Vertical Spring Research Articles

Study on Finite Element Model of Bridge Multi-Pile Foundation

In order to use finite element software to complete the design or calculation of bridge multi-pile foundation, this paper discusses the finite element model (FEM) of a bridge multi-pile based on the theory and provisions in Code for Design of Ground Base and Foundation of Highway Bridges and Culverts (CDGBFHBC 2007) of china. For the FEM of a bridge-multi pile foundation, cap is regarded as a rigid body, piles are taken as beams, and boundary constraints are a series of horizontal springs and vertical springs. First, the formula of stiffness for horizontal springs and bottom vertical spring is derived according to elastic ground base theory and winkler hypotheses. Secondly, for the friction pile, the stiffness of vertical springs on piles side is derived basis of the principle of friction generated and simplified distribution of pile shaft resistance. Then, the FEM of multi-pile needs pay attention to three issues: the simulation of connections between piles and cap, elastic modulus needs discount, and the weight for pile underneath the ground line (or local scour line) needs calculate by half. Taking pile section bending moment often control the design and calculation of pile into account, this paper gives a simplified FEM of pile. Finally, an example is used to introduce the application of the FEM of bridge multi-pile foundation.

A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset–track system

The present work proposes friction coupling at the wheel–rail interface as the mechanism for formation of rail corrugation. Stability of a wheelset–track system is studied using the finite element complex eigenvalue method. Two models for a wheelset–track system on a tight curved track and on a straight track are established. In these two models, motion of the wheelset is coupled with that of the rail by friction. Creep force at the interface is assumed to become saturated and approximately equal to friction force, which is equal to the normal contact force multiplied by dynamic coefficient of friction. The rail is supported by vertical and lateral springs and dampers at the positions of sleepers. Numerical results show that there is a strong propensity of self-excited vibration of the wheelset–track system when the friction coefficient is larger than 0.21. Some unstable frequencies fall in the range 60–1200 Hz, which correspond to frequencies of rail corrugation. Parameter sensitivity analysis shows that the dynamic coefficient of friction, spring stiffness and damping of the sleeper supports all have important influences on the rail corrugation formation. Bringing the friction coefficient below a certain level can suppress or eliminate rail corrugation.

Magnetically coupled magnet–spring oscillators

A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of mechanical, and easily adjustable by the experimenter. The coupling of this new coupled oscillator system is determined by the currents that the magnets induce in two coils connected in series, one to each magnet. It is an interesting case of mechanical oscillators with field-driven coupling, instead of mechanical coupling. Moreover, it is both a coupled and a damped oscillating system that lends itself to a detailed study and presentation of many properties and phenomena of such a system of oscillators. A set of experiments that validates the theoretical model of the oscillators is presented and discussed.

Plokščiojo Didelio Tarpatramio Rėmo Įtemptojo Ir Deformuotojo Būvio Tyrimas, Atsižvelgiant Į Atramų Poslinkius

A calculation model of a building is only a simulation of the individual properties of the construction. Such a model is expressed by many factors, the most important of which are experience and knowledge of a designer. In difference to a traditional “single-stage” solution, an effective numerical analysis of a complicated situation can be presented comparing a few different variants. Such situation is specific for high-technology industrial facilities or entertainment buildings. A typical simulation sequence cannot be used for original buildings with principally different properties because investigation should take into account features of the construction. A general solution should analyze the already existing technical possibility and an individual situation considering the qualification of engineering staff. The paper presents investigation into a transversal frame of an indoor slope of the complex facility “Ski Slopes Covered With Snow Pavement in Druskininkai, Lithuania” carried out in 2009. According to the current Eurocodes and Lithuanian design codes, the service life of the facility is 100 years and a class of responsibility is RC3. The frame has a bay of 51,5 m, columns with foundations and a truss are rigidly jointed, the middle height of the frame (depending on the angle of the slope along facility) is about 1/3 of the bay. The stiffness of all structural members is specified. For frame actions and structural design, valid design codes are used. In geomorphologic meaning, the building site is placed near (about 100 m) the river Nemunas where real difference in the altitudes of the ground initial surface makes about 40 m. On the basis of the analyzed situation in the site, a decision on making a foundation with a pile cap on displacement piles has been accepted. Each pile consists of two parts: the upper part is of 600 mm diameter and 2 m length, whereas the last one has a diameter of 380 mm. After pile mounting, the steel shell of the pipe is pulled out. For an analytical analysis of a single pile, the Vesic formula is applied. Under conditions that two piles of the building site have been tested by means of vertical load action, two pairs of piles have followed the horizontal one. Vertical 1044 kN and horizontal 120 kN test loadings have been divided into 6 equal stages. Two asymmetrical foundations of the transversal frame are designed differently and make 8 piles in axis “A” and 6 piles - in “E”. Three variants of the pile calculation model are considered: node support, one finite element (an upper part of the pile) on the elastic spring in the vertical direction at the bottom edge and a pile divided into two parts on the vertical elastic spring at the bottom edge and along it (a horizontal subgrade factor). Within a course of investigation, the pile cap is modelled applying shell finite elements while the piles - employing beam ones. The final decision about frame stress/strain state can be made on the basis of analyzing the general calculation model “over-ground frame/foundation/ground”. Thus, three new models, including 5, 6 and 7 present foundations are jointed by the over-ground frame. In these cases, the columns with the truss are subjected not only to static loads but also to kinematic actions, i. e. foundation settlements, rotations and lateral displacements. A comparison of the results of seven separate calculation models shows that support parts of the columns are loaded low in case of elastic subgrade on the piles; bending the pile cap is the same; the distribution of internal forces between foundations in case of piles is more “soft”. Conclusions and recommendations are provided.

