Vibration Limits Research Articles

Assessment of Floor Micro-Vibrations Induced by Moving Vehicles in High Technology Factories Using a Fragility-Based Method

This study presents assessment of floor micro-vibrations induced by moving vehicles in high technology factories by using a fragility-based method. A series of time history analysis of a simplified three-span continuous beam model under moving loads simulated by a modified Kanai-Tajimi power spectral density (PSD) function considering various vehicle weights and moving speeds is performed. The best-fitting surface in terms of the maximum root mean square (RMS) velocity responses and their corresponding pair of the vehicle weight and moving speed is obtained by using the least square regression method. With the regression surface denoting the mean values and the standard deviation obtained, the fragility surfaces for each vibration criterion or limit are further constructed. The assessment of the floor micro-vibration in terms of probability of exceeding a given vibration limit for various pairs of vehicle weight and moving speed can be read accordingly from the fragility surfaces.

Dynamics of a frictional system, accounting for hereditary-type friction and the mobility of the vibration limiter

Dynamics of a frictional system consisting of a rough body situated on a rough belt moving at a constant velocity is studied. The vibrations are limited by an elastic obstacle. The Coulomb-Hammonton dry friction characteristic is chosen, according to the hypothesis of Ishlinskiy and Kragelskiy, in the form of hereditary-type friction, where the coefficient of friction of relative rest (CFRR) is a monotone non-decreasing continuous function of the time of relative rest at the previous analogous time interval. A mathematical model and the structure of its phase space are presented, as well as the equations of point maps of the Poincare surface and the results of studying the dynamic characteristics of the parameters of the system (velocity of the belt, type of the functional relation of CFRR, rigidity of the elastic obstacle, etc.). A software product has been developed which makes it possible to find complex periodic motion regimes, as well as to calculate bifurcation diagrams used for determining the main variations of the motion regime from periodic to chaotic (the period doubling scenario).

Vibration isolation of buildings housed with sensitive equipment using open trenches – Case study and numerical simulations

The vibration isolation of buildings housed with sensitive equipment is always a challenging one due to the stringent vibration criteria imposed on them. The paper presents a case study on the vibration isolation scheme adopted for an important building of space research agency. The vibration levels in the building had to follow the vibration criterion which is in the form of a set of one – third octave band velocity spectra, expressed as vibration criterion curves. Various sources that can generate vibrations in the building were identified and assessed. The external sources and the internal sources of vibration were analyzed and the possible limits of vibrations were evaluated. The selection procedure of design frequency, which is the significant step in the design of vibration isolation trench under the passive isolation scheme, is explained. Numerical simulations were developed to evaluate the influence of trench parameters on the amplitude reduction of Rayleigh waves propagating across the trench. Based on the results from numerical simulations, the vibration isolation trench was designed to reduce the amplitudes of vibrations produced from external and internal sources.

Flexural-torsional vibration and buckling of thin-walled bi-directional functionally graded beams

The paper introduces an analysis of flexural-torsional vibration and buckling of thin-walled bi-directional FG beams. Several cross sections have been conducted such as mono-symmetric I-shaped and channel sections in which material properties are assumed to vary across blade thickness and along axial direction. Governing equations and finite element model are developed. The model is capable of capturing all complex eigenvalue problems, also provides a highly accurate prediction of vibrational shapes and buckling capacity. Since the material changes, the obtained results reflect the relative relation between the behaviors of the beam and the transformation of internal properties, for example, Young's modulus, density, etc. Effects of gradient parameters on the vibrational frequencies or limit loads of a thin-walled bi-directional FG beam under various configurations and boundary conditions have also been parametrically studied.

