A study of power transmissibility for the vibration isolation of coherent vibratory machines on the floor of a building

Vibration isolation is commonly adopted by engineers to reduce the vibratory effect caused by building services equipment. However, the relationship between the amount of sound power transmitted to the floor and the interaction between the mounting points of several machines is uncertain, as it is common to install several coherent machines on the same floor, for example, two water pumps of the same type in a plant room. We conduct an analytical study of the effects of the interaction between two coherent vibratory sources on the power transmitted to the floor. The study is based on two simple vibratory sources with a single contact point, two rectangular machine models of even-mass distribution with four symmetrical supports and the calculated mobilities of a simply supported concrete floor. We find that the total power obtained from coherent sources (point sources or machine models) differs considerably from that obtained from independent sources at some frequencies in a vibration isolation region. To predict the performance of isolators more accurately, the power transmissibility method proposed previously by Mak and Su should consider not only the effect of effective floor mobility and the interactions of the mounting points of the same sources, but also the interactions of the mounting points of different sources on the floor.     

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.     

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.     

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

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

Effects of isolators internal resonances on force transmissibility and radiated noise

Vibration isolators have been extensively used to reduce the vibration and noise transmitted between the components of mechanical systems. Although some previous studies on vibration isolation considered the inertia of isolators, they only examined its effects on the vibration of single degree-of-freedom (d.o.f.) systems. These studies did not emphasize the importance of the isolators’ inertia, especially from the perspective of noise reduction. This paper shows that the internal dynamics of the isolator, which are also known as internal resonances (IRs) or wave effects, can significantly affect the isolator performance at high frequencies. To study the IR problem, a model of a primary mass connected to a flexible foundation through three isolators is used. In this model, the isolator is represented as a one-dimensional continuous rod that accounts for its internal dynamics. The primary mass is modelled as a rigid body with three d.o.f.'s. The effects of the IRs on the force transmissibility and the radiated sound power from the foundation are examined. It is shown that the IRs significantly increase the force transmissibility and the noise radiation level at some frequencies. These effects cannot be predicted using a traditional model that neglects the inertia of the isolator. The influence of the foundation flexibility on the IRs is also investigated. It is shown that the foundation flexibility greatly affects the noise radiation level but it affects only slightly the force transmissibility, especially at high frequencies where the IRs occur.     

Research on performance indices of vibration isolation system

Power flow transmissibility is proposed as a performance index to evaluate the performance of isolation system. It is defined as the ratio of the power flow input into the equipment and the power flow transmitted into the receiver. Based on a simple vibration isolation system, its relationship with other performance indices is given by theoretical and numerical analysis. The results show that power flow transmissibility can reflect the response characteristics of the whole isolation system effectively. In addition, power flow transmissibility can be estimated easily according to vibration acceleration level difference and does not involve the measurement of power flow. Furthermore, the influences of several parameters such as the damping, loss factor and stiffness of isolator on power flow transmissibility are analyzed.     

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.     

Vibration isolation on floating floors

An analysis is presented of the noise problem produced when the application of standard acoustic treatment to a roof-mounted diesel generator failed to meet the design criterion. The problem was diagnosed as excessive vibration reaching the building due to the excitation of a resonance of the supporting structure. The resonance responsible was identified as a flexural mode of the partial floating floor installed below the generator set in order to provide a high transmission loss acoustic barrier. A solution to the problem was provided by converting the existing vibration isolation into a compound system. The reasons for the failure of the existing system are analysed. A simple theory is developed which illustrates that the ratio of machine mass to floating floor mass is the important parameter determining the severity of excitation of floating floor resonance. It is concluded that machines can be safely mounted via vibration isolators onto continuous floating floors provided they ahve a low mass compared with the floating floor mass and are provided with a low mounted resonant frequency compared with the floating floor resonant frequency.     

Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

Periodically layered isolators exhibit transmissibility “stop bands” or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4×10⁻⁴. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.     

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.     

船舶机械磁悬浮气囊混合隔振技术

有源无源混合隔振是控制船舶低频线谱噪声的重要技术,但工程应用的实例还非常少见。在磁悬浮-气囊混合隔振理论和原理样机研究的基础上,针对船用机械低频线谱的隔振需求,进一步突破了体积小、输出力大、功耗低、频响平直、波形失真度低等磁悬浮作动器工程化设计技术;解决了混合隔振器的稳定性和冲击、摇摆适应性等技术难题;研究了工程实用的控制算法,采用非线性逆模型补偿使控制系统线性化,并提出了窄带Fx-Newton时域算法,可在机械设备运行时的多线谱、多通道耦合、线谱振幅非稳态等情况下实现快速稳定控制;研制了船用200 kW柴发机组混合隔振装置,实验结果表明该技术具有优良的宽频隔振效果和低频线谱控制能力,性能可满足工程实用要求。      

The use of seat effective amplitude transmissibility (SEAT) values to predict dynamic seat comfort

The Seat Effective Amplitude Transmissibility (SEAT) value is the ratio of the vibration experienced on top of the seat and the vibration that one would be exposed to when sitting directly on the vibrating floor. SEAT values have been widely used to determine the vibration isolation efficiency of a seat. In this article the subjective evaluations of six persons were compared to the SEAT values estimated from experimentally obtained transmissibility curves for 16 different automobile seats ranging from sedans to SUVs and pickups. A vertical rough road stimulus was used as input for both the subjective testing and the SEAT calculations. The SEAT values were estimated using the power spectral density of the vertical vibration input at the seat track and the measured transmissibility data to compute the response in the vertical direction at the seat top. The averaged, estimated SEAT values were compared to averaged measured values and significant correlation (R²=0.94) was obtained. The subjective ratings were obtained on the Ford Vehicle Vibration Simulator using a paired comparison methodology that eliminated static comfort bias during the evaluation. The results indicated that there is good correlation (R²=0.94) between the subjective ratings and the SEAT values when the subjective ratings and transmissibilities are averaged over the six subjects.     

