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.     

Vibration reduction in piecewise bi-coupled periodic structures

The problem of minimizing transmitted vibrations through finitely long periodic structures is addressed. Bi-coupled periodic element properties and arrangement are tailored to localize the response around the excitation source within any assigned frequency range. Bi-dimensional analytical maps of the single unit free-wave propagation domains (stop, pass and complex domains) provide the optimal choice of the cell properties and ordering. Moreover, the amount of vibration suppression along the periodic structure is also controlled as it can be described through iso-attenuation curves representing the contour plot of the real part of the propagation constants. Applications to both undamped and damped beams resting on elastic supports are illustrated. The response of the periodic structures to harmonic excitations is expressed through the wave vector method taking into account the effects of wave reflection due to changes in the cell properties along the structure and boundary conditions. Such computational schemes enables one to overcome numerical difficulties arising in the transfer matrix formulation for structures with a large number of periodic units.     

Experimental study of coupled vibration in a finite periodic dual-layered structure with transverse connection

The analytical equations of the transfer matrix method are further derived for the multi-coupled vibration of flexural and longitudinal waves in a periodic dual-layered beam structure with connection branches, with full consideration given to the flexural and longitudinal motions that are tri-coupled at each connection. Measurements of mobilities at the junctions on the uni-layered beam and the cross-layered beam are made. The numerical results agree well with the experimental results at all frequencies from 10 to 2000 Hz, which verifies the theoretical methodology for the multi-coupled vibration in a finite dual-layered beam. The cross-layer energy transmission is calculated, which reveals that the transmitted longitudinal energy is enhanced not only at the longitudinal resonant modes but also at the flexural resonant modes of the connection branches due to the structural wave coupling. The flexural energy is excited by wave coupling and becomes stronger at the longitudinal resonant modes and the flexural resonant modes of the connection branches. The cross-layer vibration motions from coupled waves in the branches can be effectively controlled by the attached cantilevers with mass at the resonance modes. This method can be used to control the structure-borne sound transmission in multi-layer beam structures.     

Novel active and passive anti-vibration mountings

This paper investigates a novel design approach for a vibration isolator for use in space structures. The approach used can particularly be applicable for aerospace structures that support high precision instrumentation such as satellite payloads. The isolator is a space-frame structure that is folded in on itself to act as a mechanical filter over a defined frequency range. The absence of viscoelastic elements in such a mounting makes the design suitable for use in a vacuum and in high temperature or harsh environments with no risk of drift in alignment of the structure. The design uses a genetic algorithm based geometric optimisation routine to maximise passive vibration isolation, and this is hybridised with a geometric feasibility search. To complement the passive isolation system, an active system is incorporated in the design to add damping. Experimental work to validate the feasibility of the approach is also presented, with the active/passive structure achieving transmissibility of about 19 dB over a range of 1–250 Hz. It is shown here that the use of these novel anti-vibration mountings has no or little consequent weight and cost penalties whilst maintaining their effectiveness with the vibration levels. The approach should pave the way for the design of anti-vibration mountings that can be used between most pieces of equipment and their supporting structure.     

Passive reduction of gear mesh vibration using a periodic drive shaft

In this paper, a passive approach to reduce transmitted vibration generated by gear mesh contact dynamics is presented. The approach utilizes the property of periodic structural components that creates stop band and pass band regions in the frequency spectra. The stop band regions can be tailored to correspond to regions of the frequency spectra that contain harmonics and sub-harmonics of the gear mesh frequency, attenuating the response in those regions. A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. For the purpose of this research, only geometric variations are considered and each cell is assumed to be identical. A periodic shaft is designed and machined in order to reduce transmitted vibration of a pair of spur gears. Analytical and experimental results indicate that transmitted vibrations from gear mesh contact to the bearing supports are reduced at a variety of operational speeds under static torque preload.     

Bloch-Floquet waves and controlled stop bands in periodic thermo-elastic structures

An algorithm for controlling the stop bands for elastic Bloch-Floquet waves within a periodic structure is proposed. Explicit asymptotic estimates of frequencies of translational and rotational standing waves, together with the numerical estimates of the stop band frequencies, are given. Thermal pre-stress is introduced and used to control the position of the stop bands on the dispersion diagram.     