Protecting Museum Collections from Vibrations Due to Construction: Vibration Statistics, Limits, Flexibility and Cooperation

ABSTRACT Vibrations due to heavy construction work continue to be a major concern for museums. Although there has been an increase in research on the effect of vibrations on objects of cultural heritage in recent years, selecting measures to protect collections and remain open during construction work continues to be difficult because of a lack of data on what objects can actually withstand, the complexity of vibration loads, and the uniqueness of each situation. The major renovation of the Central Library in Liverpool, UK, which shared walls with the World Museum and Walker Art Gallery, both of which belong within National Museums Liverpool, showed how museums and other institutions can successfully deal with such situations. An integral approach was taken, beginning with an extensive risk analysis to determine which objects could remain on display, which needed extra protection and regular condition monitoring, and which had to be removed. The museums then negotiated a vibration protocol and action plan with the contractors, including continuous monitoring, and trigger levels requiring consultation or work stoppage. Vibration data were also stored and used for later analysis. This integral approach was successful in protecting the collections on exhibition, with only two incidents of reported damage directly related to vibrations. A combination of museum staff experience, excellent communications with the contractors, and some flexibility in defining vibration limits provided a successful recipe for both museums. The analysis of the vibration data using the basic engineering concept of the Palmgren-Miner rule, supports a more flexible approach to setting vibration limits based on recently published guidelines.

Optimal power, power limit and damping of vibration based piezoelectric power harvesters

Power harvesting describes the process of acquiring the ambient energy surrounding a system and converting it into usable electrical energy. Much of the work over the past two decades has focused on the conversion of ambient vibration energy sources using piezoelectric, electromagnetic and electrostatic transduction. Attempts were made to obtain a general model that could be applied to any transduction mechanism. Of the most interest is an electromagnetic generator model that was used by many researchers to model piezoelectric power harvesters. Two major results from the model are the power limit expression and the equal relationship between the electrically induced damping and the mechanical damping to reach the power limit. However, piezoelectric power harvesters cannot be accurately modeled by this electromagnetic model due to the essential difference in physics. There have also been attempts to obtain the power limit expression based on piezoelectric relationships, but they either neglect the piezoelectric backward coupling to the structure, or assume the power limit occurs at the resonance of the system. This paper obtains the power limit expression based on the piezoelectric coupled equations without those assumptions. In addition, the relationship between the electrically induced damping and mechanical damping at the power limit is studied. Furthermore, a closed-form criterion is derived and proposed to define strongly and weakly coupling power harvesters, whose differences in power characteristics are explained through analytical and numerical analysis. While most of the discussion is focused on linear power harvesters connected to a resistive circuit, the aim of this paper is to provide a comprehensive and deep understanding of this simple configuration, answers to important questions, and a starting point to develop a more general theory on power harvesters because similar system characteristics are observed in power harvesters with more complexities.

Theoretical Model Study of Interplay of Coulomb Interaction and Electron-Phonon Interaction in the Thermal Properties of Monolayer Graphene

We propose here a tight-binding (TB) model Hamiltonian for monolayer graphene-on-substrate describing the nearest-neighbor-hopping, on-site Coulomb interaction on the sub-lattices and the electron-phonon interaction under the high-frequency limit of phonon vibration. Applying Lang-Firsov canonical transformation, the electron and phonon systems are decoupled in the atomic Hamiltonian, such that the effective Coulomb interaction and effective nearest-neighbor-hopping integral respectively appear as $\tilde {U}=U-2t_{1}\lambda $ and $\tilde {t}_{1}=t_{1}e^{\frac {-t_{1}\lambda } {\omega _{0}}}$ , where U, t1, λ and ω0 are respectively Coulomb energy, nearest-neighbor-hopping integral, electron-phonon (e-ph) coupling and phonon frequency. The effective Coulomb interaction in the Hamiltonian is considered within mean-field approximation. The Hamiltonian is solved by Zubarev’s Green’s function technique. The temperature-dependent electronic entropy and specific heat are calculated from the free energy of graphene system and are computed numerically. The temperature-dependent electronic specific heat exhibits a charge gap peak at room temperature arising due to the effect of Coulomb interaction and electron-phonon interaction. The evolution of these peaks in specific heat is investigated by varying the model parameters of the system.

Investigation of Concrete Floor Vibration Using Heel-Drop Test

In recent years, there is an increased in floor vibration problems of structures like residential and commercial building. Vibration is defined as a serviceability issue related to the comfort of the occupant or damage equipment. Human activities are the main source of vibration in the building and it could affect the human comfort and annoyance of residents in the building when the vibration exceed the recommend level. A new building, Madrasah Tahfiz located at Yong Peng have vibration problem when load subjected on the first floor of the building. However, the limitation of vibration occurs on building is unknown. Therefore, testing is needed to determine the vibration behaviour (frequency, damping ratio and mode shape) of the building. Heel-drop with pace 2Hz was used in field measurement to obtain the vibration response. Since, the heel-drop test results would vary in light of person performance, test are carried out three time to reduce uncertainty. Natural frequency from Frequency Response Function analysis (FRF) is 17.4Hz, 16.8, 17.4Hz respectively for each test.

