Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.     

太赫兹波段电磁超材料吸波器折射率传感特性

太赫兹超材料吸波器作为一类重要的超材料功能器件,除了可以实现对入射太赫兹波的完美吸收外,还可以作为折射率传感器实现对周围环境信息变化的捕捉与监测.通常从优化表面金属谐振单元结构和改变介质层材料和形态两个方面出发,改善太赫兹超材料吸波器的传感特性.为深入研究中间介质层对太赫兹超材料吸波器传感特性的影响,本文基于金属开口谐...     

LARGEST LYAPUNOV EXPONENT AND ALMOST CERTAIN STABILITY ANALYSIS OF SLENDER BEAMS UNDER A LARGE LINEAR MOTION OF BASEMENT SUBJECT TO NARROWBAND PARAMETRIC EXCITATION

The first order approximate solutions of a set of non-liner differential equations, which is established by using Kane's method and governs the planar motion of beams under a large linear motion of basement, are systematically derived via the method of multiple scales. The non-linear dynamic behaviors of a simply supported beam subject to narrowband random parametric excitation, in which either the principal parametric resonance of its first mode or a combination parametric resonance of the additive type of its first two modes with or without 3:1 internal resonance between the first two modes is taken into consideration, are analyzed in detail. The largest Lyapunov exponent is numerically obtained to determine the almost certain stability or instability of the trivial response of the system and the validity of the stability is verified by direct numerical integration of the equation of motion of the system.     

Topological solitons in active optical cavities: Fundamental properties and possible applications

Fundamental properties of topological spatial solitons existing in active cavities with high (above 100) Fresnel numbers, laser and/or parametric amplification, and saturated absorber were numerically and experimentally studied. Writing and erasing of bi- and tristable laser solitons (fundamental solitons [1, 2] and vortex solitons [3]) using an external control light pulse were considered in various regions of the laser cross section. The existence of optical domain walls (separated phase domains which are in antiphase) in the form of expanding spiral waves and the localized domain soliton rotating about the Neel defect (in this connection, we called it the “Neel soliton”) in active cavities with mixed laser and parametric amplification was shown in a numerical experiment for the first time. We proposed potential possibilities of using topological solitons in optical data processing, storage, and transmission.     

Dynamic studies of railtrack sleepers in a track structure system

This paper discusses the dynamic response of a typical prestressed concrete railtrack sleeper due to wheel-track interaction dynamics, involving wheel and rail imperfections, under various parametric conditions. The interaction dynamics of the vehicle and track is first carried out in the time domain using MSC/NASTRAN. Using the resulting load time histories on an isolated sleeper, a detailed finite element model of the sleeper is used to analyze its dynamic behaviour. The dynamic amplification factors for deflection, ballast pressure and bending moments have been evaluated at the critical section (rail-seat and centre) for various exciting frequencies under different vehicle-track parametric conditions. The results provide a basis for improved and rational design of the sleeper.     

Wideband optical absorber based on plasmonic metamaterial cross structure

The optical absorber with Fano response is valuable for various applications such as solar cells or optical sensors. In this paper, we have modeled an optical plasmonic metamaterial absorber which contains a broken cross as an elementary cell along with four rectangular loads to improve the absorbance and achieve a Fano response within a wide bandwidth at 190–245 THz (25%). The bandwidth of the proposed structure is more than conventional metamaterial absorbers. The prototype absorber has a remarkable enhancement in the electric field in comparison with the simple cross model and the reflection value has reduced to ??47 dB. The parametric studies show how the gap capacitance controls the bandwidth, resonance frequency and the reflection value of the absorber, therefore we can consider this technique as a way to enhance the metamaterial absorber’s bandwidth. The proposed structure can be used as an optical refractive index sensor while the Fano line-shape provides a higher figure of merit (FOM) compared with many others. For this structure, the FOM has obtained as 10,660. The Finite Integration Technique with Perfect Boundary Approximation used for the simulation.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

Autoparametric vibration absorber effect to reduce the first symmetric mode vibration of a curved beam/panel