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.     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.     

地铁车辆段咽喉区上盖建筑振动影响

城区地铁车辆段进行上盖物业开发可节约、集约利用地铁用地,缓解城市土地资源稀缺问题。地铁车辆段特别是其咽喉区振动是上盖物业开发的环境制约因素。为研究地铁车辆段咽喉区对上盖建筑的振动影响,建立轨道-地基土-上盖建筑三维有限元模型,采用等效荷载法,将实地采样的钢轨铅垂向振动加速度转化为列车钢轨铅垂向振动线荷载,作用于轨道上。在结合实测数据验证模型合理性的基础上,定量研究上盖平台厚度和离地高度、上盖建筑层数和结构等因素对室内环境振动(铅垂向Z振级VL_Zmax)的影响。结果表明,地铁车辆段咽喉区对高层建筑的振动影响整体大于多层建筑;由于振动波在屋顶自由端发生反射并与入射波叠加,导致不同楼层楼板中央VL_Zmax随楼层升高略有增加;框架结构建筑室内VL_Zmax大于剪力墙结构;增加上盖平台厚度可减小建筑室内VL_Zmax;上盖建筑室内VL_Zmax随上盖平台离地高度增加而增加(即随建筑楼层绝对离地高度增加而增大)。研究结果可为地铁车辆段上盖物业开发振动污染防治提供理论和工程技术依据。     

Vibration transmissibility characteristics of the human hand-arm system under different postures, hand forces and excitation levels

Biodynamic responses of the hand-arm system have been mostly characterized in terms of driving-point force-motion relationships, which have also served as the primary basis for developing the mechanical-equivalent models. The knowledge of localized vibration responses of the hand-arm segments could help derive more effective biodynamic models. In this study, the transmission of z_h-axis handle vibration to the wrist, elbow and the shoulder of the human hand and arm are characterized in the laboratory for the bent-arm and extended arm postures. The experiments involved six subjects grasping a handle subject to two different magnitudes of broad-band random vibration, and nine different combinations of hand grip and push forces. The vibration transmissibility data were acquired in the z_h- and y_h-axis at the wrist and shoulder, and along all the three axes around the elbow joint. The results show that the human hand-arm system in an extended arm posture amplifies the vibration transmitted to the upper-arm and the whole-body at frequencies below 25 Hz, but attenuates the vibration above 25 Hz more effectively than the bent-arm posture, except at the shoulder. The magnitudes of transmitted vibration under an extended arm posture along the y_h-axis were observed to be nearly twice those for the bent-arm posture in the low frequency region. The results further showed that variations in the grip force mostly affect vibration transmissibility and characteristic frequencies of the forearm, while changes in the push force influenced the dynamic characteristics of the entire hand-arm system. The magnitudes of transmitted vibration in the vicinity of the characteristic frequencies were influenced by the handle vibration magnitude.     

Attenuation of flexural vibration for floating floor and floating box induced by ground vibration

This paper investigates the vibration isolation performance of floating floor and floating box structures to control rail vibration transmission. Simple theoretical and experimental methods are developed to analyze the effects of stiffener beam, mass and arrangement of isolator on the fundamental natural frequency of the flexural vibration of floating floor and box structure.The vibration reduction performances of floating floor and box structure are found to be degraded by flexural vibration of the floor or supporting stiffener beam. From the results of vibration measurements; stiffener beams increase the fundamental natural frequency of flexural vibration of floating floor and enhance vibration isolation. Also they can further alleviate the effect of flexural vibration using optimum isolator arrangement effectively. The proposed floating box design achieved a vibration reduction of 15-30 dB in frequency region of critical rail vibration (30-200 Hz).     

On the concept of a transmission absorber to suppress internal resonance

Internal resonances within vibration isolators have been shown to increase force transmission and consequently radiated noise from supporting structures. Previous research has successfully used dynamic vibration absorbers to attenuate internal resonances. This paper introduces the term transmission absorber to describe a system that exerts both restoring and inertial forces proportional to relative motion. A novel uni-axial vibration isolator concept incorporating transmission absorbers to suppress internal resonance is proposed and theoretically compared with an isolator including dynamic vibration absorbers. The designs are optimised by using a combination of particle swarm and gradient-based optimisation algorithms. It is shown that the proposed isolator concept, incorporating transmission absorbers, has the potential to outperform previous designs, demonstrating force transmissibility levels approaching those of an ideal isolator.     

Reduction of vibration and noise radiation of an underwater vehicle due to propeller forces using periodically layered isolators

Using periodic structure theory, the suppression of vibration and noise radiation from an underwater vehicle due to excitation from propeller forces is investigated. The underwater vehicle is modelled in two parts (the hull and the propeller/shafting system). A model of the propeller/shafting system is constructed using a modular approach and considers the propeller, shaft, thrust bearing, isolation structure and foundation. Different forms of isolator are considered – a simple spring-damper system, a continuous rod and a periodically layered structure. The dynamic properties of the underwater vehicle and the isolation performances of various isolators are compared and analysed. The stop band properties of the periodic isolator are used to enhance the passive control performance. Furthermore, an integrated isolation device is proposed that consists of the periodic isolator and a dynamic absorber, and its isolation performance is investigated. The effects of the absorber parameters on the performance of the integrated device are also analysed. Finally, the radiated sound pressure is calculated to verify the attenuation. The numerical results show that the vibration and noise radiation are greatly attenuated in the stop bands. By optimising the design of the periodic isolators and its integrated structures, the suppression of the vibration and noise radiation can be improved effectively.     

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.