Free and forced vibration analysis of a nonlinear system with cyclic symmetry: Application to a simplified model

This work program is devoted to studying the nonlinear dynamics of a structure with cyclic symmetry under conditions of geometric nonlinearity, through the use of the harmonic balance method (HBM). In order to study the influence of nonlinearity due to the large deflection of blades, a simplified model has been developed. This approach leads to a system of linearly coupled, second-order nonlinear differential equations, in which nonlinearity appears via cubic terms. Periodic solutions, in both the free and forced cases, are sought by applying HBM coupled with an arc-length continuation method. Solution stability has been investigated using Floquet's theorem. In addition to featuring similar and nonsimilar nonlinear modes, the unforced system is known to contain localized nonlinear modes that arise from branching point bifurcation at certain vibration amplitudes. In the forced case, these nonlinear modes give rise to a complex dynamic behavior. Many bifurcations can take place, thus leading to strong or weak localization that may or may not be stable. In this study, special attention has been paid to the influence of excitation on dynamic responses. Several cases of excitation have been analyzed herein: localized excitation, and low-engine-order excitation. In the case of low-engine-order excitation, sensitivity of the response to a perturbation of this excitation type has been investigated, and it has been shown that for a localized, or sufficiently detuned excitation, several solutions can coexist, some of which are represented by closed curves in the Frequency-Amplitude domain. These various solutions overlap when increasing the force amplitude, leading to forced nonlinear localization. Because closed curves are not tied up with the basic nonlinear solution, they can easily be overlooked. In this study, they have been calculated using a sequential continuation with the force amplitude as a parameter.     

A nonanalytic,quasistationary approximation scheme applied to a model problem

A model problem designed to incorporate several of the features of slow-motion gravity is analyzed. In common with a previous model calculation the present work supports the idea that divergent integrals which arise in analytic quasistationary perturbation schemes are artifacts of these schemes and can be eliminated by using singular perturbation techniques, in which they get replaced by finite nonanalytic terms. The new features of the present model are (1) it illustrates the necessity of straining the outgoing null coordinate to eliminate logarithmic nonuniformities in nonlinear order for large radius, and (2) it is exactly solvable for the pure-frequency case, which gives an important check on the approximation scheme. Straining the null coordinate immediately introduces time-odd terms in the near zone which are larger than the standard linear-theory damping result. However, these terms are shown to be spurious in that they are canceled by higher-order contributions in the approximation scheme. Thus the standard linear-theory damping result holds in the model, even when nonlinear effects are considered.Supported in part by The National Science Foundation under grant No. PH 79-11664.     

A simplified model for the analysis of a phase-change material-based,thermal energy storage system

The concept of a phase-change material-based, thermal energy storage system is often used for different applications. A theoretical model to determine the thermal and fluid flow characteristics of a thermal energy storage system using a phase-change material has been developed. The model can be used to predict the energy storage behavior of different phase-change materials used with different heat transfer fluids, flow geometries, flow rates and temperatures. Results have been obtained for the case where the phase-change material is Na₂SO₄·10H₂O (Glauber's salt) and the heat transfer fluid is water. The variation of the dimensionless temperatures of the fluid and the solid, and the molten fraction of the solid during the phase change process, with dimensionless time, for different values of Biot number, Stefan number, and the flow parameter have been determined. A discussion of the results obtained and the conclusions drawn from them are also given.     

Approximate step response of a nonlinear hydraulic mount using a simplified linear model

A simplified dynamic stiffness type linear model is used to analytically find the step responses of a nonlinear hydraulic mount in terms of the transmitted force and top chamber pressure. The closed form solution could be efficiently implemented with effective mount parameters, and peak value and the decay curve predictions could provide some insight into the nonlinear behavior. The analytical solutions to an ideal step input correlate well with both numerical simulations (of the same linear model) and measurements when a step-like displacement excitation is applied to fixed and free decoupler mounts.     