Exactly solvable configuration mixing scheme in the vibrational limit of the interacting boson model

An intruder configuration mixing scheme with $2n$-particle and $2n$-hole configurations from $n=0$ up to $n\ensuremath{\rightarrow}\ensuremath{\infty}$ in the U(5) (vibrational) limit of the interacting boson model is proposed. A simple Hamiltonian suitable to describe the intruder and normal configuration mixing is found to be exactly solvable, and its eigenstates can be expressed as the SU(1,1) coherent states built on the U(5) basis vectors of the interacting boson model. It is shown that the configuration mixing scheme keeps lower part of the vibrational spectrum unchanged and generates the intruder states due to the mixing. Some low-lying level energies and experimentally known $B(E2)$ ratios of $^{108,110}\mathrm{Cd}$ are fitted and compared with the experimental results.

High-Precision Displacement Sensing of Monolithic Piezoelectric Disk Resonators Using a Single-Electron Transistor

A single-electron transistor (SET) can be used as an extremely sensitive charge detector. Mechanical displacements can be converted into charge, and hence, SETs can become sensitive detectors of mechanical oscillations. For studying small-energy oscillations, an important approach to realize the mechanical resonators is to use piezoelectric materials. Besides coupling to traditional electric circuitry, the strain-generated piezoelectric charge allows for measuring ultrasmall oscillations via SET detection. Here, we explore the usage of SETs to detect the shear-mode oscillations of a 6-mm-diameter quartz disk resonator with a resonance frequency around 9 MHz. We measure the mechanical oscillations using either a conventional DC SET, or use the SET as a homodyne or heterodyne mixer, or finally, as a radio-frequency single-electron transistor (RF-SET). The RF-SET readout is shown to be the most sensitive method, allowing us to measure mechanical displacement amplitudes below 1E-13 m. We conclude that a detection based on a SET offers a potential to reach the sensitivity at the quantum limit of the mechanical vibrations.

Dynamics of a vibration system, taking into account the hereditary type friction and the mobility of a vibration limiter

The paper investigates the dynamics of some vibration systems taking into account the hereditary-type dry friction and mobility of a vibration limiter. The interaction of the vibration limiter and the vibration system occurs either according to Newton’s hypothesis (an absolutely rigid limiter) or softly (the limiter is mobile). A general mathematical model (MM) of systems has been developed, which is highly non-linear nonautonomous system with variable structure. A numerical-analytical approach using the mathematical apparatus of the point mapping method is implemented to study the dynamics of the MM. The peculiarity in the research approach is that the point mapping is not formed by the classical method (mappings of the Poincaré surface into itself), but by the duration of relative rest of the vibration system, which greatly facilitated the process of point mapping and its detailed study. The presence of floating boundaries of slip-motion plates required the creation of an original approach in constructing point mapping and interpreting the results obtained. The structure of the phase portrait of the MM as a function of the characteristics of the sliding and state friction forces, as well as on the type and position of the limiter was studied using the developed research methodology and the created software product. Based on the character of changes in bifurcation diagrams, it was possible to determine the main laws of changes in the motion regimes (occurrence of random complexity via the period possible transfer to chaos doubling process) when changing the parameters of the vibration system (amplitude and frequency of periodic action, the form of the functional dependence describing the change in the coefficient of friction of relative rest. Analytical results with and without a vibration limiter are compared.

