Vertical Spring Research Articles

Optimal sensor placement for parameter estimation and virtual sensing of strains on an offshore wind turbine considering sensor installation cost

This paper proposes an optimal sensor placement (OSP) framework for parameter estimation, virtual sensing, and condition monitoring using information theory. The framework uses a Bayesian OSP method combined with modal expansion to minimize the information entropy about quantities of interest (QoI), such as strain time histories at critical locations of the structure, without the knowledge of input excitation. The proposed optimization framework also accounts for variations in sensor installation cost at different locations on the monitored structure. The framework is evaluated numerically using a realistic model of an offshore wind turbine on a jacket support structure under installation cost assumptions and considering information entropy of the QoI. The QoI in this numerical study are considered to be the strain time history at one or more locations on the support structure in one problem and the parameters of the structure in the other. A correlation length is considered to account for the spatial correlation of data between adjacent sensors. Effects of the correlation length and input loads on the OSP results for parameter estimation are studied. The considered structural parameters for estimation in this study include (1) modulus of elasticity of tower elements (tower stiffness), (2) modulus of elasticity of jacket elements (jacket stiffness), and (3) vertical foundation spring (soil stiffness). The effect of a subjective weight between the information entropy and sensor configuration cost on the OSP results is also investigated. Different optimal designs are achieved for different weight factors, and the Pareto solutions for OSP are presented. It is found that the OSP framework is an effective tool for decision-makers considering the cost of instrumentation. The presented Pareto optimal solutions can give insight into the value of OSP given a limited budget.

Performance Verification of Vertical Seismic Isolation Equipment Using Negative Rigidity Mechanism

In recent years, various seismic isolation devices have been developed to prevent earthquake damage to valuable art works. The purpose of this study is to develop a vertical seismic isolation system that both reduces the natural frequency and solves the problems of vertical seismic isolation systems in previous studies. In this study, we developed a vertical seismic isolator that supports the load with inclined springs without using vertical springs. A motor is mounted on the ball screw that constitutes the central axis of each crank mechanism. The vertical stiffness of this seismic isolator can be changed using the motor. In this study, the seismic isolation performance was improved by using the negative stiffness property to set the natural frequency lower. The vertical seismic isolation system was modeled using SimulationX. The characteristics of the vertical seismic isolation system were verified and its performance was evaluated by various experiments and simulations. The MBS model of the newly developed device was used to accurately simulate the loading characteristics of the vertical isolator such as negative stiffness characteristics. The performance of this vertical isolator was verified by vibration experiments and simulations assuming typical seismic waves in Japan. The average response factor of acceleration in the experiment was 17.8%, and the average response factor in the simulation was 15.9%, which exceeded the performance of the device in the previous study. Finally, in the resonance avoidance test, the acceleration of the top plate of the vertical base isolation system was reduced by 57% by using the vertical natural frequency adjustment mechanism to avoid resonance.

Railway vehicle vibration mechanism induced by offsetting axlebox suspension elements position

This paper describes railway vehicle vibration mechanism whereby offset suspension elements position affect bogieframe vibration response. Primary suspension elements are often set on offset position from center of axlebox, so we hypothesized that offset primary damper position trigger axlebox rotation around axlebox bearing, which play pivotal role in inducing bogie-frame pitching via coil spring. To address this hypothesis, we conducted whole vehicle vibration analysis, focusing on axlebox damper vertical damping force and coil spring horizontal force applied on the offset position from center of axlebox. Analysis results showed that the mechanisms are suggested to involve bogie-frame vibration response mediated by axlebox rotation as well as coil spring horizontal force.

