Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper. (C) 2011 Elsevier Ltd. All rights reserved.

Energetic, ecologic and fluid-dynamic analysis of a fluidized bed gasifier operating with sugar cane bagasse

This work aims to study the thermodynamic, ecological and fluid-dynamic aspects of a circulating fluidized bed gasifier using sugar cane bagasse as biomass, in order to estimate a model of its normal operation. In the initial stage was analysed the composition of biomass selected (sugar cane bagasse) and its lower heating value (LHV) was calculated. The energy balance of the gasifier was done, being the volumetric flow of air, synthesis gas and biomass estimated. Also the power produced by this gasifier was theoretically estimated. Then the circulating fluidized bed gasifier was designed for operation with approximately 100 kg/h of processed biomass. Cross-sectional area of the reactor, feeder size, diameter of the exit zone of the gases and minimum height of the expanded bed were selected. Some bed gasifier hydrodynamic factors were also studied. The minimum fluidization velocity, fluidization terminal velocity, and average fluidizing velocity were calculated, in order to understand the fluid-dynamic behaviour of gasification of this fuel. It was obtained a theoretical model that can support a possible prototype of circulating fluidized bed gasifier biomass. Finally, there were studied the ecological aspects of the gasifier, through an overall methodology. Ecological efficiencies were estimated for two scenarios: first considering the carbon cycle and thereafter disregarding the carbon cycle. In both cases, it can be proved the ecological viability of the project. © 2013 Elsevier Ltd. All rights reserved.

Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

Fluid dynamic analysis and modelling of industrial chemical equipment

The research is aimed at contributing to the identification of reliable fully predictive Computational Fluid Dynamics (CFD) methods for the numerical simulation of equipment typically adopted in the chemical and process industries. The apparatuses selected for the investigation, specifically membrane modules, stirred vessels and fluidized beds, were characterized by a different and often complex fluid dynamic behaviour and in some cases the momentum transfer phenomena were coupled with mass transfer or multiphase interactions. Firs of all, a novel modelling approach based on CFD for the prediction of the gas separation process in membrane modules for hydrogen purification is developed. The reliability of the gas velocity field calculated numerically is assessed by comparison of the predictions with experimental velocity data collected by Particle Image Velocimetry, while the applicability of the model to properly predict the separation process under a wide range of operating conditions is assessed through a strict comparison with permeation experimental data. Then, the effect of numerical issues on the RANS-based predictions of single phase stirred tanks is analysed. The homogenisation process of a scalar tracer is also investigated and simulation results are compared to original passive tracer homogenisation curves determined with Planar Laser Induced Fluorescence. The capability of a CFD approach based on the solution of RANS equations is also investigated for describing the fluid dynamic characteristics of the dispersion of organics in water. Finally, an Eulerian-Eulerian fluid-dynamic model is used to simulate mono-disperse suspensions of Geldart A Group particles fluidized by a Newtonian incompressible fluid as well as binary segregating fluidized beds of particles differing in size and density. The results obtained under a number of different operating conditions are compared with literature experimental data and the effect of numerical uncertainties on axial segregation is also discussed.

Dynamic characterisation of four nine-story large-panel R.C. buildings in Bishkek (Kyrgyzstan): A comparison between experimental ambient vibration analysis and numerical finite element modeling

With the outlook of improving seismic vulnerability assessment for the city of Bishkek (Kyrgyzstan), the global dynamic behaviour of four nine-storey r.c. large-panel buildings in elastic regime is studied. The four buildings were built during the Soviet era within a serial production system. Since they all belong to the same series, they have very similar geometries both in plan and in height. Firstly, ambient vibration measurements are performed in the four buildings. The data analysis composed of discrete Fourier transform, modal analysis (frequency domain decomposition) and deconvolution interferometry, yields the modal characteristics and an estimate of the linear impulse response function for the structures of the four buildings. Then, finite element models are set up for all four buildings and the results of the numerical modal analysis are compared with the experimental ones. The numerical models are finally calibrated considering the first three global modes and their results match the experimental ones with an error of less then 20%.

