A power transmissibility method for assessing the performance of vibration isolation of building services equipment

Force transmissibility is commonly adopted in building services engineering to assess the performance of vibration isolation. However, it neglects the effect of floor mobility on structure-borne sound power transmitted from a vibratory machine to the floor/roof and the interactions among several contact points between the vibratory machine and the floor/roof. The problem that motivated this study is the occasional occurrence of unsatisfactory performance of vibration isolators observed in building services engineering. This problem may be due to the over-simplification of the vibratory problem in the usual definition of the un-damped force transmissibility or isolation efficiency commonly used in engineering practice. In this paper, use of a “power transmissibility”, which includes the effect of floor mobility and the interaction of all dynamic forces transmitted to the floor through the vibration isolators, is proposed.     

Effect of viscous damping on power transmissibility for the vibration isolation of building services equipment

Vibration isolation plays an important role in both the vibration and noise control of building services equipment. To evaluate vibration isolation performance, the force transmissibility method is commonly adopted. However, increasing the damping effect in the force transmissibility method reduces both the resonance peak value and the isolation performance in the “isolation region”. The limitation of the method is that the transmitted displacement of a floor structure and the interaction of mounting points are neglected. To include the floor displacement and the interaction of mounting points, Mak and Su recently proposed the power transmissibility method to assess the performance of vibration isolation. In this paper, the effect of viscous damping on power transmissibility is investigated. A practical procedure for experimentally determining the damping ratio is also given.     

Adaptive-passive vibration isolation between nonrigid machines and nonrigid foundations using a dual-beam periodic structure with shape memory alloy transverse connection

This paper examines the problem of broadband vibration control of nonrigid systems employing periodic structures with tunable parameters. It investigates this by using a semi-two-dimensional model that applies a dual-beam periodic structure with transverse branches as a parameter-tunable isolator. Conventional study of vibration control problems, including the problem of vibration control by periodic structures, usually reduces systems to equivalent single- or multi-mount models with only a unidirectional translation at a mounting point. This assumption of decoupling leads to the erroneous prediction of vibratory power transmission when designing an isolator for a nonrigid system. Such a periodic structure involves the coupling of vibrations between different mounting points and different directions of motion and is therefore a reasonable simulation of the real-life problem. However, its application as a periodic isolator has not been proposed previously. The configuration of shape memory alloy (SMA) branches and non-SMA dual beams is proposed in order that this structure can effectively exploit the advantages of SMA materials, namely their significantly varying Young?s moduli which can be tuned to adjust and widen the stop bands, and can prevent the associated limitation of hysteresis. Equations are derived governing the vibration transmitted through any number of periodic mounts between nonrigid machines and foundations. Based on the derived results, two methodologies are developed to determine the proper Young?s moduli of the SMA branches and minimize the transmitted power. The numerical results demonstrate that the adaptive SMA branches at the proper temperatures are able to attenuate broadband vibration by adjusting the locations and broadening the widths of stop bands. With the application of a semi-two-dimensional periodic structure to broadband vibration isolation, this paper provides an approach and supporting methodologies for broadband vibration control using periodic structures.     

Vibrational power flow from machines into built-up structures,part III: Power flow through isolation systems

The power flowing through the isolators and into the supporting foundation of a machine is examined by approximating the driving point frequency response function of the foundation. One and two stage isolation of machines with internal force or velocity sources is considered. Two stage isolation is superior to single stage isolation in reducing power flow in those circumstances where the excitation spectra do not cover the two resonances of the system.     

A study of the effect of inertia blocks on the stability of the vibratory system and the performance of vibration isolation

Resilient vibration isolators and inertia blocks are commonly used by building services engineers to isolate vibratory machines in buildings. They are selected in practice according to the force transmissibility method and some crude methods or the experience of building services engineers. These methods, however, can produce inaccurate predictions, and a power transmissibility method has recently been proposed to assess the performance of vibration isolation. In this paper, normalized average vibration velocities and overall rotational velocities are proposed to study the stability of the vibratory system. The result shows that the use of an inertia block primarily does not improve the performance of vibration isolation, but does increase the stability of the vibratory system regardless of whether the machine is of even or uneven mass distribution and whether it is driven by the vibratory force or the rocking moment.     