Vertical Seismic Isolation Device for Three-Dimensional Seismic Isolation of Nuclear Power Plant Equipment—Case Study

The purpose of this study was to develop a vertical seismic isolation device essential for the three-dimensional seismic isolation design of nuclear power plant equipment. The vertical seismic isolation device in this study has a concept that can be integrally combined with a conventional laminated rubber bearing, a horizontal seismic isolator with a design vertical load of 10 kN. To develop the vertical seismic isolation device, the vertical spring and the seismic energy dissipation device capable of limiting the vertical displacement of the spring were designed and their performances were verified through actual tests. In this study, the target elevation of the floor is 136 ft, where safety-related nuclear equipment, such as cabinet and remote shutdown console, etc., is installed. The sensitivity studies were carried out to investigate the optimal design vertical isolation frequencies for the target building elevation. Based on the results of the sensitivity study, a disc spring and a helical coil spring were selected for the vertical stiffness design, and the steel damper was selected for the seismic energy dissipation, and their performance characteristics were tested to confirm the design performance. For the steel damper, three types were designed and their energy dissipation characteristics by hysteretic behavior were confirmed by the inelastic finite element analyses and the tests in static fully reversed cyclic conditions. Through the study of the vertical seismic isolation device, it was found that 2.5 Hz~3.0 Hz is appropriate for the optimal design vertical isolation. With results of the vertical seismic isolation performance analysis, the appropriate number of steel dampers are proposed to limit the vertical seismic displacement of the spring within the static displacement range by the design vertical load.

An Improved Structural Analysis Method for Isolator with Quasi-Zero-Stiffness Characteristic

A typical quasi-zero-stiffness (QZS) vibration isolator consisting of a vertical spring and two oblique springs has been widely researched on its static and dynamic characteristics. A general criterion for determining structural parameters of QZS isolator is to achieve low nondimensional stiffness around the equilibrium position. However, lower nondimensional stiffness of linear isolator means lower isolation frequency, which may be invalid on QZS isolator. Because there is an implicit relationship between geometric parameter and stiffness ratio of QZS isolator, this study presents an improved optimization criterion for determining the optimal structural parameters of the typical QZS isolator. The optimization criterion is that the QZS isolator has the maximum displacement range around the equilibrium position without exceeding given natural frequency, rather than given nondimensional stiffness. The results show that isolator with these optimal parameters can achieve lower stiffness around the equilibrium position and better vibration isolation performance. Furthermore, an extended QZS isolator consisting of vertical spring with fixed stiffness and prestressed oblique springs is discussed to further improve stiffness characteristic. Better stiffness performance can be obtained when the prestressed oblique springs have softening stiffness and the exponent of the nonlinear stiffness is 2. Considering the existence of friction in practical application, the influence of friction on both static and dynamic characteristics is investigated. The analysis reveals that friction has little influence on its stiffness characteristic around the static equilibrium position and friction damping produced by friction affects the response amplitude and resonant frequency in dynamics.

An Air Spring Vibration Isolator Based on a Negative-Stiffness Structure for Vehicle Seat

This research introduces an air spring vibration isolator system (ASVIS) based on a negative-stiffness structure (NSS) to improve the vehicle seat’s vibration isolation performance at low excitation frequencies. The main feature of the ASVIS consists of two symmetric bellows-type air springs which were designed on the basis of a negative stiffness mechanism. In addition, a crisscross structure with two straight bars was also used as the supporting legs to provide the nonlinear characteristics with NSS. Moreover, instead of using a vertical mechanical spring, a sleeve-type air spring was employed to provide positive stiffness. As a result, as the weight of the driver varies, the dynamic stiffness of the ASVIS can be easily adjusted and controlled. Next, the effects of the dimension parameters on the nonlinear force and nonlinear stiffness of ASVIS were analyzed. A design process for the ASVIS is provided based on the analytical results in order to achieve high static–low dynamic stiffness. Finally, numerical simulations were performed to evaluate the effectiveness of the ASVIS. The results obtained in this paper show that the values of the seat displacement of the ASVIS with NSS were reduced by 77.16% in comparison with those obtained with the traditional air spring isolator without NSS, which indicates that the design of the ASVIS isolator with NSS allows the effective isolation of vibrations in the low-frequency region.

