Dynamic analysis of a unidirectional periodic isolator,consisting of identical masses and intermediate distributed resilient blocks

An analytical procedure for the dynamic analysis of the unidirectional periodic isolator, consisting of n concentrated masses and n intermediate arbitrary blocks is developed. Complex polynomials depending on the four pole parameters of the mounts and on the frequency of excitation are introduced, to express analytical forms for the impedances and transmissibilities of the general system. By means of these polynomials, the frequency equation of the undamped isolator can be derived directly, for free or fixed boundary conditions. Application of the method was made with isolators consisting of masses and distributed elements of rubber with internal damping.     

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.     

Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads

This paper proposes the design and experiment of a vibration isolator capable of isolating a wide range of loads. The isolator consists of two oblique springs and one vertical spring to achieve quasi-zero stiffness at the equilibrium position. The quasi-zero-stiffness characteristic makes the isolator attenuate external disturbance more at low frequencies, when compared with linear isolators. Unlike previous studies, this paper focuses on the analysis of the effect of different loads and the implementation of an adjustment mechanism to handle a wide range of loads. To ensure zero stiffness under imperfect stiffness matching, a lateral adjustment mechanism is also proposed. Instead of using coil springs, special planar springs are designed to realize the isolator in a compact space. Static and dynamic models are developed to evaluate the effect of key design parameters so that the isolator can have a wide isolation range without sacrificing its size. A prototype and its associated experiments are presented to validate the transmissibility curves under three different loads. The results clearly show the advantage of quasi-zero-stiffness isolators against linear isolators.     

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.     

Power flow through machine isolators to resonant and non-resonant beams

The parameters controlling power transmission from a vibrating machine to the seating structure, via spring-like vibration isolators, are investigated. The low frequency range is considered where the machine moves as a rigid body. It is shown that the finite seating structure can be modelled by an equivalent structure of infinite extent for frequency averaged power transmission calculations. Power transmission to a finite and an infinite beam via a mass and spring in series is measured experimentally and compared with theoretical predictions. The power transmission is measured by two proposed methods; the first involves the real component of the seating impedance, and the second the transfer impedance of the isolator.     

Characteristics of distributed parameter isolators

The widely used traditional massless isolator model is only valid at relatively low frequencies. In this paper two classes of distributed parameter isolator, non-dispersive and dispersive, which are valid over a wide range of frequencies, are studied and compared. The important characteristics of such distributed parameter isolators in isolating a mass are given, as are the parameters which control the isolator performance at various frequencies. The theoretical findings for one distributed parameter isolator are validated experimentally using a helical spring, as an example of a non-dispersive isolator.     

具有迟滞非线性的金属橡胶隔振器参数识别研究

金属橡胶隔振器具有非线性的动力学特性,对这种迟滞阻尼隔振器进行建模研究,建立了参数有物理意义的动力学模型.根据单自由度性能试验,进行了有关参数的试验识别方法研究,应用能量法及最小二乘法将非线性方程组转化为关于参数的线性方程组,从而对金属橡胶隔振器参数进行识别.识别结果与实验结果有较好的一致性,识别结果也说明了结构参数对隔振器性能的影响. 关键词： 金属橡胶隔振器 动力学模型 迟滞非线性 参数识别     

A new experimental modal analysis method based on double-exponential windowing and application to lightly damped bladed wheels

In this paper, a new method is presented for experimental modal analysis for lightly damped structures such as bladed wheels. Like most of existing methods, the one proposed here is also based on frequency response functions (FRFs). An FRF can be calculated to be the ratio of the Fourier transforms of a response and a force. For a pair of force–response time-histories generated by a force hammer impacting on a lightly damped structure, an exponential window is required to apply on both the force- and response-time histories when performing the Fourier transforms. This results in an approximate of the true FRF. Using a different decaying rate in the exponential window, a second approximated FRF is produced. These two approximated FRFs, instead of one as in existing experimental modal analysis methods, are then combined to abstract modal information and recover the true FRF.     

Moment induced structure-borne sound emission of resiliently mounted machines

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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.     

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.     

An improved design of an integrated optical isolator based on non-reciprocalMach–Zehnder interferometry

Non-reciprocal rib waveguide structures can be used to realize integrated optical isolators. In this paper, we propose a concrete design for a Mach–Zehnder interferometer type isolator for TM modes. Just one of the arms, which are of equal length, is a non-reciprocal magneto-optic waveguide. The rest of the interferometer is reciprocal. Required fabrication tolerances are estimated, and the entire isolator is simulated by applying a finite difference beam propagation method.     

Regularised finite element model updating using measured incomplete modal data

This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.     

Static and dynamic stability of pneumatic vibration isolators and systems of isolators

Pneumatic vibration isolation is the most widespread effective method for creating vibration-free environments that are vital for precise experiments and manufacturing operations in optoelectronics, life sciences, microelectronics, nanotechnology and other areas. The modeling and design principles of a dual-chamber pneumatic vibration isolator, basically established a few decades ago, continue to attract attention of researchers. On the other hand, behavior of systems of such isolators was never explained in the literature in sufficient detail. This paper covers a range of questions essential for understanding the mechanics of pneumatic isolation systems from both design and application perspectives. The theory and a model of a single standalone isolator are presented in concise form necessary for subsequent analysis. Then the dynamics of a system of isolators supporting a payload is considered with main attention directed to two aspects of their behavior: first, the static stability of payloads with high positions of the center of gravity; second, dynamic stability of the feedback system formed by mechanical leveling valves. The direct method of calculating the maximum stable position of the center of gravity is presented and illustrated by three-dimensional stability domains; analytic formulas are given that delineate these domains. A numerical method for feedback stability analysis of self-leveling valve systems is given, and the results are compared with the analytical estimates for a single isolator. The relation between the static and dynamic phenomena is discussed.     