Dynamic Effects On Culverts for High Speed Trains

Culverts are very common in recent railway lines. Wild life corridors and drainage conducts often fall in this category of partially buried structures. Their dynamic behavior has received far less attention than other structures such as bridges but its large number makes that study an interesting challenge from the point of view of safety and savings. In this paper a complete study of a culvert, including on-site measurements as well as numerical modelling, will be presented. The structure belongs to the high speed railway line linking Segovia and Valladolid, in Spain. The line was opened to traffic in 2004. Its dimensions (3x3m) are the most frequent along the line. Other factors such as reduced overburden (0.6m) and an almost right angle with the track axis make it an interesting example to extract generalized conclusions. On site measurements have been performed in the structure recording the dynamic response at selected points of the structure during the passage of high speed trains at speeds ranging between 200 and 300km/h. The measurements by themselves provide a good insight into the main features of the dynamic behaviour of the structure. A 3D finite element model of the structure, representing its key features was also studied as it allows further understanding of the dynamic response to the train loads . In the paper the discrepancies between predicted and measured vibration levels will be analyzed and some advices on numerical modelling will be proposed

Assessing the dynamic behavior of wsn motes and rfid semi-passive tags for temperature monitoring.

A notorious advantage of wireless transmission is a significant reduction and simplification in wiring and harness. There are a lot of applications of wireless systems, but in many occasions sensor nodes require a specific housing to protect the electronics from hush environmental conditions. Nowadays the information is scarce and nonspecific on the dynamic behaviour of WSN and RFID. Therefore the purpose of this study is to evaluate the dynamic behaviour of the sensors. A series of trials were designed and performed covering temperature steps between cold room (5 °C), room temperature (23 °C) and heated environment (35 °C). As sensor nodes: three Crossbow motes, a surface mounted Nlaza module (with sensor Sensirion located on the motherboard), an aerial mounted Nlaza where the Sensirion sensor stayed at the end of a cable), and four tags RFID Turbo Tag (T700 model with and without housing), and 702-B (with and without housing). To assess the dynamic behaviour a first order response approach is used and fitted with dedicated optimization tools programmed in Matlab that allow extracting the time response (?) and corresponding determination coefficient (r2) with regard to experimental data. The shorter response time (20.9 s) is found for the uncoated T 700 tag which encapsulated version provides a significantly higher response (107.2 s). The highest ? corresponds to the Crossbow modules (144.4 s), followed by the surface mounted Nlaza module (288.1 s), while the module with aerial mounted sensor gives a response certainly close above to the T700 without coating (42.8 s). As a conclusion, the dynamic response of temperature sensors within wireless and RFID nodes is dramatically influenced by the way they are housed (to protect them from the environment) as well as by the heat released by the node electronics itself; its characterization is basic to allow monitoring of high rate temperature changes and to certify the cold chain. Besides the time to rise and to recover is significantly different being mostly higher for the latter than for the former.

Cyclic behaviour of saturated sands subject to previous horizontal shear stresses

The dynamic behaviour of saturated sands has been studied from different perspectives. However, most experimental research on this field does not take into account the shear stress conditions existing prior to the application of dynamic loads; i.e., a null initial static shear stress (τo = 0) is assumed. The main objective of this work is to report on the influence that static shear stresses (τo) have on the behaviour of saturated sands under cyclic shear loads. This article presents the results and analysis of part of a wider experimental programme involving 30 monotonic and 26 cyclic simple shear tests for different combinations of static shear stress (τo) and cyclic shear stress (τc) (all undrained), besides identification and classification tests. The tested samples have been taken from the area of the North Entrance Mouth at the Port of Barcelona (Spain).

