Mass Springs Research Articles

Reliability-based design optimization of tuned mass-damper-inerter for mitigating structural vibration

The tuned mass-damper-inerter (TMDI), comprising mass blocks, springs, dampers, and two-terminal inertial elements, has garnered significant attention as an advanced iteration of the tuned mass damper (TMD) in recent years. However, previous studies of TMDI's design are primarily conducted according to the theoretical formulas based on deterministic analysis assuming harmonic excitations or stochastic analysis assuming Gaussian white noise type excitations. This treatment falls short of capturing the non-stationary and non-Gaussian characteristics exhibited by engineering excitations and thus cannot ensure the safety of controlled structure. A few studies considering non-stationary excitations and based on reliability metrics, in conjunction with stochastic simulation methods, often confront excessive computational overhead. Aiming at such a challenge, the reliability-based design optimization (RBDO) of TMDI system, combining the probability density evolution method (PDEM) and genetic algorithm (GA), for mitigating structural vibration under non-stationary excitations is performed in this study. For the purposes of illustration, a single-degree-of-freedom system attached the TMDI and subjected to stochastic ground motions is studied. Considering the cases of different levels of inertance-to-mass ratios, the RBDO of the TMDI is carried out. The solutions by the theoretical formulas and by the variance-based design optimization are compared to verify the superiority of the proposed method. For assessing the seismic mitigation performance of the optimized TMDI system, probability density evolution analysis of structure-TMDI system with three levels of inertance-to-mass ratios is performed. Comparison between the RBDO of TMDI and that of TMD under consistent mass ratio is further addressed. Numerical results reveal the technical advantages of TMDI in a probabilistic sense, i.e., high vibration mitigation performance, considerable mass reduction, and less stroke demand.

An improved passive tuned mass damper assisted by dual stiffness

A tuned mass damper (TMD) is one of the oldest and most commonly used passive control devices attached to structures to absorb lateral loads of energy from main systems. In the last decades, several novel tuned mass dampers have been designed to increase the performance of TMDs in decreasing the structural responses during excitation vibrations. Moreover, several formulations and numerical optimization methods have been developed to optimize the TMDs parameters. This paper proposes a novel passive tuned mass damper with dual stiffness (DSTMD). The DSTMD includes mass, primary and secondary springs, dashpot, and motion limiting chamber. The performance of DSTMDs depends on their properties such as mass, primary and secondary stiffness, damping coefficient, and the length of the motion limiting chamber. Thus, a metaheuristic optimization algorithm, called the Mouth Brooding Fish algorithm, was used to optimize the DSTMDs parameters. The effectiveness of the optimum DSTMD on two different linear ten-story structures under several earthquakes has been studied and compared with the effectiveness of classical optimum TMDs. According to the study, optimum DSTMDs generally show better effects for certain excitations, and as an average performance, they are superior compared to the classical optimum TMDs in reducing maximum displacement of the buildings. At last, structural yielding is considered, and the performance analysis on this structure shows that the DSTMD has a superior effect in reducing the maximum displacement and is among the best methods for the calculated absolute yielding amount.

Modeling of a lattice model for nonlinear wave propagation in phononic crystals

We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.

Ultralow-frequency band gap in a quasi-zero-stiffness multi-resonator periodic hybrid structure

For the sake of lowering the locally resonant bandgap without additional mass or softer springs, a multi-resonator periodic hybrid structure with an ultralow-frequency band gap is proposed. The hybrid structure is composed of quasi-zero-stiffness (QZS) mechanical systems and multiple mass-in-mass (MIM) lattice systems. A theoretical model is established to investigate the dispersion relation of the structure. The effects of the stiffness ratio and mass ratio on the dispersion relation are studied. It can be seen that, thanks to the introduction of the QZS system, the band gaps of the hybrid structure can be flexibly shifted to lower frequency. In theory, a reasonable parameter setting can produce an ultra-low frequency first band gap. Furthermore, both the effective stiffness and effective mass of the unit of the hybrid structure are derived for further explanation of the attenuation mechanism. And the hybrid structure presents negative stiffness and negative mass properties in certain frequency ranges. Finally, the propagation of elastic waves in the hybrid structure is calculated, which further verifies the structure’s suppression ability of ultralow-frequency elastic waves.

