Moment induced structure-borne sound emission of resiliently mounted machines

I.IntroductionInmanypractica1cnginccringsituations,suchasinbui1dings,carsandships,machinesaremountedonseatingstructurcsthroughcompliantiso1atorsinordertoreducethetransmissionofunwantedmachinevibrations.Thercsidualtransmissionresu1tsfromacombinationofforcesandmomcntsatthccontactpointsandinordcrtoidcntifytheimportanttransmissionmechanjsms,eachshou1didea1lybcasscsscdbymcasurcmcntorprediction.MuchofpreviousworkontranRmissionatmountingshasconccntratcdonvcrtica1forceinduccdpower["l.Itmaybethatsucha…     

Vibration of L-shaped plates under a deterministic force or moment excitation: a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary.     

The Orientation of the Phosphorescence Dipole Moment of Erythrosine B Within Its Molecular Frame

For an unequivocal interpretation of time-resolved phosphorescence depolarization measurements on dye molecules in biophysical systems, the orientation of the transition dipole moments within the frame of the dye has to be known. The goal of this work is to find the orientation of the phosphorescence dipole moment of erythrosine B within its molecular frame. To this end, we first determine four difference angles, exciting a molecule in two of its absorption bands and measuring the fluorescence and phosphorescence anisotropy for each excitation wavelength. The next step is to position the transition dipole moments within the molecular frame, combining the results of angle-resolved fluorescence depolarization measurements with the measured difference angles. It is shown that the phosphorescence dipole moment is tilted out of the plane of the molecule. Additionally, we find that the phosphorescence dipole moment is located above the fluorescence dipole moment and not above the absorption dipole moment. This induces an extra difference angle between the absorption and the phosphorescence dipole moments which in the past has been interpreted erroneously as a larger tilt out of the plane of the molecule.     

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.     

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.     

水下近水面锥柱组合壳声固耦合效应的半解析求解方法

针对水下近水面锥柱组合壳声固耦合多借助于数值方法求解的现状,本文提出一种半解析方法从机理上分析此类问题。首先基于能量泛函和Sanders壳体理论、虚拟弹簧法以及力与力矩平衡条件建立锥柱组合壳的结构模型;然后采用Legendre谱元法和二维傅里叶变换得到含自由液面的水下声场模型;最后由非线性迭代法和高斯积分求解耦合系统声振控制方程。通过与参考文献和数值方法结果的对比,验证了本文方法的收敛性、正确性和可靠性。研究结果表明,结构参数、浸没深度和激励频率与远场辐射声压密切相关。本文工作可推广到水下含内部结构的复杂旋转组合壳在不同结构边界及声边界下的声固耦合问题。      

The angleICI Bending Satellites in the Millimeter-Wave Rotational Spectra of CH(2)I(2) and CD(2)I(2)

Rotational transitions in the first four excited states of the low-frequency angleICI bending mode, nu(4), have been assigned in the mm-wave rotational spectra of CH(2)I(2) and of CD(2)I(2). Measurements of transition frequencies, made over the frequency region 167-326 GHz and for J" up to 190, allowed determination of sextic level spectroscopic constants for all states. The changes in spectroscopic constants with vibrational excitation show very small anharmonicity, in spite of the very low frequency of this mode (121 cm(-1)). Vibrational excitation affects the moments of inertia in such a way that the planar moment P(b), about the plane perpendicular to both angleICI and angleHCH, is practically invariant. Vibrational change in P(c), the moment along the principal axis in the HCH plane and perpendicular to the angleHCH bisector, has been successfully reproduced with an ab initio harmonic force field so that there is no discernible vibrational change in angleHCH on excitation of angleICI. Finally, the change in P(a) leads to estimated vibrational change of +0.12 degrees in the value of angleICI itself. Copyright 2000 Academic Press.     

The effect of bending vibrations on the dipole moment of a linear polyatomic molecule: A theoretical treatment of the vibrational changes and transition moments

The vibrational effect on the dipole moment of a linear molecule is theoretically considered from the aspects of the dipole moment changes with the excitation of bending vibrations and the transition moments for the overtone, combination, and difference bands associated with bending modes. Such dipole moment changes and transition moments consist of two components, one depending on the first dipole moment derivatives with respect to bond lengths and the other depending on the second dipole moment derivatives with respect to bond angles. We show that the first component normally contributes little, and propose an approximation in which only the second component is retained. This approximation is practically important because the second component can be calculated without the anharmonic force constants. We derive formulas for the dipole moment changes and transition moments to facilitate a simultaneous analysis of different isotopic species. We introduce the concept of the equivalent mode, by which we may readily understand the correlation between the dipole moment change for a bending mode and the transition moment for a vibrational band.     