Fracture-Based Method to Determine Flexural Capacity of Concrete Beams on Soil

ABSTRACT A method to predict the fracture response of concrete beams utilizing cohesive crack elements was expanded from a three-point bending beam to a beam on soil boundary condition. The simulations were compared with monotonic three-point bending beam and beam on soil tests, verifying the cohesive elements with a bilinear softening curve defined by the concrete's fracture and tensile strength properties can effectively predict the flexural capacity and post-peak behavior of both specimen configurations. Vertical and horizontal springs idealized the soil support to the beams. Whether the springs were linear or nonlinear elastic had a limited effect on the peak load capacity of the concrete beams on soil. At pre-peak and peak load levels, the two concrete beam configurations had similar stress patterns and crack propagation levels in spite of the different boundary conditions. The method simplicity and accuracy under different boundary conditions offers a promising approach that can be extended to predicting the flexural capacity of concrete slabs.

420 発電用新型炉に適用する3次元免装置の開発 : 油圧ロッキング抑制装置の高圧力下の作動性と健全性評価(耐震I,OS-2 耐震・免震・制震,総合テーマ「伝統を,未来へ!」)

Three dimensional (3D) seismic isolation devices have been developed for the base isolation system of the Fast Breeder Reactor (FBR) that is an advanced nuclear reactor power plant building. The developed seismic isolation system consists of the hydraulic type vertical springs with rocking suppression mechanism and the laminated rubber bearings for horizontal direction. The isolation performances, i.e. natural period, damping, and rocking-suppression, have already been evaluated by the technical feasibility study and performance tests on a system which consists of down-sized devices on the shaking table, but in the seismic simulation on the real size building with this system, high hydraulic pressure was generated by rocking-suppression device under an extremely large seismic motion. In this paper, it is reported the frictional characteristics on high hydraulic pressure condition from the experiments on the 1/2 size of real device and the results of the seismic simulation on the real size building with isolation-device that has those characteristics.

Semi-active vibration isolation using a near-zero-spring-rate device: steady state analysis of a single-degree-of-freedom model

A vibration isolator is described which incorporates a near-zero-spring-rate device within its operating range. The device is an assembly of a vertical spring in parallel with two inclined springs. A low spring rate is achieved by combining the equivalent stiffness in the vertical direction of the inclined springs with the stiffness of the vertical central spring. It is shown that there is a relation between the geometry and the stiffness of the individual springs that results in a low spring rate. Computer simulation studies of a single-degree-of-freedom model for harmonic base input show that the performance of the proposed scheme is superior to that of the passive schemes with linear springs and skyhook damping configuration. The response curves show that, for small to large amplitudes of base disturbance, the system goes into resonance at low frequencies of excitation. Thus, it is possible to achieve very good isolation over a wide low-frequency band. Also, the damper force requirements for the proposed scheme are much lower than for the damper force of a skyhook configuration or a conventional linear spring with a semi-active damper.