Bloch–Floquet waves and controlled stop bands in periodic thermo-elastic structures

An algorithm for controlling the stop bands for elastic Bloch–Floquet waves within a periodic structure is proposed. Explicit asymptotic estimates of frequencies of translational and rotational standing waves, together with the numerical estimates of the stop band frequencies, are given. Thermal pre-stress is introduced and used to control the position of the stop bands on the dispersion diagram.     

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).     

Photoacoustic study of the transmission of wide-band ultrasonic signals through periodic one-dimensional structures

The propagation of wide-band acoustic pulses in one-dimensional periodic structures consisting of alternating plexiglas and water layers is studied theoretically and experimentally. The experiment is carried out with the use of the wide-band photoacoustic spectroscopy based on the laser excitation of ultrasound and a wide-band signal detection. The fact that the transmission spectrum of a periodic structure has alternating pass and stop bands is confirmed experimentally. The width and localization of the stop bands strongly depend on the thickness of the layers and on the phase velocity of ultrasound in them. It is demonstrated that defects of the structure periodicity give rise to one or several local transmission maxima in the stop band and to a modification of the pass band. The amplitude and position of a local maximum in the stop band strongly depend on the position of the defective layer. The experimental data agree well with the results of numerical simulation.     

Optimal synthesis of 2D phononic crystals for broadband frequency isolation

The spatial distribution of material phases within a periodic composite can be engineered to produce band gaps in its frequency spectrum. Applications for such composite materials include vibration and sound isolation. Previous research focused on utilizing topology optimization techniques to design two-dimensional (2D) periodic materials with a maximized band gap around a particular frequency or between two particular dispersion branches. While sizable band gaps can be realized, the possibility remains that the frequency bandwidth of the load that is to be isolated might exceed the size of the band gap. In this paper, genetic algorithms are used to design squared bi-material unit cells with a maximized sum of band-gap widths, with or without normalization relative to the central frequency of each band gap, over a prescribed total frequency range of interest. The optimized unit cells therefore exhibit broadband frequency isolation characteristics. The effects of the ratios of contrasting material properties are also studied. The designed cells are subsequently used, with varying levels of material damping, to form a finite vibration isolation structure, which is subjected to broadband loading conditions. Excellent isolation properties of the synthesized material are demonstrated for this structure.     

Optimal synthesis of 2D phononic crystals for broadband frequency isolation

The spatial distribution of material phases within a periodic composite can be engineered to produce band gaps in its frequency spectrum. Applications for such composite materials include vibration and sound isolation. Previous research focused on utilizing topology optimization techniques to design two-dimensional (2D) periodic materials with a maximized band gap around a particular frequency or between two particular dispersion branches. While sizable band gaps can be realized, the possibility remains that the frequency bandwidth of the load that is to be isolated might exceed the size of the band gap. In this paper, genetic algorithms are used to design squared bi-material unit cells with a maximized sum of band-gap widths, with or without normalization relative to the central frequency of each band gap, over a prescribed total frequency range of interest. The optimized unit cells therefore exhibit broadband frequency isolation characteristics. The effects of the ratios of contrasting material properties are also studied. The designed cells are subsequently used, with varying levels of material damping, to form a finite vibration isolation structure, which is subjected to broadband loading conditions. Excellent isolation properties of the synthesized material are demonstrated for this structure.     

Spin waves in periodic magnetic structures—magnonic crystals

Propagation of spin waves (SWs) through a periodic multilayered magnetic structure is analyzed. It is assumed that the structure consists of ferromagnetic layers having the same thickness but different magnetizations. The wave spectrum obtained contains forbidden zones (stop bands) in which wave propagation is prohibited. Introduction into the structure of the ferromagnetic layer with a different thickness breaks the structural symmetry and leads to a localization of the SW mode with the frequency lying in the stop band. Reflection of the wave by the structure of the finite length and transmission of the wave through the structure are also investigated. Numerical calculations of the wave dispersion and the transmission coefficients for symmetrical periodic structures as well as the structures with a defect are presented. Drawing an analogy from photonic crystals known in optics, such magnetic structures can be called one-dimensional (1-D) magnonic crystals (MCs). The possibilities of existence of the 2-D MCs are also discussed.     