Buckling analysis of a 10 MW offshore wind turbine subjected to wind-wave-earthquake loadings

This paper investigates dynamic responses and buckling of a 10 MW monopile offshore wind turbine (OWT) subjected to multiple environmental loadings including earthquake, wind, wave and current. The finite element model (FEM) of the support structure is developed in ANSYS to obtain relatively accurate and reliable structural responses. The soil structure interaction (SSI) effects are represented using a set of lateral nonlinear springs and a vertical nonlinear spring. The SSI effects on the eigenmodes of the support structure are examined. The time series of wind and wave loads are, respectively, calculated using FAST and AQWA and then fed into ANSYS as external loads to perform the seismic analysis. The structural responses and local damage characteristics of the 10 MW OWT have been studied. The results indicate that the wind, wave and current loads in the fore-aft direction have a significant effect on the seismic responses of the OWT. It is therefore the turbulent wind, wave and current loadings cannot be ignored when performing a seismic analysis of OWTs. As a result of buckling, the change of environmental load will lead to a transition between buckling modes. These findings provide useful insights for the design of monopile offshore wind turbines.

Structural design guidelines for Delayed Coker Unit (DCU) used in hydrocarbon industry

PurposeDelays in projects execution due to improper structural design lead to substantial losses to the owners. Little guidelines are available in practice that deals with structural design of Delayed Coker Units (DCUs). This work describes effective structural criteria for design of DCU used in hydrocarbon industry. Economical procedures are described for steel and concrete design. Design of pump houses supporting DCU is also described.Design/methodology/approachNumerical procedures are developed to model pipelines and mechanical equipment loadings. Soil restraints are simulated using horizontal and vertical springs along the pile embedded length. Concrete pile-caps are integrated with steel structure in the analysis model.FindingsThe proposed design approach is cost effective to use in practice. The paper offers economical footprint for design of DCUs that can be used for multiple projects.Practical implicationsThe paper provides useful guidelines that can be utilized by engineers for design of coker heater and coker fractionation stacks, steel modules, coke pump house, deluge building, etc.Originality/valueCurrently, there are no guidelines in practice that deal with structural design of DCU. The present work bridges this gap and describes novel strategies that can be utilized for industrial projects.

Stability Design of Air Vibration Isolation Device for a High Power Density Main Engine

In order to improve the alignment stability of the air vibration isolation device of a high-powered main engine, we established a mechanical model for the air vibration isolation system and analyzed the alignment deviation of the device and the vibration decoupling conditions of the system. Additionally, an optimized design method for the dual-direction support of the air vibration isolators positioned symmetrically on the main engine was proposed. The resultant design showed that when compared to the conventional inclined support of air springs for the main engines onboard ships, the dual-direction support design proposed in this paper for air vibration isolation could eliminate the adverse effect of the output torque reaction on the alignment of the main engine and decouple the system to reduce the number of peaks in the frequency response of vertical force transmission. The optimized design could effectively improve the alignment performance of the device for tilted or swinging operating conditions and maintain the good alignment stability of the device when a single vertical support air spring fails. A single vertical support air spring failure mainly affects the stability of the main engine under the reaction of the output torque, especially the air springs arranged in the corner, while the air springs arranged in the middle have no effect. The optimized design could also improve the vibration isolation performance. This is important for the design of air spring vibration isolation devices for high power density main engines.

Design and Research of Semiactive Quasi-Zero Stiffness Vibration Isolation System for Vehicles

The vehicle-mounted equipment is easy to be disturbed by external vibration excitations during transportation, which is harmful to the measurement accuracy and performance of the equipment. Aiming at the vibration isolation of the vehicle-mounted equipment, a semiactively controlled quasi-zero stiffness (QZS) vibration isolator with positive and negative stiffness is proposed. The vertical spring is paralleled with a magnetorheological (MR) damper, and the semiactive on-off control scheme is adopted to control the vibration. The analytical expression of the isolator’s displacement transmissibility is derived via the averaging method. Then, the vibration isolation performance under different road excitations and different driving speeds is simulated and compared with the uncontrolled passive QZS vibration isolator. In addition, the mechanical structure of the semiactive QZS isolator is designed and manufactured, and the test system is built by LabVIEW software and PXI embedded system. The isolation effect of the semiactive QZS isolator is verified through test data. It is found that the proposed semiactive QZS isolator shows excellent vibration isolation performance under various road excitations, while the passive QZS isolator is effective only under harmonic excitations. The vertical acceleration of vehicle-mounted device can be decreased over 70% after isolation, and the vibration isolation effect is remarkable. The design idea and research results of the semiactive QZS isolator may provide theoretical guidance and engineering reference for vibration isolation.

