.44 MPa, specific capacitance reached 183.99 mF/g, and internal resistance decreased by 13.44%. Charge and discharge time was 5.73 seconds, maximum energy reached 2.7 J, and specific energy was 12.66 A·J/g, representing increases of 2.3 seconds, 64.63%, and 6.47 A·J/g compared to the control group. The deflection displacement of 6.62 mm in the CP-SA group at a crosslinking ratio of 4:5 was found to be 3.06 times greater than that of the control group. In conclusion, the actuating membrane of GBAM, synthesized through the cross-linking of CP with SA at a specific ratio, demonstrated superior properties. This innovation offers a novel perspective and direction for the advancement of GBAMs and is anticipated to significantly contribute to future developments in related fields.

Utilizing tuned mass damper for reduction of seismic pounding between two adjacent buildings with different dynamic characteristics

Today, population growth and the need for constructing adjacent buildings have raised the likelihood of pounding between adjacent buildings with different dynamic characteristics. The pounding force applied to adjacent buildings during an earthquake is intensive and may cause total or partial damage to structural elements, leading to collapse. It disturbs and complicates the functioning of buildings during and after an earthquake. Therefore, the main aim of this paper is to minimize and, if possible, eliminate the pounding force between two adjacent structures by considering three objective functions. For this aim, the tuned mass damper is utilized here. Also, this paper aims to reduce the number of collisions between different stories of adjacent buildings through a tuned mass damper system. For this purpose, two adjacent steel moment frames with six and ten stories are nonlinearly modeled and validated using the concentrated plasticity model in OpenSees. Moreover, the pounding element is nonlinearly modeled and validated. Then, tuned mass dampers (TMDs) are used on the roofs of the structures. They are optimized in stiffness, mass, and damping coefficient using the grey wolf optimization (GWO) algorithm. Nonlinear time history analysis (NLTHA) is performed under nine far- and near-field earthquakes. The pounding force and structural responses are analyzed, including maximum story acceleration, maximum inter-story drift, and base shear in the TMD-controlled and uncontrolled adjacent buildings. Finally, the Park-Ang damage index is evaluated for the structures with and without the TMD system. It has been found that the maximum pounding force, the maximum acceleration of the stories, the base shear, the drift ratio, and the number of collisions significantly reduce (or omit) in the presence of TMDs when the objective function is considered to be the minimization of the maximum pounding force. It is shown that the maximum pounding force generally declines to zero for this objective function.