Measuring dynamic effects on underpasses of high-speed railway lines

Underpasses are common in modern railway lines. Wildlife corridors and drainage conduits often fall into this category of partially buried structures. Their dynamic behaviour has received far less attention than that of other structures such as bridges, but their large number makes their study an interesting challenge in order to achieve safe and cost-effective structures. As ballast operations are a key life cycle cost, and excessive vibrations increase the need of ballast regulation in order to ensure track geometry, special attention is paid to accelerations, the values of which should be limited to avoid track instability according to Eurocode. In this paper, the data obtained during on site measurements on culverts belonging to a Spanish high-speed train line are presented. A set of six rectangular-shaped, closed-frame underpasses were monitored under traffic loading. Acceleration records at different points of the structures are presented and discussed. They reveal a non-uniform dynamic response of the roof-slab, with the highest observed values below the occupied track. Also, they indicate that the dynamic response is important up to frequencies higher than those usually observed for standard simply supported bridges. Finally, they are used to obtain a heuristic rule to estimate acceleration levels on the roof-slab.

Nonlinear seismic behaviour of concrete arch bridges

Arch bridge structural solution has been known for centuries, in fact the simple nature of arch that require low tension and shear strength was an advantage as the simple materials like stone and brick were the only option back in ancient centuries. By the pass of time especially after industrial revolution, the new materials were adopted in construction of arch bridges to reach longer spans. Nowadays one long span arch bridge is made of steel, concrete or combination of these two as "CFST", as the result of using these high strength materials, very long spans can be achieved. The current record for longest arch belongs to Chaotianmen bridge over Yangtze river in China with 552 meters span made of steel and the longest reinforced concrete type is Wanxian bridge which also cross the Yangtze river through a 420 meters span. Today the designer is no longer limited by span length as long as arch bridge is the most applicable solution among other approaches, i.e. cable stayed and suspended bridges are more reasonable if very long span is desired. Like any super structure, the economical and architectural aspects in construction of a bridge is extremely important, in other words, as a narrower bridge has better appearance, it also require smaller volume of material which make the design more economical. Design of such bridge, beside the high strength materials, requires precise structural analysis approaches capable of integrating the combination of material behaviour and complex geometry of structure and various types of loads which may be applied to bridge during its service life. Depend on the design strategy, analysis may only evaluates the linear elastic behaviour of structure or consider the nonlinear properties as well. Although most of structures in the past were designed to act in their elastic range, the rapid increase in computational capacity allow us to consider different sources of nonlinearities in order to achieve a more realistic evaluations where the dynamic behaviour of bridge is important especially in seismic zones where large movements may occur or structure experience P - _ effect during the earthquake. The above mentioned type of analysis is computationally expensive and very time consuming. In recent years, several methods were proposed in order to resolve this problem. Discussion of recent developments on these methods and their application on long span concrete arch bridges is the main goal of this research. Accordingly available long span concrete arch bridges have been studied to gather the critical information about their geometrical aspects and properties of their materials. Based on concluded information, several concrete arch bridges were designed for further studies. The main span of these bridges range from 100 to 400 meters. The Structural analysis methods implemented in in this study are as following: Elastic Analysis: Direct Response History Analysis (DRHA): This method solves the direct equation of motion over time history of applied acceleration or imposed load in linear elastic range. Modal Response History Analysis (MRHA): Similar to DRHA, this method is also based on time history, but the equation of motion is simplified to single degree of freedom system and calculates the response of each mode independently. Performing this analysis require less time than DRHA. Modal Response Spectrum Analysis (MRSA): As it is obvious from its name, this method calculates the peak response of structure for each mode and combine them using modal combination rules based on the introduced spectra of ground motion. This method is expected to be fastest among Elastic analysis. Inelastic Analysis: Nonlinear Response History Analysis (NL-RHA): The most accurate strategy to address significant nonlinearities in structural dynamics is undoubtedly the nonlinear response history analysis which is similar to DRHA but extended to inelastic range by updating the stiffness matrix for every iteration. This onerous task, clearly increase the computational cost especially for unsymmetrical buildings that requires to be analyzed in a full 3D model for taking the torsional effects in to consideration. Modal Pushover Analysis (MPA): The Modal Pushover Analysis is basically the MRHA but extended to inelastic stage. After all, the MRHA cannot solve the system of dynamics because the resisting force fs(u; u_ ) is unknown for inelastic stage. The solution of MPA for this obstacle is using the previously recorded fs to evaluate system of dynamics. Extended Modal Pushover Analysis (EMPA): Expanded Modal pushover is a one of very recent proposed methods which evaluates response of structure under multi-directional excitation using the modal pushover analysis strategy. In one specific mode,the original pushover neglect the contribution of the directions different than characteristic one, this is reasonable in regular symmetric building but a structure with complex shape like long span arch bridges may go through strong modal coupling. This method intend to consider modal coupling while it take same time of computation as MPA. Coupled Nonlinear Static Pushover Analysis (CNSP): The EMPA includes the contribution of non-characteristic direction to the formal MPA procedure. However the static pushovers in EMPA are performed individually for every mode, accordingly the resulted values from different modes can be combined but this is only valid in elastic phase; as soon as any element in structure starts yielding the neutral axis of that section is no longer fixed for both response during the earthquake, meaning the longitudinal deflection unavoidably affect the transverse one or vice versa. To overcome this drawback, the CNSP suggests executing pushover analysis for governing modes of each direction at the same time. This strategy is estimated to be more accurate than MPA and EMPA, moreover the calculation time is reduced because only one pushover analysis is required. Regardless of the strategy, the accuracy of structural analysis is highly dependent on modelling and numerical integration approaches used in evaluation of each method. Therefore the widely used Finite Element Method is implemented in process of all analysis performed in this research. In order to address the study, chapter 2, starts with gathered information about constructed long span arch bridges, this chapter continuous with geometrical and material definition of new models. Chapter 3 provides the detailed information about structural analysis strategies; furthermore the step by step description of procedure of all methods is available in Appendix A. The document ends with the description of results and conclusion of chapter 4.

