Pendulum Tuned Mass Damper Research Articles

Study on vibration control performance of pendulum TMD with additional stoppers and its application on high-rise buildings

Although pendulum tuned mass damper (PTMD) is one of the most classic and commonly used vibration control devices, it has clear limitation due to the natural feature of linear TMD. Additional stoppers for the pendulum string (PTMD-AS) were proposed and introduced to improve the PTMD's performance by triggering its nonlinearity. A 2-DOF model was established to analyze the dynamic response of the system subjected to harmonic excitation, and the governing equations were formulated using the Lagrange equation. The extended incremental harmonic balance (EIHB) method and the Runge-Kutta (R-K) method were utilized to calculate the frequency response and time history of the system. Nonlinear dynamic characteristics of the pendulum with stiffness hardening were explored in detail. Sensitivity analyses were performed to investigate the effect of stopper position. It was found that aperiodic responses or multiple solutions could be induced when the pendulum underwent significant stiffness hardening upon passing the additional stoppers. Finally, the effectiveness and robustness of PTMD-AS are demonstrated in a numerical simulation of a high-rise building subjected to random wind excitation based on wind tunnel experiments.

Passive control and damage assessment with a pendulum tuned mass damper using mean square equations and second-order eigen-perturbation techniques

This paper proposes a novel framework for damage detection and retuning of a Pendulum Tuned Mass Damper (PTMD) addressing effects of stochasticity via mean-square equations and establishing rapid change detection. The framework was made possible via a Stochastic Differential Equation (SDE) formulation of the equations of motion considering a two degree of freedom base and structure system equipped with a PTMD. The system was assumed to be excited at the base with Gaussian white noise and the solutions were computed using a stochastic integration scheme. A Second Order Eigen-Perturbation (SOPS) estimate is used to carry out detection of sudden stiffness reduction in the base floor of the structure. Once damage is detected, mean square equations on monitored displacements were used to retune the PTMD by adapting the length of the pendulum. It was found that damage could be detected rapidly and successive retunings were able to minimize the mean square displacement of the damaged structure and stabilise it over time.

Experimental investigation on vibration suppression of a new prestressed TMD for wind turbine towers

The pendulum tuned mass damper (PTMD) has been popular for vibration suppression due to its particular configuration form and frequency-tuning pattern. Based on the theoretical and numerical methods, a new prestressed TMD (PSTMD) has recently been presented which has better performances than the PTMD. To verify the improvement advantage and applicability comparatively, a comprehensive experimental study is carried out to investigate the vibration suppression of PSTMD in this paper. A wind turbine tower (WTT) with the lump-mass of the PSTMD can be represented by a two-degrees-of-freedom system, and its optimal design parameters can be analytically derived. Three test specimens, including the uncontrolled WTT, and the WTT with the PTMD or the PSTMD were tested in the laboratory with different equivalent wind and seismic loads via a shaking table. The presence of the PTMD or the PSTMD is noted changing only slightly the natural frequency and mode shape of the WTT, and the PSTMD exhibits the superior vibration suppression capability compared with the traditional PTMD.

Risk mitigation/performances incrementation of an offshore wind turbine with a flexible monopile foundation by means of a pendulum-tuned mass damper

Risk mitigation/performances incrementation of an offshore wind turbine with a flexible monopile foundation by means of a pendulum-tuned mass damper

Optimal design of pendulum-tuned mass damper for the vibration control of offshore wind turbines with a flexible monopile foundation

Optimal design of pendulum-tuned mass damper for the vibration control of offshore wind turbines with a flexible monopile foundation

Optimal path shape of friction-based Track-Nonlinear Energy Sinks to minimize lifecycle costs of buildings subjected to ground accelerations