Effects of full-height nonstructural partitions on modal properties of two nominally identical building floors

This paper presents a combined experimental and numerical investigation of the modal properties of two full-scale and nominally identical steel–concrete composite floors. The floors were one above the other in the same fully operational multi-storey building. Both floors accommodated open-plan as well as partitioned offices. Multi-input-multi-output (MIMO) modal testing was employed to measure as-built modal properties of both floors. It was found that the two nominally identical floors had different modal characteristics, likely due to the different arrangement of partitions in the floor. It was also found that the measured modes on both floor levels experienced a considerable level of complexity, likely to be caused by nonproportional damping. Finite element (FE) models were developed in ANSYS for both floors using best engineering judgement and their features and properties were then tuned to match the measured counterparts. The tuning was done manually by trial-and-error and then automatically using sensitivity-based FE model updating procedure implemented in the FEMtools software. It was found that the initial and geometrically very detailed FE models, which did not feature any nonstructural components, underestimated the measured natural frequencies by up to a considerable 20%–25%, depending on the floor level. When full-height plasterboard and glass partitions were explicitly modelled as vertical springs connected to the floor and grounded at the other end, the correlation between the experimental and FE results improved considerably.

Suppression of vertical bending and rigid-body-mode vibration in railway vehicle car body by primary and secondary suspension control: Results of simulations and running tests using Shinkansen vehicle

To improve ride comfort in railway vehicles, the suppression of vertical bending vibration and rigid-body-mode vibration in the car body is essential. In this paper, a system is proposed that aims to reduce bending and rigid-body-mode vibration simultaneously by introducing damping control devices in the primary and secondary suspensions. The technique involves a control system of primary vertical dampers and air springs; the former are used to suppress the first bending mode vibration; the latter, to suppress the rigid-body-mode vibration. The results of both simulations and vehicle running tests on the Sanyo—Shinkansen line demonstrate that this system reduced vertical vibrations in the bogies and the car body using the sky-hook control theory. In the running tests in particular, the system reduced the vertical vibration acceleration PSD peak value in the first bending mode to almost 20 per cent and in the rigid body mode to almost 50 per cent compared with the case when the system was not used. As a result, the ride quality level LT (a widely used index of ride comfort in Japan) decreased by at least 3 dB, indicating greater ride comfort.

On the force transmissibility of a vibration isolator with quasi-zero-stiffness

In this article the force transmissibility of a quasi-zero-stiffness (QZS) isolator is considered. The isolator comprises a vertical spring and two oblique springs that are either linear, linear with pre-stress or softening nonlinear with pre-stress. The force transmissibility of such a system is derived and compared with that of a linear system. Assuming light damping, simple approximate expressions for the maximum transmissibility and jump-down frequencies are derived. It is shown that there are advantages in having nonlinear and pre-stressed oblique springs compared to the other configurations, and that all the QZS systems can outperform the linear system provided that the system parameters are chosen appropriately.

A lateral active suspension for conventional railway bogies

The present paper describes an active centring system for railway vehicles. The proposed solution is based on lateral pneumatic actuators placed between bogie and car body connected to the vertical secondary suspension air springs. The objective of the developed centring system is twofold: the improvement of the curving behaviour of the train and the decrease of the lateral acceleration perceived by the passenger in curve negotiation thanks to the reduction of the ‘souplesse’ coefficient. The system is described in detail in the paper. Results from simulations are included considering a bidimensional model of the vehicle, and a detailed model of the air spring and control valves. The performance in curve negotiation of a vehicle equipped with this system and a conventional one is compared. Specifically, lateral displacements of the secondary suspension, roll angle and lateral accelerations are analysed. The results show noticeable performance improvements in the vehicle curving behaviour. The proposed centring system can be implemented in a conventional bogie without special design requirements; and due to the low air consumption, additional pressurised reservoirs are not required.

Development of a wide-tuning range and high Q variable capacitor using metal-based surface micromachining process

This study aims to improve the tuning range and quality-factor ( Q) of micro variable capacitors for wireless communication applications. A suspending 0.5 μm-thick gold thin-plate with two-gap structure in one-to-three ratio of spacing is designed for the maximization of tuning range. To enhance effectively the flexural rigidity of top metal-plate and improve further the tuning range of the varactor, a double-cross-type microstructure with two vertical fixed-fixed beam springs and four horizontal fixed-guided cantilever beams is introduced. Besides, a glass substrate (Corning 7740) was used to reduce substantially the power dissipation and improve the Q-factor of variable capacitor. The new glass-based double-cross-type micro variable capacitor has demonstrated many superior performances, including the wide-tuning range (2100%, at 1.0 MHz with 6.0 V), the moderate capacitance (0.56 pF, at 2.4 GHz and without DC bias), 6.5 V pull-in voltage, and the high Q-factor (40.6, at 2.4 GHz). These characteristics approximately match with the theoretical derivation or simulated results from Agilent-ADS, Ansoft-HFSS, and IntelliSuite software.