A quasi-zero-stiffness device capable of vibration isolation and energy harvesting using piezoelectric buckled beams

A quasi-zero-stiffness (QZS) device is proposed for both vibration isolation and energy harvesting based on a concept of converting part of the vibrational energy into electrical energy and concurrently reducing the energy transmitted to the vibration receiver. The proposed device is constructed by four piezoelectric buckled beams and a vertical spring. The structural layout of the piezoelectric buckled beams has two benefits: firstly it produces negative stiffness in the vibration direction and thus offers the benefit of lowering the beginning frequency of isolation; secondly it always enables large strain and stress for the piezoelectric patches and thus leads to higher electrical output. The harmonic balance method is employed for the dynamic analysis based on the electromechanical coupled equations. The isolation performance is compared with a linear isolator and a conventional QZS isolator, which indicates that the proposed device can achieve lower isolation frequency and lower peak transmissibility. The energy harvesting performance is compared with the cantilever-beam energy harvester, which indicates that the proposed device can achieve higher output power and lower operating frequencies. The superior performances are also demonstrated by experiments, in which the lowest isolation frequency of 2.5 Hz and the maximum output power of 8.31 mW are obtained.

Interface friction effects on scaling a vertical spring-viscous damper isolation system in a shaking table test

A vertical spring had a changeable horizontal stiffness to avoid resonance under a seismic displacement, and a viscous damper had a perfect energy dissipation function to reduce the seismic displacement. They were joined together to achieve a seismic isolation system considerably reducing the seismic acceleration response, however, their displacement should be paid more attentions under an earthquake or in a shaking table test. Because the interface friction in the system affected the scaling process of the system in the shaking table test and the corresponding displacement responses, the system was numerically scaled before a real shaking table test. The comparison between the displacement responses of scaled models and prototype models shows that the spatial friction variation and the gravity distortion are the error sources of the relative and residual displacements of scaled models. The error of scaled relative displacement is reduced by the means of increasing PGA, damping constant, spring constant or reducing vertical spring length with zero stress, however, the error of scaled residual displacement is still chaotic under these means. Only if the error sources above are eliminated fundamentally will the error of scaled models be avoided. The conclusions are validated correct by a real shaking table test.

Cost effective design procedures to support modular catalytic reactors

PurposeThe purpose of this paper is to describe cost effective structural design procedures to support catalytic reactors used in hydrocarbon industry. Three case studies are presented using various reactor models. Modularization and transportation challenges are also discussed. The scope of the paper is limited only to the structural and construction aspects. The chemical and mechanical designs are not covered in this paper.Design/methodology/approachFinite element strategies are developed to model load transfer to reactor’s supports and to simulate soil/structure interaction. Fictitious nodes are generated at bolt locations to transfer the reactor’s loadings from the skirt to the pile cap. Soil-pile interaction is modeled using horizontal and vertical springs along the pile embedded length. Flexible supports are used at the bottom of the piles to stimulate the end bearing of the soil bed. The approach is demonstrated for several case studies of reactors support system.FindingsThe described algorithm is accurate and computationally efficient. Furthermore, the procedure can be used in practice for design catalytic reactor support.Practical implicationsThe paper provides very useful guidelines that can be utilized in practice for design of catalytic reactor supports system. The procedure is cost effective and computationally efficient.Originality/valueExtensive efforts were made in the past to develop economical procedures for catalytic reactors design. Much of the work focused on the process and mechanical aspects of catalytic reactors. Very limited work addressed the structural design aspects. Furthermore, no guidelines are available in current codes of practice.