Track Nonlinear Energy Sinks (T-NES) are Pendulum Tuned Mass Dampers (PTMDs) whose nonlinear restoring forces are obtained from curved path shapes. They combine the abilities of traditional spring-based NESs with the operational advantages of PTMDs. T-NES can resonate with broad frequency content, becoming effective even under damage to the host structure originating from strong ground motions. In the published literature, the integration of Friction Dampers (FDs) into T-NESs (so-called T-NES Type II) has only been studied on PTMDs with circular tracks, and in deterministic settings. Herein, a novel Reliability-Based Design Optimization (RBDO) procedure is presented to find the optimal track shape of T-NES Type II in buildings subjected to earthquakes. The objective is to minimize expected life-cycle damage costs corresponding to slight damage, moderate damage, and extensive damage limit states. A set of rational functions encompassing a wide range of generic curvatures is constructed to describe the T-NES track shape. The nonlinear description is used for restoring force and also in the dissipative mechanism. The case study is a medium-rise building located in Chile. The results indicate that, for the studied building, the optimal path is multimodal, and quite different track profiles can significantly reduce oscillation of the host structure.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Global vibration control of offshore wind turbines with a flexible monopile foundation using a pendulum-tuned mass damper: Risk mitigation and performance incrementation

This study investigates an optimized design approach for a passive-adaptive pendulum-tuned mass damper (PTMD). The PTMD is used to mitigate structural vibrations in offshore wind turbines (OWTs) with flexible monopile foundations considering Pile-Soil Interaction (PSI). The model OWT is based on the 5-MW design proposed by the National Renewable Energy Laboratory (NREL). The PSI incorporates a pile that is modeled as beam–column elements supported by nonlinear springs and accounts for lateral loads (p-y curves) and axial loads (t-z and Q-z curves) at nodal points. Wind and wave spectra estimation, as well as hydrodynamic and aerodynamic load analysis, are performed using a bespoke MATLAB® program operated in conjunction with an ANSYS® 3-D finite element global model. The resultant peak response at the OWT hub was evaluated through power spectral density (PSD) analysis. Optimal design choices for PTMD parameters are obtained via parametric analysis, which assesses the dynamic response in the along and across directions at the hub and stress at the tower base. A systematic representation considers the uncertainties stemming from the geometric and mechanical properties of the tower, environmental loads, and rotating blade dynamics. To address these uncertainties, a Monte Carlo simulation is employed to assess the structural risk via the Performance-Based Wind Engineering (PBWE) framework. Consequently, the probabilistic evaluation of structural response, foundation stresses, and power production assists in the optimal design process of PTMDs that mitigate the global structural vibrations of OWTs.

Bi-directional wind-induced vibration control of high-rise buildings using bi-directional rail variable friction pendulum-tuned mass damper

Flexible high-rise buildings are extremely vulnerable to wind, especially when synchronously subjected to alongwind and crosswind forces. In this scenario, acceleration-sensitive targets (such as delicate instruments) are at risk of damage. Moreover, occupant comfort and structural safety may be degraded due to excessive bi-directional vibrations. To resolve this problem, a bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) is used to achieve optimal bi-directional wind-induced vibration control. The modeling of the BRVFP-TMD for bi-directional high-rise buildings under bi-directional winds was performed. Further, the physical interaction forces of the BRVFP-TMD with a multi-degree-of-freedom structure and the governing equations for the modal structure with the BRVFP-TMD were derived, with experimental results confirming the effectiveness of the linear variable friction force. For the BRVFP-TMD with a lightly damped structure, acceleration optimizations were conducted to obtain closed-form solutions for optimal parameters. However, the deployment position of the tuned mass damper (TMD) was found to degrade the optimal control performance significantly. Therefore, for the convenience of engineers, improved optimal solutions were obtained by considering the actual deployment position of the TMD and the influence of inherent structural damping. The stochastic linearization method was used to evaluate the effect of linear hysteretic damping (HD) with equivalent viscous damping (VD) in the field of random theory. Accordingly, a closed-form expression for the VD ratio was proposed to represent HD. Numerical verifications of a Chinese landmark (Canton Tower) subjected to bi-directional winds were assessed through time history and frequency decomposition analyses. The results verified the effectiveness, correctness, and necessity of the BRVFP-TMD; the improved optimal solutions were also confirmed. Compared with the closed-form solution, which neglects the deployment position of the TMD, and the classic TMD, the improved optimal solutions of the BRVFP-TMD demonstrated superior performance in mitigating both structural displacement and acceleration. The vibration reduction ratios achieved were 44.55% for the displacement at the top of the mast and 46.69% for the acceleration at the top of the main tower.