Power flow in the coupled dynamic system of machinery and building floor

I.IntroductinnWithmoreandmoremulthetoreyworkshopsandmultifunctinnaltallbuildingsarebeingconstructednowadays,thereshowsanincreasingtrendformachinesandequlpmentstobemoulltedonupperlloors.Inthesituationofmachinesrunningonupperfloors,thetraditionaltheoryisnotValidbecausetheflooritselfisaflewhlestructure.Therefore,itisinagreatdemandtostudyonthedynaInicillteractionofmachinescoupledwithflekiblefoundationsalldtoproposearesonableandeffectiveapproachtocontrolvibrationandtosuppressnoise.Formachineryonu…     

On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure,part I: Theoretical background and basic experimental studies

The general mobility matrix formulation of the problem of multi-point, coupled structures is discussed and some of the disadvantages are emphasized. Two principally different ways of rearranging the general mobility matrix into corresponding effective mobilities, useful for expressing the vibratory power input to the receiving structure, are investigated theoretically. The two concepts of effective mobility, namely effective point mobility in which the points are considered individually with the interaction between the points taken into account and effective overall mobility in which a space averaged point mobility is deduced, have also been verified experimentally. In addition, some useful approximations of these quantities are derived.     

VIBRATIONAL POWER TRANSMISSION FROM A MACHINE TO ITS SUPPORTING CYLINDRICAL SHELL

Power flows from a vibratory machine to its supporting structure are of primary concern in a passive or active isolation system design. Although in the literature there is a fair number of investigations on the power inputs to beams, plates or the like, few attempts have been made for other commonly used structures such as cylindrical shells. In this paper, the vibratory power flows from a rigid-body machine to an elastic cylindrical shell are studied considering the contributions of the non-radial (tangential and axial) displacements and forces. In particular, it is argued that the notion that the motion of a thin shell is primarily radial does not necessarily dictate that the power transmissions are predominantly carried out by the radial displacement. This point is subsequently illuminated through numerical examples. Another issue discussed here is concerned with the effects on the power flows of the cross couplings of the (different) displacement components. It is shown that even though the contributions of the cross couplings are usually insignificant, they may become important if the vibration isolators are substantially hard as compared with the local shell stiffness or impedance. This assertion is particularly useful when an experimental technique is used to measure the vibratory power flows into a supporting structure.     

Approximate method for obtaining source quantities for calculation of structure-borne sound transmission into lightweight buildings

An approximate approach is described, for obtaining the source quantities required for the calculation of structure-borne sound power from machines into supporting lightweight building elements. The approach is in two stages, which are based on existing international Standards for measurement. The first stage involves direct measurement of the source free velocity at each contact, to give the sum of the square velocities. The second stage is based on the reception plate method and yields the single equivalent blocked force, which approximates the sum of the square blocked forces. The applicability of the source data obtained has been investigated in a case study of a fan unit on a timber joist floor. The approach contains several significant simplifying assumptions and the uncertainties associated with them are considered. For the case considered, the power transmitted into the floor is estimated by the approximate method to within 5 dB of the true value, on average.     

Reception plate method for characterisation of structure-borne sound sources in buildings: Installed power and sound pressure from laboratory data

In a companion paper, a laboratory method is described to obtain the structure-borne sound power of machines before they are installed in heavy-weight buildings. The laboratory method is based on the concept of the reception plate. In this paper, the method is shown to provide appropriate input data for the prediction of the installed structure-borne power, and thence the resultant sound pressure level in rooms removed from the room containing the machine. Case studies of two common sources are described: a whirlpool bath and a water cistern. It is shown that the method can be incorporated into recently proposed standard prediction models and that sound pressure levels in buildings can be predicted.     

Multipole expansion of the vibration transmission between a source and a receiver

The vibrational power transmitted by N forces applied, for example, by a machine upon isolators is regarded as the power transmitted by N independent poles of vibration: e.g., monopole, dipole, etc. The machine or source of vibration moves in a set of vibrational poles. The receiver is defined by a set of polar mobilities or impedances. The power transmission expressions were implemented on a practical structure, one using the source acceleration to measure the power transmitted by the isolators, the other using the receiving structure to estimate the magnitude of power by all sources of vibration, including the airborne noise.     