Dynamic simulation of chemical plant

A CSSL- type modular FORTRAN package, called ACES, has been developed to assist in the simulation of the dynamic behaviour of chemical plant. ACES can be harnessed, for instance, to simulate the transients in startups or after a throughput change. ACES has benefited from two existing simulators. The structure was adapted from ICL SLAM and most plant models originate in DYFLO. The latter employs sequential modularisation which is not always applicable to chemical engineering problems. A novel device of twice- round execution enables ACES to achieve general simultaneous modularisation. During the FIRST ROUND, STATE-VARIABLES are retrieved from the integrator and local calculations performed. During the SECOND ROUND, fresh derivatives are estimated and stored for simultaneous integration. ACES further includes a version of DIFSUB, a variable-step integrator capable of handling stiff differential systems. ACES is highly formalised . It does not use pseudo steady- state approximations and excludes inconsistent and arbitrary features of DYFLO. Built- in debug traps make ACES robust. ACES shows generality, flexibility, versatility and portability, and is very convenient to use. It undertakes substantial housekeeping behind the scenes and thus minimises the detailed involvement of the user. ACES provides a working set of defaults for simulation to proceed as far as possible. Built- in interfaces allow for reactions and user supplied algorithms to be incorporated . New plant models can be easily appended. Boundary- value problems and optimisation may be tackled using the RERUN feature. ACES is file oriented; a STATE can be saved in a readable form and reactivated later. Thus piecewise simulation is possible. ACES has been illustrated and verified to a large extent using some literature-based examples. Actual plant tests are desirable however to complete the verification of the library. Interaction and graphics are recommended for future work.

An investigation of the dynamic characteristics of a bolted-rotor system

A Jeffcott rotor consists of a disc at the centre of an axle supported at its end by bearings. A bolted Jeffcott rotor is formed by two discs, each with a shaft on one side. The discs are held together by spring loaded bolts near the outer edge. When the rotor turns there is tendency for the discs to separate on one side. This effect is more marked if the rotor is unbalanced, especially at resonance speeds. The equations of motion of the system have been developed with four degrees of freedom to include the rotor and bearing movements in the respective axes. These equations which include non-linear terms caused by the rotor opening, are subjected to external force such from rotor imbalance. A simulation model based on these equations was created using SIMULINK. An experimental test rig was used to characterise the dynamic features. Rotor discs open at a lateral displacement of the rotor of 0.8 mm. This is the threshold value used to show the change of stiffness from high stiffness to low stiffness. The experimental results, which measure the vibration amplitude of the rotor, show the dynamic behaviour of the bolted rotor due to imbalance. Close agreement of the experimental and theoretical results from time histories, waterfall plots, pseudo-phase plots and rotor orbit plot, indicated the validity of the model and existence of the non-linear jump phenomenon.

