The effects of floating slab bending resonances on the vibration isolation of rail viaduct

This paper compared the performance of several isolation designs to control vibration transmissions from concrete rail viaducts. The isolation systems analysed includes medium- and short-length floating slabs, and floating ladders. The vibration was measured in Japan, Korea and Hong Kong. The study aimed to assess the effects of bending resonances of the floating slab systems. Simple formulae of estimating the significant bending resonance frequency and support passage frequency of a floating slab system are proposed. The resonance peaks obtained in site measurement are found to be in agreement with the calculation results. The results show that other than the vertical rigid body resonances for the isolation systems, the bending resonances of slabs have significant effects on vibration isolation performance. In particular, bending resonance frequencies should not coincide with the vertical isolator resonance and support passage frequency. According to the in-situ measurement results, a mini-type concrete floating slab can reduce the vibration level by more than 30 dB in the frequency range of 63-200 Hz. This should be achieved by designing the first bending resonances of the floating slab to be out of the dominant frequency range of concrete rail viaduct vibration.     

Coupling resonance of floating slab and supporting concrete box structure

This paper mainly investigates the effect of coupling resonance of floating slab and supporting short concrete box. The similarities and differences in vibration behaviors between long (30 m) and short (1.5 m) lengths of concrete box structures with the same cross-section were analyzed with finite element model (FEM). The results suggest that the major local modes for vibration and structure-borne sound radiation for long and short box structures are the same. A short concrete hollow box was constructed to verify the theoretical vibration results, and six combinations of floating slabs were installed on the box to identify the vibration and structure-borne sound control by experimental method. The resonance modes due to either concrete box or floating slab should degrade the vibration isolation performance of the floating system. There may be strong coupling between roll mode (rigid body rotation mode in the y-z plane) of the floating slab and local distortion mode of the short box structure and this can change the vibration resonance frequencies and amplify the vibration.     

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.     

Insertion loss prediction of floating floors used in ship cabins

In this paper, vibration reduction in ship cabins by using floating floor is studied. Two theoretical models are developed and predicted insertion losses of floating floors are compared to experimental results, where measurements are done in the mock-up built for simulating typical ship cabins. The floating floor consists of upper board and mineral wool, which is in turn laid on the deck plate. The first model (M-S-Plate Model) is that upper plate and mineral wool are assumed as a one-dimensional mass-spring system lying on the simply supported elastic floor. The second model (Wave Model) is that mineral wool is assumed as elastic medium, in which longitudinal wave propagates. The comparisons show that M-S-Plate model is in good agreement with experimental results, while mass-spring model on the rigid floor behaves very poorly in the low frequency ranges, particularly near the natural frequency associated with mass-spring system. On the other hand, the wave model significantly underestimates the insertion loss. It is found that including elastic behavior of the deck plate is essential in improving accuracy of the insertion loss prediction for low frequency range below 100-200 Hz.     

Application of dynamic vibration absorbers in floating raft system

To improve the isolation performance of the traditional floating raft system, dynamic vibration absorber (DVA) is introduced into floating raft in this research. The mathematical models of floating raft system consisting of beams are implemented by assembling the mobility matrices of the subsystems. Then the power flow transmission characteristics of the coupled system with/without the DVAs are investigated to evaluate the vibration reduction performance of DVAs. Numerical simulations are performed to explore the influence of several parameters, such as the setting positions, damping and mass of the passive DVAs, on the vibration reduction effects of DVAs. Moreover the vibration reduction performance of the semi-active absorber adjusting its stiffness adaptively is analyzed for the case of time-varying frequency excitation. In addition, the vibration reduction effects of semi-active DVAs under multi-frequency excitation are investigated. The results show that DVAs can significantly improve the isolation performance of floating raft system.     

Theoretical design and experimental verification of a tunable floating vibration isolation system

A fluid-type floating vibration isolation system was developed based on anti-resonance mechanism. The mathematical model was derived for theoretical analysis. The system enables completely isolate vibration at any specific frequency, when the frequency of anti-resonance of the floating vibration isolation system is adjusted to the vibration frequency by tuning the added mass of flowing fluid. Since the approach only alters the inertial force of added mass rather than changing the entire system stiffness, the robustness of the system’s static stability remains during a tuning process, and the system can perform vibration isolation superbly at very low frequencies. A prototype of fluid-type floating vibration isolation system was designed, built and tested to validate the mathematical model. The experimental results illustrated a good agreement with the theoretical analysis.     