This paper presents the implementation of autoparametric phenomena to reduce the symmetrical vibration of a curved beam/panel under external harmonic excitation. The internal energy transfer of a first symmetric mode into first anti-symmetric mode in a curved panel is one example of autoparametric vibration absorber effect. This is similar to the vibration energy transfer from the resonance of a primary structure to the resonance of a secondary spring–mass (tuned mass damper). The nonlinear response of a curved beam is analyzed using an equation with two modes, and a shaker test. The effect of different configurations of the curve beam/panel, including damping ratios and excitation levels, on the energy transfer of the first symmetric mode to the first anti-symmetric mode was studied.The conventional tuned mass damper (TMD) can reduce the resonance response by energy transfer using damping dissipation, whereas an autoparametric vibration absorber (AVA) can reduce the resonance response by energy transfer using parametric interaction. The results indicate that there is a non-absorption region in which vibration is amplified. For the AVA, the non-absorption region can be minimized by tuning the resonance frequency of the first anti-symmetric mode to half of the first symmetric mode resonance frequency using additional mass. No additional damping material is required for achieving sufficient vibration reduction. The AVA can maintain reliable performance in hot and corrosive environments where damping material cannot perform effectively. This paper presents the first successful experimental results of an autoparametric vibration absorption mechanism in a curved beam.     

Multi-band metamaterial absorber topology for infrared frequency regime

In this paper, a new multiband metamaterial absorber design is proposed and the numerical characterization is carried out. The design is composed of three layers with differently sized quadruplets in which the interaction among them causes the multiband absorption response in the infrared frequency regime. In order to characterize the absorber and explain the multiband topology, some parametric studies with respect to the dimensions of the structure are carried out and the contributions of the quadruplets to the absorption spectrum are analyzed. According to the results, it is found that the proposed metamaterial absorber has five bands in the infrared frequency regime with the absorption levels of: 98.90%, 99.39%, 86.46%, 92.80% and 97.96%. Moreover, the polarization dependency of the structure is examined and it is found that the design operates well as a perfect absorber with polarization independency in the studied frequency range.     

DESIGN SENSITIVITY ANALYSIS AND OPTIMIZATION OF AN ENGINE MOUNT SYSTEM USING AN FRF-BASED SUBSTRUCTURING METHOD

The FRF-based substructuring method is one of the most powerful methods in analyzing the responses of complex built-up structures with high modal density. In this paper, a general procedure for the design sensitivity analysis of a vibro-acoustic system has been presented using the FRF-based substructuring formulation. For an acoustic response function, the proposed method gives a parametric design sensitivity expression in terms of the partial derivatives of the connection element properties and the transfer functions of the substructures. The derived noise sensitivity formula is combined with a non-linear programming module to obtain the optimal design for the engine mount system of a passenger car. The objective function is defined as the area of the interior noise graph integrated over a concerned r.p.m. range. The interior noise variations with respect to the dynamic characteristics of the engine mounts and bushings have been calculated using the proposed sensitivity formulation and transferred to a non-linear optimization software. To obtain the FRFs, a finite element analysis was used for the engine mount structures and experimental techniques were used for the trimmed body including the cabin cavity. The optimization based on the sensitivity analysis gives the ideal stiffness of the engine mount and bushings. The resultant interior noise in the passenger car shows that the proposed method is efficient and accurate.     

First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries

Abstract

We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of “known” functions.     

时间域电子自旋共振

时间域电子自旋共振(ESR)是研究顺磁弛豫机理和动力学过程不可缺少的方法,也是提高检测信号的灵敏度和分辨率的重要途径之一。然而,目前在ESR技术中较常用的还是频率域,而时间域ESR(包括付里叶变换法)却远远不如脉冲付里叶变换核磁共振(PFT-NMR)那样迅速的发展。本文对此进行了讨论,认为:如采用与PFT-NMR稍为不同的方法,并在微波技术、快速脉冲电路和电子计算技术等不断改善的基础上,时间域ESR势将成为今后发展的大方向。近年来,在时间域ESR技术方面,最引人重视的是:饱和恢复法和电子自旋回波(ESE)法。本文着重对这两种方法的基本原理、实验方法、应用场合及其优越性和局限性进行了评述。例如,用付里叶变换法(包括二维付里叶变换)把电子自旋回波调制的包络自时间域变换成频率域,从而获得高分辨率的频谱,则可分析出取向或无规取向样品的微弱超精细结构。又如,ENDOR(电子-核双共振)自旋回波与通常的ENDOR相比,前者具有较高的灵敏度以及可检测较低的ENDOR频率等独特之处。此外,文中对瞬态顺磁中间产物的时间分辨ESR和三重态分子在零场中的ESR也分别进行了简短的评介。最后,对时间域ESR发展的远景作了预计。     