Some aspects of the dynamic performance of machine tool structural joints

The work presented in this thesis is concerned with the dynamic behaviour of structural joints which are both loaded, and excited, normal to the joint interface. Since the forces on joints are transmitted through their interface, the surface texture of joints was carefully examined. A computerised surface measuring system was developed and computer programs were written. Surface flatness was functionally defined, measured and quantised into a form suitable for the theoretical calculation of the joint stiffness. Dynamic stiffness and damping were measured at various preloads for a range of joints with different surface textures. Dry clean and lubricated joints were tested and the results indicated an increase in damping for the lubricated joints of between 30 to 100 times. A theoretical model for the computation of the stiffness of dry clean joints was built. The model is based on the theory that the elastic recovery of joints is due to the recovery of the material behind the loaded asperities. It takes into account, in a quantitative manner, the flatness deviations present on the surfaces of the joint. The theoretical results were found to be in good agreement with those measured experimentally. It was also found that theoretical assessment of the joint stiffness could be carried out using a different model based on the recovery of loaded asperities into a spherical form. Stepwise procedures are given in order to design a joint having a particular stiffness. A theoretical model for the loss factor of dry clean joints was built. The theoretical results are in reasonable agreement with those experimentally measured. The theoretical models for the stiffness and loss factor were employed to evaluate the second natural frequency of the test rig. The results are in good agreement with the experimentally measured natural frequencies.

The study and measurements of the behaviour and characteristics of electromagnetic relays

The thesis presents a theoretical and practical study of the dynamic behaviour of electromagnetic relays. After discussing the problem of solving the dynamicc equations analytically and presenting a historical survey of the earlier works in the relay and its dynamics, the simulation of a relay on the analogue computer is discussed. It is shown that the simulation may be used to obtain specific solutions to the dynamic equations. The computer analysis provides the dynamic characteristics for design purposes and may be used in the study of bouncing, rebound oscillations and stability of the armature motion. An approximate analytical solution to the two dynamic equations is given based on the assumption that the dynamic variation of the pull with the position of the armature is linear. The assumption is supported by the Computer-aided analysis and experimental results. The solution is intended to provide a basis for a rational design. A rigorous method of analysing the dynamic performance by using Ahlberg's theory is also presented. This method may be justified to be the extension of Ahlberg's theory by taking the mass and frictional damping forces into account. While calculating the armature motion mathematically, Ahlberg considers the equilibrium of two kinds of forces, namely pull and load, and disregards the mass and friction forces, whereas the present method deals with the equilibrium of all four kinds of forces. It is shown how this can be utilised to calculate the dynamic characteristics for a specific design. The utility of this method also extends to the study of stability, contact bounce and armature rebound. The magnetic circuit and other related topics which are essential to the study of relay dynamics are discussed and some necessary experimental results are given.

Numerical simulation for dynamic positioning in pack ice

This thesis investigates the numerical modelling of Dynamic Position (DP) in pack ice. A two-dimensional numerical model for ship-ice interaction was developed using the Discrete Element Method (DEM). A viscous-elastic ice rheology was adopted to model the dynamic behaviour of the ice floes. Both the ship-ice and the ice-ice contacts were considered in the interaction force. The environment forces and the hydrodynamic forces were calculated by empirical formulas. After the current position and external forces were calculated, a Proportional-Integral-Derivative (PID) control and thrust allocation algorithms were applied on the vessel to control its motion and heading. The numerical model was coded in Fortran 90 and validated by comparing computation results to published data. Validation work was first carried out for the ship-ice interaction calculation, and former researchers’ simulation and model test results were used for the comparison. With confidence in the interaction model, case studies were conducted to predict the DP capability of a sample Arctic DP vessel.