Dynamics of an elastic beam and a jumping oscillator moving in the longitudinal direction of the beam

An oscillator of two lumped masses linked through a vertical spring moves forward in the horizontal direction, initially at a certain height, over a horizontal Euler beam and descends on it due to its own weight. Vibration of the beam and the oscillator is excited at the onset of the ensuing impact. The impact produced by the descending oscillator is assumed to be either perfectly elastic or perfectly plastic. If the impact is perfectly elastic, the oscillator bounces off and hits the beam a number of times as it moves forward in the longitudinal direction of the beam, exchanging its dynamics with that of the beam. If the impact is perfectly plastic, the oscillator (initially) sticks to the beam after its first impact and then may separate and reattach to the beam as it moves along the beam. Further events of separation and reattachment may follow. This interesting and seemingly simple dynamic problem actually displays rather complicated dynamic behaviour and has never been studied in the past. It is found through simulated numerical examples that multiple events of separation and impact can take place for both perfectly elastic impact and perfectly plastic impact (though more of these in the case of perfectly elastic impact) and the dynamic response of the oscillator and the beam looks noisy when there is an event of impact because impact excites higher-frequency components. For the perfectly plastic impact, the oscillator can experience multiple events of consecutive separation from the beam and subsequent reattachment to it.

Three‐dimensional vibration characteristics of the permanent magnet–HTSC magnetic bearing

AbstractThe three‐dimensional vibration of the rotor in a permanent magnet– HTSC magnetic bearing system is studied. We have developed a magnetic bearing system which can revolve at up to 12,000 rpm, and three‐dimensional vibration of the rotor is measured with laser displacement sensors. To consider the rotor vibration in a mechanical resonance state, the static lateral and vertical pinning forces of the magnetic bearing are measured. The results are used to obtain the resonant frequency. There are two factors in the mechanical resonance caused by the magnetic bearing. One is the lateral equivalent spring coefficient and the other is the vertical equivalent spring coefficient. The influence of mechanical resonance caused by the lateral spring coefficient is large, and that of the vertical one is small. The three‐dimensional vibration of the rotor position around the mechanical resonant frequency is measured. Because the revolution of the rotor increases the lateral force to the center, the resonant frequency obtained in a free revolution experiment is larger than that obtained from pinning force measurement. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 165(3): 58–64, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20586

Advanced finite element modelling of perforated composite beams with flexible shear connectors

An extensive research and development programme has been undertaken by the authors to develop advanced analysis and design tools for practical design of long span composite beams in buildings. Both two- and three-dimensional finite element models employing solid and shell elements with material, geometrical and interfacial non-linearity were established to examine the full range structural behaviour of composite beams. In this paper, two-dimensional finite element models employing plane stress elements are established to examine the structural behaviour of perforated composite beams, and shear connectors with non-linear deformation characteristics are incorporated into the models through the use of both vertical and horizontal springs. It is demonstrated that after careful calibration against test data, the finite element models are able to predict the load carrying capacities of composite beams with large rectangular web openings against ‘Vierendeel’ mechanism satisfactorily. Moreover, a number of important structural quantities such as local axial and shear forces together with local bending moments acting onto the composite and the steel tee sections at failure are obtained after data analyses. Together with the load carrying capacities, these quantities compare favourably with the values obtained from a design method proposed previously by the authors, and hence, this provides quantitative justification to the proposed design method. Furthermore, the finite element models provide detailed information on the structural behaviour of shear connectors along the beam length, such as the longitudinal shear forces, the pull-out forces as well as the slippage of the shear connectors. Based on the findings of the finite element modelling, a number of recommendations on the design and construction of perforated composite beams are suggested.