A Multi Tuning-Frequency Passive/On-demand Active Pendulum Tuned Mass Damper

The use of tuned mass dampers (TMDs) in high-rise buildings, towers, and other tall structures for mitigating wind-induced vibration has resulted in significant improvements in serviceability of such structures. In applications where more than one mode of vibration with distinctly different natural frequencies are in need of damping, multiple passive TMDs each tuned to one of the natural frequencies are needed. In many such applications, the excessive cost, weight, and space requirement of multiple passive TMDs are not acceptable. This paper presents a novel passive pendulum tuned mass damper (PTMD) which on-demand can switch to an active PTMD. In its default passive state, the proposed device is tuned to the first mode of the structure and acts as a traditional passive PTMD. In its active state, while staying tuned to the first mode passively, the PTMD simultaneously tunes itself to multiple higher order modes adding tuned damping and providing a multi-directional vibration control.

Seismic performance improvement of liquid storage tank based on base-isolation and pendulum tuned mass damper

It is necessary to ensure the safety of liquid storage tanks under earthquakes, but the damage probability of the non-damping liquid storage tanks is higher under earthquakes. Based on the damping principle of tuned mass damper (TMD) and the characteristics of the liquid storage tank, a new pendulum TMD (PTMD) system is proposed. Considering the material nonlinearity, the fluid–structure interaction and liquid sloshing characteristics, the three-dimensional numerical calculation models of the non-damping, PTMD, base-isolation (BI) and BI-PTMD liquid storage tanks are established, respectively. The seismic responses of different types of liquid storage tanks under the action of near-field pulse-like earthquakes are investigated, the damping performance of the hybrid control system with the isolation and the PTMD is analyzed, and the influence laws of the mass ratio of PTMD-structure and base-isolation period on the dynamic responses of the liquid storage tanks are discussed. The results show that the BI-PTMD hybrid control system has a significant damping effect on the seismic responses of the liquid storage tank. The damping rate of the base shear is the largest, reaching 86.0%, and the control rate of the PTMD on the displacement of the isolation layer is about 20.0%. The hoop stress, effective stress, liquid pressure and displacement of isolation layer decrease with the increase of the mass ratio of PTMD to structure. With the increase of base-isolation period, the hoop stress, axial compressive stress, effective stress and liquid pressure decrease, and the control effect of PTMD on the liquid storage tank is weakened.

Bidirectional vibration control for fully-coupled floating offshore wind turbines

The vast and stable wind resources present in deep waters have made deep-sea floating wind power the mainstream trend for future development. However, the operating environment of offshore floating wind turbines is complex and variable. The joint action of wind and waves causes significant platform motion and turbine vibration, reducing power generation efficiency, causing structural damage, and shortening the service life of turbines. Hence, this study focuses on the NREL 5 MW DeepCwind semi-submersible wind turbine and establishes a fully-coupled floating wind turbine model utilizing the SIMPACK multi-body dynamics software. The model includes aero-, hydro-, flexible body structure, mooring, control, and transmission chain components. 3D pendulum tuned mass dampers (3D-PTMD) and bilinear tuned mass dampers (2TMDs) are designed to control the bidirectional vibration causes due to wind-wave misalignment in the platform motion and nacelle displacement of the floating wind turbine. The research results show that: For the roll and pitch of the platform, there is only one platform roll or pitch main frequency, and the amplitude at the main frequency can be effectively reduced by setting the frequency of 2TMDs near the main frequency, thereby suppressing the vibration of the platform; For the displacement of the nacelle, in addition to the main frequency of platform roll or pitch, there is also a secondary frequency of first-order bending of the tower, 2TMDs corresponding to the main frequency can effectively reduce the amplitude at the main frequency, and 3D-PTMD corresponding to the secondary frequency can effectively reduce the amplitude at the secondary frequency, it is better to configure 2TMDs alone than 3D-PTMD alone, and it is best to configure both at the same time.