The identification of the source of machine noises contained within a multiple-source environment

For the purpose of monitoring the condition of machine components there is evidence to suggest that the logging of sound spectra and comparison with a reference spectrum can aid in the formation of decisions regarding individual components of a machine. Since most machines operate in enclosures among other machinery, it is important to assess the problems involved in isolating individual sound sources under such conditions.This investigation explored the response of six machine tools in a workshop when operating individually (solo) and together (simultaneously). Studies are made of the respective time-domain wave forms, decibel-frequency spectra (sound signatures) and power spectral density-frequency spectra. A comparison has been made between the resulting power spectral density spectra when all machines are working together and the computer-summated spectra of the machines when running individually.There is reason to believe that the discrete frequencies of separate components within a machine can be separated from the sound in a multiple-source sound environment. Results suggest that the greatest sensitivity is likely to be achieved within the frequency range 100 to 600 Hz and that higher frequency effects may be influenced by field reverberation effects of the enclosure.     

A new temporal method for the identification of source directions in a reverberant hall

The study presented here is related to the reduction of noise in factory halls. The type of factory hall considered here has large dimensions and contain several industrial machines, running 24 h a day. A method is presented to determine the angular directions which provide the main contributions to the sound levels at any point in the hall. These directions correspond to the sources and their images on the walls and on the obstacles. The method is based on the use of cross-correlation functions of sound signals measured on a microphone array. It is adapted to the constraints of the problem (short measurement time, no possibility to stop the machines, small dimensions of the array, etc.). Experimental results are shown first for several test cases carried out in a semi-anechoic room and in a rectangular room, and, then, for the case of a surface-planing machine in a cluttered hall.     

Predicting transmission of structure-borne sound power from machines by including terminal cross-coupling

Structure-borne sound generated by audible vibration of machines in vehicles, equipment and house-hold appliances is often a major cause of noise. Such vibration of complex machines is mostly determined and quantified by measurements. It has been found that characterization of the vibratory source strength and the prediction of power transmission to a supporting structure or the machine casing itself can be greatly simplified if all mobility cross-terms and spatial cross-coupling of source velocities can be neglected in the analysis. In many cases this gives an acceptable engineering accuracy, especially at mid- and high-frequencies. For structurally compact machines, however, the influence of cross-coupling cannot always be ignored. The present paper addresses this problem and examines the transmission of structure-borne sound power by including spatial cross-coupling between pairs of translational terminals in a global plane. This paired or bi-coupled power transmission represents the simplest case of cross-coupling. The procedure and quality of the predicted transmission using this improved technique is demonstrated experimentally for an electrical motor unit with an integrated radial fan that was mounted resiliently in a vacuum cleaner casing. It is found that cross-coupling plays a significant role, but only at frequencies below 100 Hz for the examined system.     

Signatures of polaron formation in systems with local and non-local electron-phonon couplings

Polaron formation is investigated in a one-dimensional chain by taking into account both the local Holstein and the non-local SSH electron-phonon interactions. The study of the adiabatic regime points out that the combined effects of the two interactions are important mainly in the weak coupling regime. Thus, using the weak-coupling perturbation theory, spectral weights, effective masses, polaronic phase-diagram, and band structures are discussed. Contrarily to what happens in the Fröhlich and Holstein models, we find that the ratio between the coherent spectral weight and the mass renormalization ratio is greater than 1. Moreover, we show that the non-local electron-phonon interaction is responsible for the largest deviations of the band structure from the cosine shape of the free energy band.     

Optimized design of suspension systems for hand–arm transmitted vibration reduction

This paper describes a systematic approach for optimizing suspension systems to reduce the vibrations transmitted to workers by hand-held power tools. The optimization is based on modeling tool-operator interactions using a mobility scheme. The tool is modeled as a vibration generator, and its internal impedance is included. A hand–arm impedance matrix is used to model the operator upper limbs. The mobility model is used to identify the optimal suspension characteristics, which in our study were the set of parameters that minimizes the frequency-weighted acceleration at the hand–tool interface. Different handling conditions (one and two hands) and different working cycles with the same tools can be included in the optimization process. The constraints derived from the limitation on the increase in the tool mass and the static deflection of the mounting system under the working loads are also considered. The proposed method has been applied to the reduction of the vibrations transmitted to the operator by a small pneumatic hammer. The designed system reduced the worker’s exposure so that it is within the limits of the EU directive. The agreement between the model predictions and the measured suspension performances validates the effectiveness of this approach.     