Numerical Study of the Seismic Response of an Instrumented Building with Underground Stories

Engineering practitioners do not usually include soil-structure interactions in building design; rather, it is common to model and design foundations as embedded joints with joint–based reactions. In some cases, foundation structures are modeled as rigid bodies, embedding the first story into lower vertical elements. Given that the effects of underground floors on the seismic response are not generally included in current building design provisions, it has been little explored in the literature. This work compares and analyzes models to study the effects of different underground stories modeling approaches using earthquake vibration data recorded for the 16–story Alcazar building office in downtown Viña del Mar (Chile). The modeling expands beyond an embedded first story structure to soil with equivalent springs, representing soil-structure interaction (SSI), with varying rigid soil homogeneity. The building was modeled in a finite element software considering only dead load as a static load case because the structure remained in the framing stage when the monitoring system was operating. The instruments registered 72 aftershocks from the 2010 Maule Earthquake, and this study focused on 11 aftershocks of different hypocenters and magnitudes to collect representative information. The comparisons between empirical records and models in this study showed a better fit between the model and the real vibration data for the models that do consider the SSI using horizontal springs attached to the retaining walls of the underground stories. In addition, it was observed that applying a stiffness reduction factor of 0.7 to all elements in deformation verification models for average-height buildings was suitable to analyze the behavior under small earthquakes; better results are obtained embedding the structure in the foundation level than embedding in the street level; the use of horizontal springs with Kuesel’s model with traction for the analysis of the structure yields appropriate results; it is necessary to carefully select the spring constants to be used, paying special attention to the vertical springs. Even though the results presented herein indicate that the use of vertical springs to simulate the SSI of the base slab can result in major differences concerning the real response, it is necessary to obtain more data from instrumentation across a wider variety of structures to continue to evaluate better design and modeling practices. Similarly, further analyses, including nonlinear time-history and high-intensity events, are needed to best regulate building design.

Second-order Nonlinear Differential Equations: Oscillation Tests and Applications

The 2nd order Differential Equations (DEs) are applied to analyze various phenomena in physics and it is extended to engineering. Specifically 2nd order linear DEs are having a big role in this field. We already observed this working rule in moving systems like a vertical spring attached with a mass. Another example is an electric circuit with a resistor, an inductor, and a capacitor in series connection. These models are applicable to approximate more complex situations like bond structure between atoms or molecules. They are generally patterned as vibrating springs which is explained by the same DEs. Qualitative theory analysis of DEs is an active area of investigation in theory and application point of view. For instance, oscillatory behavior of 2nd order DEs have many applications in the research related to distributed networks where in high-speed computations lossless transmission lines evolve. These lossless transmission lines are employed to connect switching circuits. Recently the study the functional DEs of neutral type is an active area of research. Many researchers are working in the field of oscillation theory and studying only sufficient conditions. Merely few are considering the necessary and sufficient conditions. We have attempted to set up the necessary and sufficient conditions for oscillation of solutions of 2nd order nonlinear neutral DEs. Mathematics Subject Classification (2010): 34K.

Vibration bandgap of a locally resonant beam considering horizontal springs

Structural vibrations could seriously affect the working performance and even cause fatal hazards to host structures. To reduce low frequency vibrations, a locally resonant metamaterial beam coupled by horizontal springs is proposed. The dynamic model of the metamaterial beam is established with the finite element method. The frequency response function of the metamaterial beam is derived, and the bandgap of the locally resonant beam is obtained. The effects of the number of locally resonator units, damping, mass, and stiffness of the vertical spring and horizontal spring are analyzed. The results show that with the increase of the number of units, damping ratio, mass, and stiffness, the bandgap changes significantly, resulting in the enhanced vibration suppress performance in the low-frequency region (f < 200 Hz). The resonator with the horizontal spring is conducive to suppress vibrations of the beam.