A tunable high-static-low-dynamic stiffness vibration isolator

In this study, a novel vibration isolator is developed. The developed isolator possesses the characteristics of high-static-low-dynamic stiffness (HSLDS) and can act passively or semi-actively. The HSLDS property of the isolator is obtained by connecting a mechanical spring, in parallel with a magnetic spring that is constructed by a pair of electromagnets and a permanent magnet. The mechanical spring is a structural beam whose stiffness exhibits a hardening behavior. The stiffness of the magnetic spring can be positive or negative, depending on the polarity of the current to the electromagnets. A passive HSLDS isolator is obtained when the electromagnet current is zero. In the stiffness characterization study, the analytical model for each of the springs is established and the tuning parameters are identified. Using the stiffness models, the design optimization issues are investigated. In the experimental study, the effectiveness of the isolator for vibration isolation is tested. The analytical natural frequencies of the isolator are validated experimentally. The relationships between the displacement transmissibility and the exciting frequency are measured both under the passive mode and under the semi-active mode. The on-line tuning capability of the isolator is investigated.     

多振子梁弯曲振动中的局域共振带隙

从梁的弯曲振动方程出发,利用传递矩阵法,给出了无限周期结构的一维多振子声子晶体梁的弯曲振动能带结构,并利用有限元方法计算了有限周期结构梁的弯曲振动频率响应.建立了多振子声子晶体梁的简化模型,推导出带隙起始截止频率公式.结果表明:一维多振子声子晶体梁具有比单振子声子晶体梁更宽更丰富的振动带隙,可应用于呈倍频关系的减振降噪中;振动在带隙频率范围内频率响应具有明显的衰减;所建立的简化模型与理论模型结果符合较好.研究工作为梁类结构的减振提供一种新的思路.     

双稳态结构中的1/2次谐波共振及其对隔振特性的影响

以典型的双稳态系统——屈曲梁结构为例,基于等效模型,结合解析、数值和实验手段,研究了双稳态结构中的1/2次谐波共振特性、演化过程、参数调节规律及其对隔振特性的影响.研究发现,当非线性刚度系数或激励幅值增加到一定程度时,系统会在一定带宽下产生显著的1/2次谐波共振;随着激励幅值增加,阻尼系统的1/2次谐波遵循“产生-增强-衰退-消失”的过程,该过程对峰值频率和峰值传递率有重要影响;适当提高非线性强度能有效改善双稳态结构隔振特性.针对双稳态屈曲梁结构开展的实验验证了1/2次谐波特性和隔振特性变化规律.     

Direct energy flow measurement in magneto-sensitive vibration isolator systems

The effectiveness of highly nonlinear, frequency, amplitude and magnetic field dependent magneto-sensitive natural rubber components applied in a vibration isolation system is experimentally investigated by measuring the energy flow into the foundation. The energy flow, including both force and velocity of the foundation, is a suitable measure of the effectiveness of a real vibration isolation system where the foundation is not perfectly rigid. The vibration isolation system in this study consists of a solid aluminium mass supported on four magneto-sensitive rubber components and is excited by an electro-dynamic shaker while applying various excitation signals, amplitudes and positions in the frequency range of 20–200 Hz and using magneto-sensitive components at zero-field and at magnetic saturation. The energy flow through the magneto-sensitive rubber isolators is directly measured by inserting a force transducer below each isolator and an accelerometer on the foundation close to each isolator. This investigation provides novel practical insights into the potential of using magneto-sensitive material isolators in noise and vibration control, including their advantages compared to traditional vibration isolators. Finally, nonlinear features of magneto-sensitive components are experimentally verified.     

Difference thresholds for vibration of the foot: Dependence on frequency and magnitude of vibration