An admissible function for vibration and flutter studies of FG cylindrical shells with arbitrary edge conditions using characteristic orthogonal polynomials

A general approach for the vibration and aeroelastic stability of the functionally graded cylindrical shell with arbitrary boundary conditions is firstly presented. The Sanders' shell theory, a steady-state heat transfer equation and the piston theory are employed to establish the motion equation, where the thermo-mechanical properties of material are set to be location- and temperature- dependent. The orthogonal polynomials series generated by employing the Gram–Schmidt process are taken as the admissible functions to express the general formulations of displacement. Moreover, the artificial spring technique is introduced to simulate the elastic constraints imposed on the cylinders' edges. The frequency equations are derived considering the strain energy of artificial springs during the Rayleigh–Ritz procedure, and the motion equation of cylindrical shells subjected to combined thermal and aerodynamic loads is established based on the Hamilton principle. A few comparisons for the frequency and critical flutter pressure are performed to validate the proposed approach. The influences of the volume fraction, thermal gradient, boundary conditions and spring stiffness on the flutter characteristics are highlighted. This paper overcomes the limitations of previous vibration and flutter studies which are confined to the structure under simply supported or clamped boundaries.

Vibration analysis for the comfort assessment of superyachts

Comfort levels on modern superyachts have recently been the object of specific attention of the most important Classification Societies, which issued new rules and regulations for evaluating noise and vibration maximum levels. These rules are named “Comfort Class Rules” and set the general criteria for noise and vibration measurements in different vessels’ areas, as well as the maximum noise and vibration limit values. As far as the vibration assessment is concerned, the Comfort Class Rules follow either the ISO 6954:1984 standard or the ISO 6954:2000. After an introduction to these relevant standards, the authors herein present a procedure developed to predict the vibration levels on ships. This procedure builds on finite element linear dynamic analysis and is applied to predict the vibration levels on a 60 m superyacht considered as a case study. The results of the numerical simulations are then benchmarked against experimental data acquired during the sea trial of the vessel. This analysis also allows the authors to evaluate the global damping ratio to be used by designers in the vibration analysis of superyachts.

Optimum Design of Castellated Beams: Effect of Composite Action and Semi-Rigid Connections

Castellated beams and composite action of beams are widely applicable methods to increase the capacity of the beams. Semi-rigid connections can also redistribute internal moments in order to attain a better distribution. Combination of these methods helps to optimize the cost of the beam. In this study, some meta-heuristic algorithms consisting of the particle swarm optimization, colliding bodies optimization, and enhanced colliding bodies optimization are used for optimization of semi-rigid jointed composite castellated beams. Profile section, cutting depth, cutting angle, holes spacing, number of filled end holes of the castellated beams and rigidity of connection are considered as the optimization variables. Constraints include the construction, moment, shear, deflection and vibration limitations. Effect of partial fixity and commercial cutting shape of a castellated beam for a practical range of beam spans and loading types are studied through three numerical examples. The efficiency of three meta-heuristic algorithms is compared.

Analytical formulation of an oscillatory system with hereditary-type dry friction and oscillation constraints

The dynamics of a shock-vibrating system is analyzed. The system consists of a pair of bodies of friction, one of which is under the effect of an external periodic force; the vibration of one of the bodies is limited by a rigid obstacle, and the hereditary-type dry friction forces during their interaction are taken into account. A numerical-analytical approach using the mathematical apparatus of the point mapping method is implemented to analyze the phase portrait structure of the mathematical model as a function of the characteristics of the sliding and state friction forces, as well as of the type and position of the vibration limiter. Based on the character of changes in the bifurcation diagrams, the authors have determined the main laws of changes in the motion regimes (occurrence of random complexity periodic motion regimes and possible transfer to chaos via the period doubling process) when changing the parameters. Analytical results with and without a vibration limiter are compared.

Stark-induced adiabatic Raman ladder for preparing highly vibrationally excited quantum states of molecular hydrogen

We present a multi-color ladder excitation scheme that exploits Stark-induced adiabatic Raman passage to selectively populate a highly excited vibrational level of a molecule. We suggest that this multi-color coherent ladder excitation provides a practical way of accessing levels near the vibrational dissociation limit as well as the dissociative continuum, which would allow the generation of an entangled pair of fragments with near-zero relative kinetic energy. Specifically, we consider four- and six-photon coherent excitation of molecular hydrogen to high vibrational levels via intermediate vibrational levels, which are pairwise coupled by two-photon resonant interaction. Using a sequence of three partially overlapping, single-mode, nanosecond laser pulses we show that the sixth vibrational level of H2, which is too weakly coupled to be easily accessed by direct two-photon Raman excitation from the ground vibrational level, can be efficiently populated without leaving any population stranded in the intermediate level. Furthermore, we show that the fourteenth vibrational level of H2, which is the highest vibrational level in the ground electronic state with a binding energy of 22 meV, can be efficiently and selectively populated using a sequence of four pulses. The present technique offers the unique possibility of preparing entangled quantum states of H atoms without resorting to an ultracold system.