Shells and plates loaded by dynamic moments with special attention to rotating point moments

The response of thin shells to line or point moment excitation is formulated by way of distributed moment fields. Twisting moments in the tangent plane are part of this formulation. The approach is illustrated by using Love's thin shell theory, but is valid for any other thin shell theory as well. Dirac delta functions are used to describe line and point moments. As a first example, the response of a plate to a rotating moment is evaluated and shown to be identical to the solution obtained by Bolleter and Soedel [1] by a Green function approach. The three-directional response of a circular cylindrical shell to a rotating moment is given as the second example. It is a technically significant case that has not been treated in the literature before.     

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.     

次级源近场和管壁弹性对充液管路有源消声性能的影响EI北大核心CSCD

建立了含次级源结构的充液直管有源消声系统数值模型,重点分析了声激励下次级源近场和管壁弹性对有源消声性能的影响。结果表明:次级源近场为非均匀声场,误差点位于该区域时部分频点控制效果较差甚至放大,而处于声场均匀区域时可使降噪量提高10 dB以上,增加误差点数量可使绝大多数频点的降噪量提高5 dB以上;管壁弹性使次级源与管壁间的耦合较强,非对称分布的次级源容易激起管壁振动,导致降噪谷值的出现,采用对称分布的次级源可显著提升控制效果;增加次级源数量能够提高系统的有源无源复合控制效果,但使得管内声场变得复杂,多次级源模型的有源消声效果随频率升高而有所降低。     

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.     

Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: A theoretical and experimental study

This paper concerns the vibration isolation characteristics of a nonlinear isolator using Euler buckled beams as negative stiffness corrector. Both analytical and experimental studies are carried out. The Harmonic Balance Method (HBM) is used to determine the primary resonance response for the single degree of freedom (SDOF) nonlinear system composed by a loaded mass and the nonlinear isolator. The distuning of the loaded mass is taken into consideration, resulting in a Helmoholtz–Duffing equation. The performance of the nonlinear isolator is evaluated by the defined two kinds of transmissibility and compared with that of the linear isolator without the stiffness corrector. The study shows that the asymmetric SDOF nonlinear system can behave like a purely softening, a softening–hardening or a purely hardening system, depending on the magnitude of the excitation level. An experimental apparatus is set up to validate the analytical results. The transmissibility results of the SDOF nonlinear system under base excitation with both discrete sinusoidal frequencies and slowly forward and backward sweeps are given and discussed. The complex jump phenomena under different excitation levels are identified. By introducing the stiffness corrector, the starting frequency of isolation of the nonlinear isolator is found to be lower than that of the linear one with the same support capacity. The proposed nonlinear isolator performs well in applications where the excitation amplitude is not too large.     

Sources of spurious force oscillations from an immersed boundary method for moving-body problems

When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132–150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.     

Efficiency of the structure analysis of complex molecules in the gas phase by their optical rotation

It was shown in the dipole approximation of optical rotation that in the general case only in orientationally anisotropic vapors is the rotational force dependent on the intramolecular orientation of both the electric and magnetic dipole moments. Expressions relating the optical rotational force to the intramolecular orientation of these moments, the orientational distribution in an anisotropic ensemble, and the configuration of a measurement have been obtained. Calculated dependences of the rotational force on the intramolecular orientation of the magnetic moment at a fixed electric moment and “rotational force excitation spectra” obtained for different types of rigid asymmetric top molecules and rotational contours are presented. It is proposed to measure the intramolecular orientation of the electric and magnetic dipole moments with the use of the rotational force normalized to that detected in the case of observation at a “magic” angle to the direction of the exciting light electric vector. Institute of Molecular and Atomic Physics of the Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 6, pp. 843–849, November–December, 1998.     