Improvements in Carrier-to-Noise-Ratio (CNR) of Lightwave Amplitude Modulated Vestigial-Sideband (AM-VSB) Transmission Systems by the Use of Optical Isolators

In lightwave community antena television (CATV) systems as well as other optical fiber communication networks, a transmitted optical signal is known to be degraded by an intensity noise produced within the fiber due to the interference between the signal and doubly reflected light. We report on the improvements to the signal degradation due to the double Rayleigh backscattering by inserting optical isolators in the trunk lines of the systems. A carrier-to-noise ratio (CNR) has been calculated as a function of the number and the insertion loss of the isolators. The calculated results indicate that there is an optimum number of isolators, and if the insertion loss is less than 0.3 dB, the CNR degradation can be restored by more than 60%. To test the calculated results, we conducted experiments for the specific case of employing one isolator, and obtained good agreements between the two.     

Non-linear parameter estimation with Volterra series using the method of recursive iteration through harmonic probing

Volterra series provides a platform for non-linear response representation and definition of higher order frequency response functions (FRFs). It has been extensively used in non-parametric system identification through measurement of first and higher order FRFs. A parametric system identification approach has been adopted in the present study. The series response structure is explored for parameter estimation of polynomial form non-linearity. First and higher order frequency response functions are extracted from the measured response harmonic amplitudes through recursive iteration. Relationships between higher order FRFs and first order FRF are then employed to estimate the non-linear parameters. Excitation levels are selected for minimum series approximation error and the number of terms in the series is controlled according to convergence requirement. The problem of low signal strength of higher harmonics is investigated and a measurability criterion is proposed for selection of excitation level and range of excitation frequency. The procedure is illustrated through numerical simulation for a Duffing oscillator. Robustness of the estimation procedure in the presence of measurement noise is also investigated.     

Asymmetric multimode interference isolator based on nonreciprocal phase shift

This paper presents an asymmetric multimode interference-based (MMI) optical isolator, by utilizing the magneto-optical nonreciprocal phase shift (NPS). Equivalent beam propagation method (BPM) simulation of symmetric and asymmetric isolators are performed using configuration of Air/Ce:YIG/SiO₂ on silicon substrate for integration. The asymmetric isolator is found to be much more compact in size and efficient in isolation compared with symmetric isolator. Simulation results show that the isolation of asymmetric structure is 23.8 dB higher than that of symmetric one. It is mainly because both symmetric mode and anti-symmetric mode are excited in asymmetric structure and hence can interfere destructively. The proposed device may play an important role in the optical communication systems and photonic integrated devices.     

Vibrations of carbon nanotube-reinforced composites

This work deals with a study of the vibrational properties of carbon nanotube-reinforced composites by employing an equivalent continuum model based on the Eshelby-Mori-Tanaka approach. The theory allows the calculation of the effective constitutive law of the elastic isotropic medium (matrix) with dispersed elastic inhomogeneities (carbon nanotubes). The devised computational approach is shown to yield predictions in good agreement with the experimentally obtained elastic moduli of composites reinforced with uniformly aligned single-walled carbon nanotubes (CNTs). The primary contribution of the present work deals with the global elastic modal properties of nano-structured composite plates. The investigated composite plates are made of a purely isotropic elastic hosting matrix of three different types (epoxy, rubber, and concrete) with embedded single-walled CNTs. The computations are carried out via a finite element (FE) discretization of the composite plates. The effects of the CNT alignment and volume fraction are studied in depth to assess how the modal properties are influenced both globally and locally. As a major outcome, the lowest natural frequencies of CNT-reinforced rubber composites are shown to increase up to 500 percent.     

超声Lamb波二次谐波发生效率分析与模式选择

在导波模式展开分析方法的基础上,提出激发效率参量来定量表征超声Lamb波积累二次谐波的发生效率。以P92钢板为例,理论计算得到了与频散曲线对应的理论激发效率参量分布图谱,从图谱中选择理论激发效率参量大小不同的两种基频Lamb波模式:纵波型S1模式和交点型A2/S2模式,分别测量这两种基频Lamb波模式在钢板中传播时产生的二次谐波信号。理论计算和实验测量结果表明,这两种基频Lamb波模式的理论和实验激发效率参量的比值基本一致,且激发效率参量较大的纵波型S1模式能激发出效率更高的二次谐波信号。研究结果表明激发效率参量可以有效的用于Lamb波二次谐波发生效率的表征及模式选择。      

Free vibration analysis of the completely free rectangular plate by the method of superposition

While the subject of free vibration analysis of the completely free rectangular plate has a history which goes back nearly two centuries it remains a fact that most theoretical solutions to this classical problem are considered to be at best approximate in nature. This is because of the difficulties which have been encountered in trying to obtain solutions which satisfy the free edge conditions as well as the governing differential equation. In a new approach to this problem, by using the method of superposition, it is shown that solutions which satisfy identically the differential equation and which satisfy the boundary conditions with any desired degree of accuracy are obtained. Eigenvalues of four digit accuracy are provided for a wide range of plate aspect ratios and modal shapes. Exact delineation is made between the three families of modes which are characteristic of this plate vibration problem. Accurate modal shapes are provided for the response of completely free square plates.