The smallest change in vibration intensity for the change to be perceptible (i.e. intensity difference threshold) has not previously been reported for vibration of the foot. This study investigated the influence of vibration magnitude and vibration frequency on intensity difference thresholds for the perception of vertical sinusoidal vibration of the foot. It was hypothesised that relative intensity difference thresholds (i.e. Weber fractions) for 16-Hz vibration mediated by the non-Pacinian I (NPI) channel would differ from relative intensity difference thresholds for 125-Hz vibration mediated by the Pacinian (P) channel. Absolute thresholds, difference thresholds, and the locations of vibration sensation caused by vertical vibration of the right foot were determined for 12 subjects using the up-down-transformed-response method together with the three-down-one-up rule. The difference thresholds and locations of sensation were obtained at six reference magnitudes (at 6, 9, 12, 18, 24, 30 dB above absolute threshold—i.e. sensation levels, SL). For 16-Hz vibration, the median relative difference thresholds were not significantly dependent on vibration magnitude and were in the range 0.19 (at 30 dB SL) to 0.27 (at 9 dB SL). For 125-Hz vibration, the median relative difference thresholds varied between 0.17 (at 9 dB SL) and 0.34 (at 30 dB SL), with difference thresholds from 6 to 12 dB SL significantly less than those from 18 to 30 dB SL. At vibration magnitudes slightly in excess of absolute thresholds (i.e. 6-12 dB SL) there were no significant differences between Weber fractions obtained from the P channel (at 125 Hz) and the NPI channel (at 16 Hz). At 24 and 30 dB SL, the 125-Hz Weber fractions were significantly greater than the 16-Hz Weber fractions. Differences in the 125-Hz Weber fractions may have been caused by a reduction in the discriminability of the P channel at high levels of excitation, resulting in one or more NP channel mediating the difference thresholds at magnitudes greater than 18 dB SL. At high magnitudes, a change of channel mediating the Weber fractions may have been responsible for different Weber fractions with 16- and 125-Hz vibration.     

The vibration discomfort of standing persons: 0.5-16-Hz fore-and-aft, lateral, and vertical vibration

To minimise the discomfort of standing people caused by vibration of a floor, it is necessary to know how their sensitivity to vibration depends on the frequency of the vibration. This study was designed to determine how the discomfort of standing people exposed to horizontal and vertical vibration depends on vibration frequency over the range 0.5-16 Hz. Using the method of magnitude estimation, sixteen subjects judged the discomfort caused by fore-and-aft, lateral, and vertical sinusoidal vibration at each of the sixteen preferred one-third octave centre frequencies from 0.5 to 16 Hz at each of nine magnitudes. Subjects also reported the main cause of their discomfort. Equivalent comfort contours were constructed, reflecting the effect of frequency on subject sensitivity to vibration acceleration. With horizontal vibration, at frequencies between 0.5 and 3.15 Hz the discomfort was similar when the vibration velocity was similar, whereas at frequencies between 3.15 and 16 Hz the discomfort was similar when the vibration acceleration was similar. At frequencies less than 3.15 Hz, the subjects experienced problems with their stability, whereas at higher frequencies vibration discomfort was mostly experienced from sensations in the legs and feet. With vertical vibration, discomfort was felt in the lower-body and upper-body at all frequencies. The frequency weightings in current standards for predicting the vibration discomfort of standing persons have been greatly influenced by the findings of studies with seated subjects: the weightings are consistent with the experimentally determined frequency-dependence of discomfort caused by vertical vibration but inconsistent with the experimentally determined frequency-dependence of discomfort caused by horizontal vibration. The results suggest that the responses of seated and standing people are similar for vertical vibration, but differ for horizontal vibration, partly due to greater instability in standing persons.     

轨道交通箱型梁腔室结构的减振降噪研究

轨道交通箱型梁在列车荷载作用下产生的低频振动与噪声对人体健康危害很大,针对箱型梁的减振降噪研究具有重要意义。将有限元振动分析理论与声辐射分析边界元法相结合,计算列车荷载作用下箱型梁的结构噪声,并对比分析不同的腔室结构对箱型梁结构噪声辐射的影响。计算结果表明:箱型梁场点结构噪声的辐射受振动水平影响较大;对于不同的腔室结构的箱型梁,跨中场点的最大线性声压级从大到小依次为单箱单室、单箱双室、单箱三室、双箱单室箱型梁;箱型梁采用双箱单室结构形式最有利于结构噪声的控制,且随辐射距离的增加,噪声辐射衰减越快;降低翼缘和腹板振动水平能够有效降低箱型梁结构噪声。分析结果可为城市轨道交通箱型梁的结构减振降噪设计提供一定的理论参考。     

Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm

In this paper, the superior mid-frequency vibration isolation of a geometrically optimized lightweight structure is demonstrated. The initial structure under test here was a 4.5 m long satellite boom consisting of 10 identical bays with equilateral triangular cross-sections. An unusual geometric variant of this, with inherent isolation characteristics, has been designed by the use of genetic algorithm (GA) methods. In order to obtain the best design, the joints in the boom were allowed to move around by 20% of the length of each bay (i.e., ±9 cm in all three translational directions). This work is based on results from a Fortran code (which was derived from receptance analysis) that are fully validated against detailed finite element (FE) models of the structure. The experimental forced response of the regular boom structure has been measured and compared with predicted curves. Finally, having obtained the geometrically optimized boom structure, its experimental response is compared with the theoretical results predicted by the receptance method. It is shown that the average of 30 dB isolation in the vibration energy transfer between the ends of the network of beams, over a 100 Hz bandwidth predicted in the design process, is achieved experimentally in an essentially undamped structure.     