A simplified method to calculate the field distribution of pistonlike source

I.IntroductionThesoundfieldproducedbyanidealbaflledplanartransducerhasbeenoneofthemostfundamentalproblernsinacousticsforaverylongtime.TheproblemcanbereducedtothewellknownRayleighintegralorKing'sintegral.Inmostcases,however,theirsolutionsarenotanalyticalandcdnnotberepreselltedinclosedformbygeneralorspecialfunctions.AsanexaInPleoftheuniformpistonsource)todescribethesoundbeamdistributionsinthenearandtransitionzones,itisnecessarytomakecalculationsbyusingthenumericalintegrations(point-by-poillt)o…     

活塞类声场的简化算法

本文提出了计算活塞型声场一种简单方法,将声源分布函数作为某一函数与矩形函数高斯和的乘积,而无需对每个声源分布函数的高斯分解系数进行数值求解,这种方法可大大减化声场计算,并计算了几种活塞型声场分布,结果表明这一方法相当有效。     

Explosion model applied to an intense pulsed plasma source for thinfilm deposition

A pulsed plasma source for deposition of thin polymer films was modeled numerically with the one-dimensional (1-D) time dependent fluid transport equations describing an explosion for an ideal gas. Initial number density, explosion temperature, and velocity were made consistent with values in an experimental reactor. These quantities as well as pressure and fluence were modeled for a distance of 2 m and for a time duration of 93 μs. The trajectory for maximum pressure calculated from the model was observed to be consistent with the experimentally measured trajectory of maximum emitted light from an acetylene plasma. Measured axial profiles of areal density for the deposited polymer films were compared with modeled fluence     

A simplified way to compute partial coherence function in noise source identification

A simplified way to compute multiple coherence function,partialcoherence function,partial multiple coherence function,as well as all typesof coherent output spectra are deduced in this paper by applying multivariatelinear regression theory to multiple coherence analysis.The conceptof"residual cross spectrum"is avoided.The formulas are simple and easy tobe programmed.The problems in noise source identification by partial coher-ence function are discussed.The results for noise source identification in asimulated model are given.     

A simplified nonlinear dynamic model for the analysis of pipe structures with bolted flange joints

Bolted flange joints are widely used in engineering structures; however, the dynamic behavior of this connection is complex in nature. In this paper, a simplified nonlinear dynamic model with bi-linear springs is proposed and validated for pipe structures with bolted flange joints. First, static mechanical properties of the bolted flange joint are investigated. The analytical solution reveals that the axial stiffness of the bolted flange joint is different in tension and compression. Then, nonlinear springs with different stiffness in tension and compression are employed to represent the bolted flange joint. A special type of dynamic behavior, coupling vibration in the transverse and longitudinal directions, is observed in analytical derivation. Finally, relevant physical experiments and numerical simulations are performed. The physical experiments confirm the existence of the coupling vibration behavior. The relationship of longitudinal and transverse vibration frequencies is discussed. The numerical solutions reveal that the simplified nonlinear dynamic model better fits the physical response than conventional reduced linear beam model.     

偏相干函数的简化计算及其噪声源识别

把多元线性系统的偏相干分析看作是多元线性回归中相关分析的直接推广,得到了求复相干、偏复相干、偏相干以及各种相干功率谱的简化计算方法。避免了引进“残互谱”等物理意义模糊的概念。公式简单,编程容易。并讨论了偏相干函数、偏复相干函数在噪声源识别中的问题。给出了模拟飞机机舱噪声源识别的结果。     

A remark on the KAM theorem applied to a four-vortex system

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation number=(5—1)/2 and compare our result with numerical experiments.     

A relativistic oscillator model applied to lepton-nucleon reactions

A relativistic oscillator model is applied to lepton-nucleon reactions. It agrees quantitatively with data on hadron energy distribution, multiplicity, and $\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ ratios.     

A new contribution to nonlinear stability of a discrete velocity model

For a class of discrete velocity models of kinetic theory we prove exponential nonlinear conditional stability of the constant basic state in the slab [0, 1].     