一种广义三模腔光机械系统的相干完美吸收与透射

提出了一种广义的三模式腔光机械系统,系统的中间是一个反射率为100%的可移动的全反射机械振子,两侧均由一个部分透射的固定光学腔镜构成.其中两个光学腔由一束较强的控制场和一束较弱的信号场驱动与同一个机械振子实现耦合.较弱的信号场将会被该系统完全吸收而不产生任何能量输出,并且当相干完美吸收产生时,输入信号场的能量将由两个腔场和机械模共同分担;较弱的输入信号场由一个腔完美透视到另一个腔而不产生任何的能量损耗.分析与数值结果显示,在不同参数机制下,在该三模光机械系统中可以实现相干完美吸收、相干完美透射和相干完美合成的量子现象.此外,改变腔与腔之间的耦合度,可以实现输出探测场在相干完美吸收和相干完美透射之间转换;通过简单的相位调制,可以实现探测场左腔-右腔的输出和输入方向的互换.这些动态控制在量子信息网络可用来构造光子开关、光子路由、光子交换机等一些特殊功能的光子学器件.     

VIBRATION POWER TRANSMISSION OVER A RECTANGULAR AREA OF AN INFINITE PLATE SUBJECT TO UNIFORM CONPHASE VELOCITY EXCITATION

In the study of vibration isolation, mobility is normally used to reflect the characteristics of power transmission over the contact region between the exciting machine and its supporting structure. However, recent investigations indicated that power transmission is influenced by the dimensions and shape of the contact region and the use of classical point mobility can lead to significant errors. The surface mobility of an infinite plate over a rectangular contact region subject to a uniform conphase velocity excitation has been derived using the effective point mobility concept for various aspect ratios of the contact region. Results show that power transmission is distributed in a ring-like manner, with the transmission in the central region and along the edges of the contact area being rather small. As the width-based Helmholtz number kw/2 increases, the ring-like region expands outward but less power is transmitted. The surface mobility decreases rapidly as Helmholtz number increases. For the same Helomholtz number, the surface mobility decreases as the aspect ratio of the contact region increases and for the same contact area, it is virtually independent of the shape of the contact region for aspect ratio less than 2 or at large Helmholtz numbers (greater than 4). Experimental measurements of a simulated infinite plate confirm the theoretical calculations. Unlike uniform conphase force excitation, the surface mobility due to uniform conphase velocity distribution does not oscillate with Helmholtz number.     

Reception plate method for characterisation of structure-borne sound sources in buildings: Assumptions and application

A method for characterisation of structure-borne sound sources is proposed and investigated for the special but common case of machines in heavy-weight homogeneous building structures. The method is based on the concept of the reception plate where the total structure-borne sound power from the machine under test is assumed equal to the power dissipated by a plate attached to the machine. The method is relatively simple and allows comparison of sources on a power basis, and of tests results at different laboratories. Additionally the data obtained is in a form suitable for transformation into an installed structure-borne power and thence for the resultant sound pressure generated in buildings. The method is validated by cross-spectral and mobility methods. A study of the uncertainty of the power estimate was performed by numerical modelling and measurement.     

An analytical formulation of the forced responses of damped rings

An analysis in which an interaction formulation is used for the forced vibratory responses of a ring having a number of mass segments adhered to it by a viscoelastic material is presented. The mass segments are discretely distributed around the circumference of the ring, and the excitation is a concentrated vibratory radial force located on the surface of the ring. The mass segments may not have to be identical, nor do their distributions have to be uniform. The analysis can readily be extended to more complicated damped shell structural systems. The driving point mechanical impedances at a location midway between two mass segments for a given damped system are given as an example. These solutions compare very well with experimental data and theoretical results available. Also presented is a comparison of driving point mechanical impedances for two damped systems with different thicknesses of the viscoelastic layers.