Deciphering groundwater flow-paths in fault-controlled semiarid mountain front zones (Central Chile)

The Mountain-Block Recharge (MBR), also referred to as the hidden recharge, consists of groundwater inflows from the mountain block into adjacent alluvial aquifers. This is a significant recharge process in arid environments, but frequently discarded since it is imperceptible from the ground surface. In fault-controlled Mountain Front Zones (MFZs), the hydrogeological limit between the mountain-block and adjacent alluvial basins is complex and, consequently, the groundwater flow-paths reflect that setting. To cope with the typical low density of boreholes in MFZs hindering a proper assessment of MBR, a combined geoelectrical-gravity approach was proposed to decipher groundwater flow-paths in fault-controlled MFZs. The study took place in the semiarid Western Andean Front separating the Central Depression from the Principal Cordillera at the Aconcagua Basin (Central Chile). Our results, corroborated by field observations and compared with worldwide literature, indicate that: (i) The limit between the two domains consists of N-S-oriented faults with clay-rich core (several tens of meters width low electrical-resistivity subvertical bands) that impede the diffuse MBR. The “hidden recharge” along the Western Andean Front occurs through (ii) focused MBR processes by (ii.a) open and discrete basement faults (mass defect and springs) oblique to the MFZ that cross-cut the N-S-oriented faults, and (ii.b) high-hydraulic transmissivity alluvial corridors in canyons. Alluvial corridors host narrow unconfined mountain aquifers, which are recharged by indirect infiltration along ephemeral streams and focused inflows from oblique basement faults. This study also revealed seepage from irrigation canals highlighting their key role in the recharge of alluvial aquifers in the Central Depression. The proposed combined geophysical approach successfully incorporated (hydro)geological features and geophysical forward/inverse modelling into a robust hydrogeological conceptual model to decipher groundwater flow-paths in fault-controlled MFZs, even in the absence of direct observation points.

Discrete mechanical growth model for plant tissue.

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall’s microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke’s law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.

Free vibration of summation and difference resonance of the vertical cable and other coupled structural members

Free vibration of summation and difference resonance of the vertical cable and other coupled structural members were investigated in this article. A model of a vertical cable and two mass–springs was built, with the sling considered to be geometrically nonlinear, and the upper and lower connecting structural members were taken as two mass–springs. Assuming the displacement of the sling, modal superposition method and D’Alembert principle were used to derive the dynamic equilibrium equations of the coupled structure. The nonlinear dynamic equilibrium equations were studied by means of multiple scales method, and the second-order approximation solutions of single-modal motion of the system were obtained. Numerical examples were presented to discuss the amplitude responses as functions of time of free vibration, with and without damping, respectively. Additionally, fourth-order Runge–Kutta method was directly used for the nonlinear dynamic equilibrium equations to complement and verify the analytical solutions. The results show that the coupled system performs strongly nonlinear and coupled characteristics, which is useful for engineering design.

Dynamic analysis of an axially moving robot manipulator supported by bearings

In this study, a robot manipulator is modelled as a cantilever beam, which moves in an axial direction, has a lumped mass at the end, and is supported by intermediate springs. Considering the tip mass and intermediate springs in the modeling, we derive the equations of motion in which the rigid-body motion is coupled with the flexible motions, and then analyze the transverse vibrations of the beam. Furthermore, we study the tip mass effects on the natural frequencies and the corresponding mode shapes. The natural frequency loci veering is analyzed for variations in the tip mass and the spring position/stiffness. In addition, we investigate the exchange and localization of modes around these veering regions as well as the parameter effects on the mode shapes. Using a Short-time Fourier transform (STFT), the relationship between the dynamic characteristics and dynamic responses are described. It is found that the dynamic characteristics of the beam are dependent on the veering distance. It is also shown via dynamic responses that the mode exchanges occur when a veering distance is close.

A Low-G Silicon Inertial Micro-Switch with Enhanced Contact Effect Using Squeeze-Film Damping

Contact time is one of the most important properties for inertial micro-switches. However, it is usually less than 20 μs for the switch with rigid electrode, which is difficult for the external circuit to recognize. This issue is traditionally addressed by designing the switch with a keep-close function or flexible electrode. However, the switch with keep-close function requires an additional operation to re-open itself, causing inconvenience for some applications wherein repeated monitoring is needed. The switch with a flexible electrode is usually fabricated by electroplating technology, and it is difficult to realize low-g switches (<50 g) due to inherent fabrication errors. This paper reports a contact enhancement using squeeze-film damping effect for low-g switches. A vertically driven switch with large proof mass and flexible springs was designed based on silicon micromachining, in order to achieve a damping ratio of 2 and a threshold value of 10 g. The proposed contact enhancement was investigated by theoretical and experimental studies. The results show that the damping effect can not only prolong the contact time for the dynamic acceleration load, but also reduce the contact bounce for the quasi-static acceleration load. The contact time under dynamic and quasi-static loads was 40 μs and 570 μs, respectively.

Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness

A quasi-zero stiffness (QZS) vibration isolator outperforms other passive control strategies in vibration attenuation especially in a low-frequency band, but it also has an intrinsic limitation of low roll-off rate in the effective frequency range of vibration isolation. To overcome this limitation, a two-stage QZS vibration isolation system (VIS) is proposed, in which the QZS feature is realized by combining a vertical liner spring with two parallel cam–roller–spring mechanisms. Considering a possible disengagement between the cam and the roller under large amplitude vibration, a piecewise nonlinear dynamical model is developed and approximately solved by the averaging method. The analytical solutions for amplitude–frequency relationship and force transmissibility are derived. The results reveal that the two-stage QZS VIS has both advantages of low-frequency vibration isolation and high roll-off rate. It is also found that the second resonance can be eliminated when heavy damping is present in the upper stage, and hence, a broader effective frequency range of isolation can be achieved. High intermediate mass and soft vertical springs in the lower stage are also found to result in high-quality isolation performance.

Utilization of Human-Like Pelvic Rotation for Running Robot

The spring loaded inverted pendulum (SLIP) is used to model human running. It is based on a characteristic feature of human running, in which the linear-spring-like motion of the standing leg is produced by the joint stiffness of the knee and ankle. Although this model is widely used in robotics, it does not include human-like pelvic motion. In this study, we show that the pelvis actually contributes to the increase in jumping force and absorption of landing impact. On the basis of this finding, we propose a new model, SLIP2 (spring loaded inverted pendulum with pelvis), to improve running in humanoid robots. The model is composed of a body mass, a pelvis, and leg springs, and, it can control its springs while running by use of pelvic movement in the frontal plane. To achieve running motions, we developed a running control system that includes a pelvic oscillation controller to attain control over jumping power and a landing placement controller to adjust the running speed. We also developed a new running robot by using the SLIP2 model and performed hopping and running experiments to evaluate the model. The developed robot could accomplish hopping motions only by pelvic movement. The results also established that the difference between the pelvic rotational phase and the oscillation phase of the vertical mass displacement affects the jumping force. In addition, the robot demonstrated the ability to run with a foot placement controller depending on the reference running speed.

2A1-I04 骨盤運動に着目した2足走行ロボットの開発 (第1報 : 骨盤運動と脚弾性を活用した走行モデルの考案)(移動知と身体性基盤)

A human running motion can be modeled by a spring-loaded inverted pendulum (SLIP). However, the SLIP model does not include human-like pelvic movement which can contribute to increase a jumping force and absorb a landing impact. Based on a running gait analysis, we propose a novel model, named SLIP2 (Spring-Loaded Inverted Pendulum using Pelvis), that is composed of a body mass, a pelvis and leg springs. This model can store elastic energy during running by utilizing pelvic movement in the frontal plane. Additionally, we developed pelvic oscillation control and running velocity control. To evaluate the proposed model and control methods, we performed hopping and running simulations. The simulation results show that the SLIP2 model achieved hopping and running motions. Moreover, it shows that the difference of the pelvic oscillation phase affects the jumping force.

Discrete mass and stiffness modifications for the inverse eigenstructure assignment in vibrating systems: Theory and experimental validation

The inverse eigenstructure assignment in structural dynamics and control aims at determining the mass and stiffness parameters to ensure the desired dynamic behavior expressed in terms of the prescribed eigenstructure. Several methods have been developed for the solution of this problem in the past. However, in the techniques proposed so far, all the design variables are assumed to be continuous. In practice, some design variables can only be changed through discrete modifications since either standard mass modules or springs are available. The determination of the discrete optimal solution of the structural modification problem cannot be performed by simply rounding the continuous optimal solution to the “nearest” integer, since rounded solutions can be considerably far from the optimality. On the other hand, the total enumeration as a solution method is infeasible for medium and large scale problems. To overcome this limitation, in this work, the eigenstructure assignment is formulated firstly as an inverse eigenvalue problem within the frame of constrained nonlinear integer programming, and then is solved by means of a partial enumeration technique with a reduced number of iterations. The experimental validation of the method on a five-degree-of-freedom lumped-parameter rig demonstrates its capability to compute effective modifications meeting the prescribed requirements and satisfying all the constraints.

Jitterbot: A Mobile Millirobot Using Vibration Actuation

Microrobotics is a rapidly growing field with promising applications in microsurgery and microassembly. A challenge in these systems is providing power and control signals to the robot. This project explores crawling robots that are powered and controlled through a global mechanical vibration field. Structures within the robot will cause it to respond to particular frequencies with different motion modalities. A prototype, dubbed the “jitterbot”, was cut out of a 0.75 mm sheet of steel using electric discharge machining (EDM), and has a total footprint of approximately 30 mm × 20 mm in the xy-plane. The “robot” has a tripod body (8 mm × 16 mm) with three small legs, and two suspended masses that are designed for specific resonance frequencies. The robot was tested on a plate that was vibrated vertically at frequencies ranging from 20 to 2,000 Hz. For particular resonant frequencies, the robot moves forward and turns in either a clockwise or counterclockwise direction. Finite element modeling confirms that the mechanism for motion is a rocking mode that is influenced by two arms that are suspended mass springs tuned to different frequencies. This lays the groundwork for further miniaturization.