Whole-body vibration exposure on board a Polar Supply and Research Vessel in open water and in ice

The Requirements for Polar Ships specify the requisites by the International Association of Classification Societies to ensure a safe journey for crew travelling on steel ships that navigate in ice-infested polar waters. One identified problem in these requirements is that they do not yet contain guidelines to direct shipbuilders as to the allowable vibration limits for human vibration exposure. This is attributed to the absence of scientifically reported field research on vibration conditions in human environments gathered when ships break through ice. This study investigated the levels of whole-body vibration exposure associated with open water and ice passage of a Polar Supply and Research Vessel. It was found that occupants are exposed to perceivable vibration for most of the voyage and are likely to experience vibration at levels considered “not uncomfortable”. As a result of high crest factors r.m.s. metrics do not offer a robust means of quantifying in-service ship-borne vibration. In comparison with sailing in calm water, whole-body vibration exposure increased by 21 times in rough open water and up to elevenfold during ice-passage.

Design of highly sensitive floors for human induced vibrations

This paper presents an assessment method that allows an easy design of floors for highly vibration sensitive equipment (i.e. nanotechnology) Therefore, the dynamic response of floors with different dynamic behaviors and due to different walking loads as well as different body weights are taken into account. The results are graphically visualized so that an easy tool for an engineer or planner is available to predict the floor vibrations due to human load and compare them with the VC-curves, which define vibration limits for different levels of manufacturing precision of the equipment.

The Role of Advanced Technologies of Vibration Diagnostics to Provide Efficiency of Helicopter Life Cycle

Vibration diagnostic techniques (VDT) application to helicopters is growing gradually both in production stage and in technical operation and maintenance. The development of appropriate technologies requires considerable investment and is often hampered by the lack of a clear perspective, understanding of the possibilities and areas of application. The article presents new opportunities for the use of VDT for helicopter diagnostics at different stages of its life cycle, providing increased efficiency of production and operation. In paper, the taxonomy of VDT applicable to most of critical machines, mechanisms and structures of a helicopter is presented and discussed. The paper illustrates effective diagnostic techniques applications on helicopter engines exceeded vibration limits in delivery trials. In the paper, the capabilities of advanced VDT are considered using samples of experimental operating systems application. Advanced VDT is possible platform for design of Health and Usage Monitoring Systems (HUMS). In article the general approach for development of HUMS using the VDT and application of HUMS to provide condition-based maintenance for more efficiency of helicopter life cycle on criteria reliability/cost are discussed.

Life Cycle Cost Evaluation of Noise and Vibration Control Methods at Urban Railway Turnouts

A focus of the railway industry over the past decades has been to research, find and develop methods to mitigate noise and vibration resulting from wheel/rail contact along track infrastructure. This resulted in a wide range of abatement measures that are available for today’s engineers. The suitability of each method must be analysed through budget and timeframe limitations, which includes building, maintenance and inspection costs and time allocation, while also aiming at delivering other benefits, such as environmental impact and durability of infrastructure. There are several situations that need noise and vibration mitigation methods, but each design allocates different priorities on a case-by-case basis. Traditionally, the disturbance caused by railways to the community are generated by wheel/rail contact sound radiation that is expressed in different ways, depending on the movement of the rolling stock and track alignment, such as rolling noise, impact noise and curve noise. More specifically, in special trackworks such as turnouts (or called “switches and crossings”), there are two types of noise that can often be observed: impact noise and screeching noise. With respect to the screeching (or flanging), its mitigation methods are usually associated with curve lubrications. In contrast, the impact noise emerges from the sound made by the rolling stock moving through joints and discontinuities (i.e., gaps), resulting in various noise abatement features to minimise such noise impact. Life cycle analysis is therefore vital for cost efficiency benchmarking of the mitigation methods. The evaluation is based on available data from open literature and the total costs were estimated from valid industry reports to maintain coherency. A 50-year period for a life cycle analysis is chosen for this study. As for the general parameters, an area with a high density of people is considered to estimate the values for a community with very strict limits for noise and vibration.