Generation of waves in an elastic plate by a torsional moment and a horizontal force

An approximate solution is determined for the motion of an infinite elastic plate, excited by a torsional moment (with the axis of the moment normal to the plate) and by a horizontal force (parallel to the plate). The driving moment and force are sinusoidal in time and applied to a small rigid indenter with a circular base, fixed to the plate. The solution is obtained from a three-dimensional approach but is evaluated only for low frequencies, where the wavelengths of the quasi-longitudinal, tranverse and bending waves are much larger than the thickness of the plate. For the case of excitation with a torsional moment, the solution contains two parts, one describing a travelling transverse wave and the other a local reaction. The local reaction is built up of two infinite sums of Love waves with imaginary wave numbers. The driving-point admittance due to the local reaction is larger than the admittance due to the tranverse wave when the diameter of the indenter is smaller than about twice the thickness of the plate. For the case of excitation with a horizontal force, the solution contains three parts that describe travelling waves (quasi-longitudinal, transverse and bending) and two parts that describe the local reaction (infinite sums of Lamb and Love waves). The admittances due to the three types of travelling waves are all of the same order of magnitude. The admittance due to the local reaction is of importance when the frequency is relatively high and the diameter of the identer much smaller than the thickness of the plate. For both cases of excitation, the admittance due to the local reaction increases with increasing thickness of the plate and tends to the value found for a semi-infinite medium.     

Efficient semi-analytical methods for the vibration response of and acoustic radiation from a periodical orthogonally rib-stiffened plate

In order to theoretically predict and analyze the vibration response and acoustic radiation characteristics of a periodical orthogonally rib-stiffened plate,its vibro-acoustic equations of an underwater infinite model are established.The rib-stiffened plate is stimulated by a harmonic plane pressure.By using the Fourier transforms,Poisson's summation formula and space harmonic method,the structural vibration response and acoustic radiation pressure are expressed as functions of displacement harmonic components.Efficient semi-analytical methods are proposed in this work,and then approximate solutions for finite terms of the harmonic components are obtained by employing the truncation technique.Effects of the vibration response,rib spacing and torsional moment of the ribs on the radiation pressure are examined,and the validity of the present methods is also verified.Theoretical results show that the torsional moment of the ribs affects the modal frequencies of the stiffened plate,which should not be neglected in engineering applications with high precision requirement.With attachment of the ribs to the thin plate,its far field radiation pressure can be reduced in the low frequency range by adjusting rib spacing and cross sectional size of the ribs.     

Postbuckling and vibration of end-supported elastica pipes conveying fluid and columns under follower loads

Fluid-conveying pipes with supported ends buckle when the fluid velocity reaches a critical value. For higher velocities, the postbuckled equilibrium shape can be directly related to that for a column under a follower end load. However, the corresponding vibration frequencies are different due to the Coriolis force associated with the fluid flow. Clamped–clamped, pinned–pinned, and clamped–pinned pipes are considered first. Axial sliding is permitted at the downstream end. The pipe is modeled as an inextensible elastica. The equilibrium shape may have large displacements, and small motions about that shape are analyzed. The behavior is conservative in the prebuckling range and nonconservative in the postbuckling range (during which the Coriolis force does work and the motions decay). Next, related columns are studied, first with a concentrated follower load at the axially sliding end, and then with a distributed follower load. In all cases, a shooting method is used to solve the nonlinear boundary-value problem for the equilibrium configuration, and to solve the linear boundary-value problem for the first four vibration frequencies. The results for the three different types of loading are compared.     

Non-linear resonances in the forced responses of plates,part II: Asymmetric responses of circular plates

The dynamic analogue of the von Karman equations is used to study the forced response, including asymmetric vibrations and traveling waves, of a clamped circular plate subjected to harmonic excitations when the frequency of excitation is near one of the natural frequencies. The method of multiple scales, a perturbation technique, is used to solve the non-linear governing equations. The approach presented provides a great deal of insight into the nature of the non-linear forced resonant response. It is shown that in the absence of internal resonance (i.e., a combination of commensurable natural frequencies) or when the frequency of excitation is near one of the lower frequencies involved in the internal resonance, the steady state response can only have the form of a standing wave. However, when the frequency of excitation is near the highest frequency involved in the internal resonance it is possible for a traveling wave component of the highest mode to appear in the steady state response.     

The design and dynamic performance of a moment actuator

I.IntroductionMachinenoiseisanenvironmcnta1po11utantanditscontrolremainsamajorunresolvedprob1cm.Inadditiontoair-bornesound,machinesimpartvibrationalenergyintosupportingandconnectedstructuresbybothtrans1ationa1androtationa1motions.Translationa1compo-nentsarerelative1yeasytoestimatesinccnearpureforcescanbegeneratedandmeasured.ThisisnotthecaseforrotationalcomponentSsincemomcntsaremoredifficu1ttogenerateandmeasure.Suchmeasurementswould1eadtoafu11undcrstandingofthis1ittleunderstoodbutoftenimporta…