High‐Efficiency Vibration Isolation for a Three‐Phase Power Transformer by a Quasi‐Zero‐Stiffness Isolator

The vibrations generated by a three‐phase power transformer reduce the comfort of residents and the service life of surrounding equipment. To resolve this tough issue, a quasi‐zero‐stiffness (QZS) isolator for the transformer is proposed. This paper is devoted to developing a QZS isolator in a simple way for engineering practices. The vertical springs are used to support the heavy weight of the transformer, while the oblique springs are employed to fulfill negative stiffness to neutralize the positive stiffness of the vertical spring. Hence, a combination of the vertical and oblique spring can yield high static but low dynamic stiffness, and the vibration isolation efficiency can be improved substantially. The dynamic analysis for the QZS vibration isolation system is conducted by the harmonic balance method, and the vibration isolation performance is estimated. Finally, the prototype of the QZS isolator is manufactured, and then the vibration isolation performance is tested comparing with the linear isolator under real power loading conditions. The experimental results show that the QZS isolator prominently outperforms the existing linear isolator. This is the first time to devise a QZS isolator for three‐phase power transformers with heavy payloads in engineering practices.

Synchronous characteristic of three homodromy motors in vibrating isolation system

This paper researched the synchronous characteristic of three homodromy motors in a secondary isolation system. Firstly, the motion differential equations of the system were established via employing Lagrange’s equation. The Laplace transform was used to deduce approximate solutions of displacement. Next, the ability of vibrating isolation was determined through amplitude ratio. Secondly, the synchronous condition and steady criterion was obtained via employing the average small parameters method and Lyapunov criterion. And then the influence of structural parameters of the system on synchronous ability was analyzed. Moreover, the synchronous characteristics of the system, including the difference of residual torque among induction motors, the synchronous ability, the output torque of motors and the stable phase difference, were discussed through numerical analyses. Finally, the accuracy of theoretical analyses was proved through computer simulation results. It is shown that, the ability of vibrating isolation is principally impacted by vertical spring stiffness; the greater the installation distance among three motors, the easier to achieve synchronous motion of the rotors; meanwhile, the output torque of asynchronous motors is affected by the synchronous state of the vibrating system; the synchronous characteristic is mainly affected by the mounting dip angle of motors and the installation distance among motors. The research results can promote development of vibration engineering and related fields.

Shear wall modeling with asymmetric openings by macro elements

In this study MVLEM (Multiple Vertical Line Element Model) is utilized to model a shear wall made of concrete with asymmetric openings. For this aim, an experimental RC shear wall with asymmetric openings was studied and modeled by the 3D microscopic FEM (Finite Element Method) via ABAQUS software package. To achieve a macroscopic model with a high accuracy two macroscopic shear walls were modeled. These macroscopic walls are identical whereas the main difference is the stiffness in the beam at the connection zone. The macroscopic modeling for different members of the studied concrete shear wall column next to the openings coupling beams and the wall is developed by horizontal and vertical springs that simulate shear and flexural behaviors. Modeling of these parts depends on the moment distribution from horizontal loading. Responses of the macroscopic models under static cyclic and monotonic loading were compared with the validated microscopic model. According to the results the proposed macroscopic model in which low connection stiffness was used shows acceptable accuracy with the microscopic model.

Dynamic Response of Rigid Pavement Plate due to Localized Blast Load

In structural and transportation engineering applications, the dynamic response of orthotropic plates is an essential matter. Engineers did not consider the effects of dynamic loads such as those from machine vibrations or blast load. Dynamic analysis of rigid pavement plates due to local blast loads on concrete slabs in this research is modeled as concrete slabs with boundary condition that every edges of plates have a dowel-tie bar support and The rigid concrete pavement sitting on elastics Pasternak foundation is modeled by using the Kirchhoff theory of thin plates. Pasternak foundation have elastic vertical spring support and continuous shear layer. The main system responses that are observed are the transversal deflections at midspan and the internal stresses of the plate, particularly the maximum principle stress, minimum principle stress and maximum shear stress. Three loading phases are included in the analysis, namely: the positive phase, the negative phase, and the free vibration phase. Analyses are carried out utilizing a numeric approach termed the Modified Bolotin Method with two trancedental equation. The analysis is performed when the load is above the plate (0 ≤ t ≤ t0). Deflections resulting from various load positions on the set of slab models throughout all three phases are then compared side-by-side. Bending moment, shear forces, and stresses are calculated on all slab models with the Friedlander localized blast loading applied at midspan and the results are presented as stress contours that are then compared between each model.