Optimum Design of Pendulum Tuned Mass Dampers Considering Control Performance Degradation from Damper Connection

Optimum Design of Pendulum Tuned Mass Dampers Considering Control Performance Degradation from Damper Connection

Analysis of Flow-Induced Vibration Control in a Pontoon Carrier Based on a Pendulum-Tuned Mass Damper

The pendulum-tuned mass damper (PTMD) is a widely used vibration-damping device capable of transferring and dissipating structural vibration energy, resulting in reduced structural amplitude, and offering both structural and performance advantages. Given the susceptibility of the submerged expendable conductivity, temperature, and depth profiler (SSXCTD) buoyancy platform to flow-induced vibrations during the upwelling process, the PTMD effectively suppresses the main structure’s amplitude under flow field effects. To this end, we investigated the application and design of the PTMD in the SSXCTD buoyancy platform and analyzed its vibration reduction performance. Moreover, we conducted finite volume simulations of the structure using ANSYS FLUENT fluid simulation software, providing insights into its motion under flow field effects and validating the PTMD’s effectiveness in mitigating the buoyancy platform’s flow-induced vibrations. Our research results demonstrate that the PTMD effectively alleviates the impact of seawater flow on the buoyancy platform, leading to a significant improvement in its operational stability. The proposed research methodology and findings serve as valuable references for the design and optimization of other expendable marine detection equipment.

Pendulum tuned mass damper (PTMD) with geometric nonlinear dampers for seismic response control

In engineering applications, the geometric nonlinear (GN) arrangement of pendulum-tuned mass dampers (PTMDs) may induce the damping force to deviate from its intended state. Therefore, this study extends the scope of the structural control strategy by introducing a pendulum-tuned mass damper considering geometric nonlinear dampers (GND). Specifically, the damper developed in this study, termed PTMD with GND, is an inconspicuous pendulum-type tuned mass damper with different GN settings in the initial state. A nonlinear mathematical model of the PTMD with GND is developed, identifying its significant nonlinear characteristics, particularly the "unavailable" locations. The stochastic linearization method (SLM) is adopted to simplify the nonlinear model using the Kanai-Tajimi modified spectrum. The SLM agrees well with the numerical results obtained using the Monte Carlo simulation method. Furthermore, the control strategy of PTMD with GND is proposed with the consideration of filtered random excitation. Several numerical cases have been conducted to investigate the availability of PTMD with GND and the proposed optimal design strategy under 178 real seismic excitations. The results show that the PTMD with GND is nearly as effective as the ideal transitional TMD in mitigating the seismic response of the primary structure and more effective than the inverted rough linear adjustment. It can be concluded that the proposed optimal design strategy for the PTMDs with GND efficiently suppressed the structural vibration through multiple performance indices and used the nonlinearity of the damping mechanism of the GND to provide a sufficient damping energy dissipation effect adaptively.

Inerter-assisted pendulum-tuned mass damper for across-wind response control of tall buildings

The present study proposes an inerter-assisted pendulum-tuned mass damper (IA-PTMD) to control across-wind response in tall buildings. An inerter is introduced between the pendulum’s mass and structure, thereby enhancing the structural control effectiveness of a classical one-story pendulum-tuned mass damper (PTMD). Across-wind response of a benchmark tall building with IA-PTMD is investigated in this study. The combined equations of motion were solved numerically using the state-space variable method. The design of the IA-PTMD was carried out using this numerical analysis, and optimum parameters were obtained. It is found that with a lower mass and inerter ratio, the structure does not require the addition of viscous dampers. With an identical structure mass ratio, IA-PTMD outperforms the PTMD and was found fairly robust against off-tuning due to uncertainties in building stiffness. From the results observed in this study, it can be concluded that an optimally designed IA-PTMD effectively controls across-wind response in tall buildings.