An asymptotic approximation applied to a simple model

An asymptotic approximation scheme based on a sequence of solutions is applied to a simple model problem of a harmonic oscillator coupled to a scalar field. We evaluate explicitly the evolution of the field off the initial hypersurface and discuss an appropriate choice of the initial data for the field in order for a sequence of solutions to have a Newtonian limit. The study may help to understand the more complicated situation in general relativity. We also discuss an alternative sequence of solutions that may be useful in studying instabilities that occur for large values of the coupling constant.     

Sensitivity analysis applied to a dynamic railroad model

An analytical method of analyzing sensitivity is presented. It is shown that in a special case, when the dynamical problem is described by differential equations (of any order) with constant coefficients, first and second order semilogarithmic (semirelative) sensitivity functions can be determined analytically. The method is applied to the practical problem of railway track vibration, with the intention of using it for the identification of railway track model parameters in the future. The railway track model is an infinite beam resting on multi-parameter viscoelastic subsoil.     

A method for predicting psychological response to meaningless random noise based on fuzzy system model

By examining the memory effect and the fuzziness of human subjective judgment, the fuzzy relation between physical meaningless random noise stimuli and the psychological response is clarified quantitatively based on bivariate membership functions. Two variables describing the sound pressure level of the random noise stimulus and the temporal change in the level are employed as the fundamental variables for the bivariate membership functions. A method for predicting the psychological response to such stimuli is proposed, introducing the concept of fuzzy probability. The validity and usefulness of the proposed method is confirmed experimentally by applying the method to observed data. The theoretical calculations are in good agreement with the experimental results.     

A simplified holography based superresolution system

In this paper we are proposing a simple idea based on holography to achieve superresolution. The object is illuminated by three fibers which maintain the mutual coherence between the light waves. The object in-plane rotation along with fiber-based illumination is used to achieve superresolution. The object in a 4f optical system is illuminated by an on-axis fiber to make the central part of the object׳s spectrum to the pass through the limiting square-aperture placed at the Fourier plane and the corresponding hologram of the image is recorded at the image plane. The on-axis fiber is switched off and the two off axis fibers (one positioned on the vertical axis and the other positioned on diagonal) are switched on one by one for each orientation of the object position. Four orientations of object in-plane rotation are used differing in angle by 90°. This will allow the recording of eight holographic images in addition to the one recorded with on-axis fiber. The three fibers are at the vertices of a right angled isosceles triangle and are aligned toward the centre of the lens following the fiber plane to generate plane waves for object illumination. The nine holographic images are processed for construction of object׳s original spectrum, the inverse of which gives the super-resolved image of the original object. Mathematical modeling and simulations are reported.     

A fast pulsed power source applied to treatment of conductingliquids and air

Two pilot pulsed power sources were developed for fundamental investigations and industrial demonstrations of treatment of conducting liquids. The developed heavy-duty power sources have an output voltage of 100 kV (rise time 10 ns, pulse duration 150 ns, pulse repetition rate maximum 1000 pps). A pulse energy of 0.5-3 J/pulse and an average pulse power of 1.5 kW have been achieved with an efficiency of about 80%. In addition, adequate electromagnetic compatibility is achieved between the high-voltage pulse sources and the surrounding equipment. Various applications, such as the use of pulsed electric fields (PEFs) or pulsed corona discharges for inactivation of microorganisms in liquids or air, have been tested in the laboratory. For PEF treatment, homogeneous electric fields in the liquid of up to 70 kV/cm at a pulse repetition rate of 10-400 pps could be achieved. The inactivation is found to be 85 kJ/L per log reduction for Pseudomonas fluorescens and 500 kJ/L per log reduction for spores of Bacillus cereus. Corona directly applied to the liquid is found to be more efficient than PEF. With direct corona we achieve 25 kJ/L per log reduction for both Gram positive and Gram negative bacteria. For air disinfection using our corona pulse source, the measured efficiencies are excellent: 2 J/L per log reduction