1A1-K11 仮想斥力を用いたロボットマニピュレータの自動動作生成手法(動作計画と制御の新展開)

We propose an algorithm for automatic motion generation of a manipulator using virtual repulsive forces whose size is defined on the basis of the distance between the manipulator and obstacles, and its force direction is defined as outward way from the surface of obstacles. The motion path of the end effecter is modeled as the structure with mass points and springs, and its form is changed by the repulsive forces to generate collision-free path. The collision-free posture of the manipulator is also generated using repulsive forces, the posture is modified by the amount of joints torques which is transformed from acting repulsive forces. We have applied this algorithm to the 7-DOF manipulator, and it is confirmed that this method is able to automatically generate collision-free approach and trace motions.

2418 二重円管の振動解析モデルについて(OS24.一般セッション(4),オーガナイズドセッション)

An analytical model is proposed for analyzing the vibration characteristics of doubly walled pipes, and three different shell theories of Flugge, Love and Donnell are used to compare the applicability. The model is assumed to have filling material between two walls, and the mass and elastic springs are included in the sets of equations to represent the material property. Based on the comparison, some conclusions will be drawn on the issue.

Accident assessment of vehicles on long-span bridges in windy environments

Currently, there are very few systematic analyses of vehicle performance on bridges in windy environments. There are thus no scientific data to support bridge management in this regard, such as when to close traffic on bridges. This paper presents a framework of vehicle accident analysis model on long-span bridges in windy environments. In the accompanying paper, a three-dimensional analysis of the coupled bridge–vehicle–wind system is developed. Each vehicle is modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers. Dynamic interaction analysis is then conducted on the vehicle–bridge system to predict the “global” bridge and vehicle dynamic responses without considering accident occurrences. The results of the global bridge–vehicle vibrations serve as the basis for the present accident analysis of the “local” vehicle vibrations. With the global vibrations as inputs of the accident model, the lateral response, yaw response of the vehicle, and the reaction forces of each individual wheel are obtained and the stability condition of the vehicles are analyzed. The vehicle accidents on long-span bridges are then identified with given accident criteria. The developed framework can be used in not only analyzing the vehicle performance on highways and on bridges, but also in predicting useful information for emergency preparedness agencies in developing evacuation plans.

Framework of vehicle–bridge–wind dynamic analysis

This paper presents a framework of dynamic analysis of coupled three-dimensional vehicle–bridge system under strong winds. A general formulation of this system is introduced to simulate a series of vehicles consisting of different numbers and different types of vehicles running on bridges under hurricane-induced strong winds. Each vehicle is modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers, considering wind and road roughness loads. With this vehicle–bridge model, coupled dynamic analysis of vehicles running on bridges is conducted with a numerical example. Effects of driving speeds on the dynamic performance of the vehicles as well as the bridge are discussed. It is found that the driving speeds mainly affect the vehicle's vertical relative response while they have insignificant effect on the rolling response of vehicles. Vehicle's absolute response is dominated by the bridge response when wind speed is high, while it is dominated by road roughness when the wind speed is low. Detailed accident analysis of vehicles on bridges under strong winds will be reported in an accompanying paper.

Modeling and Control of Elastic Bodies. 1st Report. Proposals the Extended Reduced Order Physical Model.

This paper proposes a new modeling method of elastic body to represent the rigid motion and elastic deformation. This model can be used to control flexible multibody systems like flexible manipulators, vehicles, and space structures etc. The model consists of mass particles, springs, and rigid bodies and the behavior of mass particles represents rigid motion and deformation of elastic bodies. The mass and stiffness matrices are calculated using the modal mass, natural frequencies, and mode shapes. The efficacy of the model is verified by considering an example of an elastic car body supported by a rectangular plate. This modeling procedure is also extended to represent the dynamics of flexible multibody systems.

A symmetrically piecewise linear oscillator: Design and measurement

A simple piecewise linear system with symmetrical flexible constraints was designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piecewise models. The design choice was based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness. The system consists of a block mass attached to two leaf springs, the stiffness of which can easily be varied by changing their length. The secondary stiffness in the form of cantilever beams can be widely varied in the same way. The clearance between the mass and secondary springs can also be varied by adjusting the screws at the ends of the beams. A variable pneumatic damper is mounted on the upper surface of the mass and provides a means of changing the viscous damping coefficient. The experimental set-up, calibration procedures and typical results are discussed.