A novel bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD)

The shape of hysteretic loops for a friction pendulum system transforms when excited by bi-directional motion, which exhibits unexpected dynamic behavior compared with unidirectional motion. Therefore, a novel bidirectional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) with two independent rails that satisfied the purpose of bidirectional structural response control and provided a full bidirectional friction force was proposed. The variable friction arrangement was applied to the rails so that the BRVFP-TMD could be accomplished with a linear hysteretic damping property that is contributed by the displacement-dependent variable friction force. Using unidirectional harmonic excitations with attack angle as bi-directional loading, illustrations were created to investigate the control effect of traditional pendulum friction TMDs with a spherical sliding surface. This demonstrated the collapse of hysteretic loops of traditional pendulum friction TMDs and superiority of BRVFP-TMD in terms of mechanism. For the BRVFP-TMD with a lightly damped structure, the optimizations of the fixed-point theory were accessed to obtain the closed-form solutions of the optimal parameters of the BRVFP-TMD. Numerical verifications based on bidirectional motions were conducted to evaluate the performance of the BRVFP-TMD. The bidirectional earthquake results indicated stable and excellent performance of the BRVFP-TMD in terms of either frequency response reduction or friction energy dissipation efficiency. Meanwhile, bidirectional wind-induced vibrations confirmed the correctness of the optimization and the stable robustness of the optimized BRVFP-TMD.

Seismic Optimization for Hysteretic Damping-Tuned Mass Damper (HD-TMD) Subjected to White-Noise Excitation

The hysteretic damping tuned mass damper (HD-TMD) is composed of a spring element, a hysteretic damping (HD) element, and a mass. The HD force is proportional to the displacement of the tuned mass damper (TMD). Recently, the application of HD-TMD has emerged, but its optimal design is still lacking. To fill this academic gap, numerical solutions for optimal parameters of HD-TMD subjected to white-noise excitation were obtained based on the H2 optimization criterion. Performance balance optimization with a weighting factor was carried out to improve the response of a structure with the HD-TMD system. A set of earthquake records and harmonic excitations were conducted to prove the effectiveness of the optimal numerical solutions and the performance balance design. It was found that the performance of the HD-TMD is slightly better than that of the traditional optimized TMD. As a real TMD application of HD-TMD, the variable friction pendulum TMD (VFP-TMD) was selected to experience earthquakes with the proposed optimal methods. Results showed that the optimal solutions provided the best performance but raised the problem of difficulty in maintaining linearity with a large displacement. Nevertheless, the performance balance design helped reduce this defect and provided impressive seismic mitigation capacity. Compared with the optimal numerical solution results, the performance balance design demonstrated 2.847% of loss in the maximum structural displacement reduction rate and 3.709% of loss in the root mean square reduction rate during the earthquake-excited period, respectively.

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

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

A novel active tendon pendulum tuned mass damper and its application in transient vibration control

Enhancing the performance characteristics of Tuned Mass Dampers (TMDs), in particular extending their narrow frequency band of operation, has been the subject of many researches. In the adaptive type of TMDs, the device's properties can be adjusted gradually in response to a slight alteration in the excitation characteristics and physical properties of the main structure. A novel vibration absorbing system, namely Active Tendon Pendulum TMD (AT-PTMD), is proposed in the present study. The device consists of a simple pendulum whose horizontal movement is restricted by a tendon with an adjustable tensile force which is attached to the pendulum’s rod. The device is designed and formulated, and its efficiency is assessed numerically and experimentally. For this purpose, a 3-degree of freedom structure is considered. Scrutinizing the responses of the uncontrolled, passively controlled and actively controlled structure shows the appropriate performance of the AT-PTMD in comparison with the passive TMD system in transient vibration reduction, particularly in reducing the total vibrational energy of the structure's response. Considering the achieved results, the proposed AT-PTMD system is capable of reducing the maximum displacement and acceleration of the main structure up to 43% and 37%, respectively, which substantiates its excellence over the common passive vibration absorbing devices. The case study also proves that the utilized mechanism for adjusting the equivalent stiffness of AT-PTMD increases its operating frequency range by 105% compared to common TMDs. Unlike active structural control systems, the suggested approach will not induce structural instability in any operating mode.