On the design of a high-static–low-dynamic stiffness isolator using linear mechanical springs and magnets

The frequency range over which a linear passive vibration isolator is effective is often limited by the mount stiffness required to support a static load. This can be improved upon by incorporating a negative stiffness element in the mount such that the dynamic stiffness is much less than the static stiffness. In this case, it can be referred to as a high-static–low-dynamic stiffness (HSLDS) mount. This paper is concerned with a theoretical and experimental study of one such mount. It comprises two vertical mechanical springs between which an isolated mass is mounted. At the outer edge of each spring, there is a permanent magnet. In the experimental work reported here, the isolated mass is also a magnet arranged so that it is attracted by the other magnets. Thus, the combination of magnets acts as a negative stiffness counteracting the positive stiffness provided by the mechanical springs. Although the HSLDS suspension system will inevitably be nonlinear, it is shown that for small oscillations the mount considered here is linear. The measured transmissibility is compared with a comparable linear mass–spring–damper system to show the advantages offered by the HSLDS mount.

Resonance frequency analysis for surface-coupled atomic force microscopy cantilever in ambient and liquid environments

Shifts in the resonance frequencies of surface-coupled atomic force microscope (AFM) probes are used as the basis for the detection mechanisms in a number of scanning probe microscopy techniques including atomic force acoustic microscopy (AFAM), force modulation microscopy, and resonance enhanced piezoresponse force microscopy (PFM). Here, we analyze resonance characteristics for AFM cantilever coupled to surface in liquid environment, and derive approximate expressions for resonant frequencies as a function of vertical and lateral spring constant of the tip-surface junction. This analysis provides a simplified framework for the interpretation of AFAM and PFM data in ambient, liquid, and vacuum environments.

A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic

A vibration isolator consisting of a vertical linear spring and two nonlinear pre-stressed oblique springs is considered in this paper. The system has both geometrical and physical nonlinearity. Firstly, a static analysis is carried out. The softening parameter leading to quasi-zero dynamic stiffness at the equilibrium position is obtained as a function of the initial geometry, pre-stress and the stiffness of the springs. The optimal combination of the system parameters is found that maximises the displacement from the equilibrium position when the prescribed stiffness is equal to that of the vertical spring alone. It also satisfies the condition that the dynamic stiffness only changes slightly in the neighbourhood of the static equilibrium position. For these values, a dynamical analysis of the isolator under asymmetric excitation is performed to quantify the undesirable effects of the nonlinearities. It includes considering the possibilities of the appearance of period-doubling bifurcation and its development into chaotic motion. For this purpose, approximate analytical methods and numerical simulations accompanied with qualitative methods including phase plane plots, Poincaré maps and Lyapunov exponents are used. Finally, the frequency at which the first period-doubling bifurcation appears is found and the effect of damping on this frequency determined.

A novel x-axis tuning fork gyroscope with “8 vertical springs-proofmass” structure on (111) silicon

A novel x-axis tuning fork gyroscope with “8 vertical springs-proofmass” structure is presented. Wafer-thick proofmasses are made out of (111) silicon with bulk micromachining processes to achieve lower thermo-mechanical noise. Each proofmass is supported by 8 vertical springs, which are symmetrically distributed around the proofmass. The dimensions of 8 vertical springs are precisely confined by thermal oxide protected sidewalls and the extreme slowly etched (111)-planes in KOH etching. A mode mismatch of less than 30 Hz is achieved before tuning. Initial test shows a sensitivity of 0.15 mV/(deg/s) and a rate resolution around 0.1 deg/s under atmosphere pressure.

Analysis of static axial load capacity of single piles and large diameter shafts using nonlinear load transfer curves

A modified analytical model is proposed in this study for the analysis of pile axial load capacity with the load transfer method using nonlinear T-z and Q-z curves to model soil-pile behavior in skin friction or side shear and end bearing respectively. The method uses a three-dimensional (3D) pile model using solid finite elements with nonlinear load transfer curves resolved into components and mobilized around the pile perimeter. The use of multiple T-z component springs is demonstrated to accurately capture the total side resistance of the pile. The 3D pile method produces results of predicted pile axial load capacities from the load-settlement curves comparable to the one-dimensional analysis (1D) method. For a combined vertical and lateral loading on the pile, the proposed 3D pile method can address the limitation of the 1D pile method having vertical and lateral springs only acting at the pile center without rotational springs, which neglects the contribution of the side shear in the computation of pile bending moments. In the case of 3D pile model the moment or couple developed by the side shear around the perimeter can be taken into account, where this moment can be significant especially in strong soil material or in the case of large diameter pile/shafts.