Optimal design of beams under flexural vibration

The minimum weight design of a cantilever beam in flexural vibration is considered. The aim is the maximization of a given natural bending frequency (usually the first) for a given beam weight or equivalently the minimization of beam weight for a specified value of a natural frequency. The beams considered are of rectangular section and are subject, in a range of cases presented, to a variety of constraints on lower and upper bounds on the cross-section dimensions or to the specification of a point mass at the end of the beam. Simple bending theory is regarded as applicable to the problem. A variational statement of the problem is made and the necessary conditions for a minimum are obtained as a system of non-linear equations which are solved numerically. Results are given in the form of tables and of figures showing computed optimum profiles. Some experiments on a sample set of beams of equal mass are described briefly. The optimum profile beam was found to have the greatest fundamental frequency, in support of the theoretical predictions.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

A reduction method for problems of vibration of orthotropic plates

It is shown that the problem of vibration of an orthotropic plate can be reduced to that of another orthotropic plate by a simple co-ordinate transformation, and reduction formulae are obtained. To justify the reduction formulae, fundamental natural frequencies of orthotropic rectangular plates with various boundary conditions and of a clamped orthotropic elliptical plate are discussed. As an example, an exact natural frequency of a simply supported generally orthotropic skew plate with special flexural rigidities is obtained from that of a simply supported isotropic rectangular plate.     

Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform

Reaction wheel assemblies (RWAs) are momentum exchange devices used in fine pointing control of spacecrafts. Even though the spinning rotor of the reaction wheel is precisely balanced to minimize emitted vibration due to static and dynamic imbalances, precision instrument payloads placed in the neighborhood can always be severely impacted by residual vibration forces emitted by reaction wheel assemblies. The reduction of the vibration level at sensitive payloads can be achieved by placing the RWA on appropriate mountings. A low frequency flexible space platform consisting of folded continuous beams has been designed to serve as a mount for isolating a disturbance source in precision payloads equipped spacecrafts.Analytical and experimental investigations have been carried out to test the usefulness of the low frequency flexible platform as a vibration isolator for RWAs. Measurements and tests have been conducted at varying wheel speeds, to quantify and characterize the amount of isolation obtained from the reaction wheel generated vibration. These tests are further extended to other variants of similar design in order to bring out the best isolation for given disturbance loads. Both time and frequency domain analysis of test data show that the flexible beam platform as a mount for reaction wheels is quite effective and can be used in spacecrafts for passive vibration control.     

Control of ground-borne noise and vibration

Ground-borne noise and vibration created by train operations is one of the major environmental problems faced by rail transit systems. In the past 10–20 years there have been a number of developments in the control and prediction of ground-borne noise and vibration although it is evident that further research is needed. In this paper the focus is on two methods of controlling the vibration radiated by the transit structure. First is the use of floating slab trackbeds, a method that has proven to be very effective at reducing vibration at frequencies above the resonance frequency of the floating slab system. Second is to modify the design of transit car bogies such that the wheel/rail forces are reduced. Although this method is still in the exploratory phase it has been shown that proper design of the bogie suspension can significantly reduce the levels of ground-borne noise and vibration.     

多源激励下双层隔振浮筏系统的线谱混沌化

采用混沌化技术可以重构水下航行器的水声线谱特征,改善隐声性能.基于这一特殊应用背景,研究了多源激励下双层隔振浮筏系统的非线性时延反馈混沌化问题.在二维简化浮筏系统模型的基础上,完整地呈现了非线性时延反馈控制的线谱混沌化方法,为隔振浮筏的线谱混沌化设计提供了标准流程.仿真结果表明了该方法的可行性,探讨了多源激励条件下控制增益、时延和反馈频率等控制参数对系统混沌化效果的影响,并与单源激励进行了对比分析.