Symmetry coordinates of nonrigid molecules

Motivated by Altmann’s definition of symmetry groups of nonrigid molecules, Wigner’s method of obtaining the symmetry coordinates of a molecule is extended to nonrigid molecules with free internal rotations. The molecule BF₂ CH₃ is exemplified.     

Control of a unique active vibration isolator with a phase compensation technique and automatic on/off switching

This work examines the characteristics of a unique active vibration isolator and develops a control strategy for it. The proposed active vibration isolator is introduced and its dynamic model is presented. A characterization study is conducted to identify system parameters. It is shown that with a simple proportional feedback the closed-loop system has a very narrow stability margin due to the inherent dynamics of the actuator. To improve the stability of the closed-loop system and enhance the performance of vibration isolation, a phase compensator is incorporated in the control scheme. An optimization problem is formulated to determine the optimum controller parameters by minimizing the 2nd norm of the displacement transmissibility. Both absolute position feedback and relative position feedback are considered. In real time implementation, an automatic on/off switching strategy is devised to take full advantage of both the active isolator and passive isolator. The experimental results show that with the proposed control scheme, the isolator is capable of suppressing base excitations effectively.     

Experimental and numerical evidence for the existence of wide and deep phononic gaps induced by inertial amplification in two-dimensional solid structures

The aim of this paper is to show that a two-dimensional periodic solid structure with embedded inertial amplification mechanisms can possess a wide and deep phononic gap at low frequencies. The width and depth of the inertial amplification induced phononic gaps (stop bands) are determined both analytically using a distributed parameter model and numerically using one-dimensional (1D) and two-dimensional (2D) finite element models. The inertial amplification mechanisms are optimized to yield wide and deep gaps at low frequencies. These optimized mechanisms are used to form one- and two-dimensional periodic structures. Frequency responses of these periodic structures are obtained numerically using 1D and 2D finite element models. A deeper gap is generated with the two-dimensional periodic structure when compared with the one-dimensional periodic structure that has the same number of unit cells along the excitation direction. Then, the two-dimensional periodic structure is manufactured and its frequency response is determined via experimental modal analysis. The experimental and numerical frequency response results match quite well, which validate that the two-dimensional periodic solid structure has a wide and deep phononic gap.     

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.     

Active vibration isolation of a system with a distributed parameter isolator using absolute velocity feedback control

This paper is concerned with the active isolation of a system containing a distributed parameter isolator using absolute velocity feedback control. The main differences between this type of system and one with a massless isolator, is that there are isolator resonances. It is shown that the vibration at these resonance frequencies cannot be suppressed using a simple velocity feedback control strategy. Moreover, it is found that the isolator resonances can cause the control system to become unstable, if the isolated equipment is supported on a flexible base. A stability criterion based on the mode shapes of the system is presented. Two techniques to stabilise the system are investigated and compared. The first involves the addition of mass on the base structure, and the second involves an electronic lead compensator. Experimental results are presented to support the theoretical findings. It is shown that even if the instability due to the isolator resonances and flexibility of the base can be prevented, the instability due to the flexibility of the equipment remains a problem.     

激光全息法制作二、三维光子晶体的模拟计算及禁带分析

激光全息法制作二、三维光子晶体相比于传统半导体微加工及精密机械加工技术具有很多优势，比如通过一次光辐射就可以制作出大体积、均匀的周期性结构，且能更自由、更容易地控制光子晶体结构.提出一种多光束干涉模型，通过设计模型中光束的各项参数，计算分析出二、三维光子晶体的结构.基于平面波展开法，理论计算了fcc结构光子晶体的完全禁带随填充率和介电常数比变化的情况.以上计算结果为后期实验中采用激光全息法制作二、三维光子晶体结构提供了良好的指导方向和理论依据. 关键词： 光子晶体 激光全息 多光束干涉 完全禁带     

On the relation between the energy level classification of a nonrigid molecule and the symmetry of its equilibrium configurations

The problem of changes in the energy level classification of a nonrigid molecule upon a change in its equilibrium configurations, in the case in which different possible geometries of such configurations correspond to different point groups, is considered for the example of the nonrigid dimethylacetylene molecule CH₃C₂CH₃ in the ground electronic state.     

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.