Bloch domain walls in type II optical parametric oscillators

Evidence of Bloch domain walls in nonlinear optical systems is given. These walls are found in the transverse fields of optical parametric oscillators when the polarization degree of freedom, the cavity birefringence, and (or) dichroism are taken into account. These domain walls arise spontaneously and exhibit defects where Bloch walls of different chirality join together. Two dynamic regimes are found:In the first one the vector field approaches a final homogeneous state, and in the other the walls are continually generated and annihilated. This dynamic behavior is caused by the fact that walls of opposite chirality move spontaneously with opposite velocity.     

Use of modal energy transfer as a new damping device with controllable bandwidth

This paper presents a new design of nonlinear dynamic absorber (NDA) using the phenomenon of modal energy transfer between the symmetric mode and the anti-symmetric mode of a curved beam. It can reduce the resonance vibration of a primary structure with a controllable operational frequency range. The energy transfer is initiated by an autoparametric vibration and the excitation force required is lowest when the ratio of the resonance frequencies of the first symmetric mode (ω₁) and first anti-symmetric mode (ω₂) is close to 2.The resonance frequency of the first anti-symmetric mode (ω₂) can be altered to control the operational frequency range. The autoparametric vibration response can be used to create an energy-dissipative region with a controllable bandwidth. It is also possible to create a non-dissipative region in between two dissipative regions. This is useful for providing damping for a conventional dynamic absorber without adding high damping material. The damping is due to the dissipation of energy to anti-symmetric mode. Numerical calculations indicate that the resonance vibration of a primary structure can be successfully reduced using this approach. The results are verified with experimental data.     

PERFORMANCE AND DYNAMIC STABILITY OF GENERAL-PATH CENTRIFUGAL PENDULUM VIBRATION ABSORBERS

Centrifugal pendulum vibration absorbers are a type of tuned dynamic absorber used for the attenuation of torsional vibrations in rotating and reciprocating machines. They consist of masses that are constrained to move along specific paths relative to the rotational axis of the machine. Previous analytical studies have considered the performance of single absorber systems with general paths and of multi-absorber systems with a specific path type. In this paper, we investigate the performance and dynamic stability of systems comprised of multiple, identical centrifugal pendulum vibration absorbers riding on quite general paths. The study is carried out by considering a scaling of the system parameters, based on physically realistic ranges of dimensionless parameters, which permits application of the method of averaging. It is found that the performance of these systems is limited by two distinct types of instabilities. In one type, the system of absorbers lose their synchronous character, while in the other a classical non-linear jump affects all absorbers identically, leading to highly undesirable system behavior. These results are used to evaluate two common types of absorber paths, namely circles and cycloids, including intentional mistuning of the absorber frequencies. The results are used to make some recommendations about the selection of paths to achieve design goals in terms of absorber performance and operating range. The analytical predictions are confirmed by numerical simulations.     

FREQUENCY RESPONSE OF A MODERATELY THICK ANTISYMMETRIC CROSS-PLY CYLINDRICAL PANEL USING MIXED TYPE OF FOURIER SOLUTION FUNCTIONS

A hitherto unavailable analytical solution to the boundary-value problem of the free vibration response of shear-flexible antisymmetric cross-ply laminated cylindrical panels is presented. The laminated shell theory formulation is based on the first order shear deformation theory (FSDT) including rotatory and surface-parallel inertias. The governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns—three displacements, and two rotations. The assumed solution functions for the eigen/boundary-value problem are selected in terms of mixed-type double Fourier series. Numerical results presented for parametric effects, such as length-to-thickness ratio and radius-to-thickness ratio, should serve as a bench mark for future comparison. A four-node shear-flexible finite element is selected to compare the results with the present solution.     

Mean relaxation time approximation for dynamical correlation functions in stochastic systems near instabilities

We present a simple approximation for dynamical correlation functions in stochastic systems which reproduces the high as well as the low frequency behaviour of the exact correlation functions. The approximation is applied in its lowest order to diffusion in a quartic potential and to autocatalytic chemical reaction systems as described by the Schlögl models. The results are compared to those from the conventional Mori-Zwanzig projection operator approach which reproduces only the short-time relaxation of the systems considered. The new approximation describes correctly slow relaxation processes, e.g. barrier crossing in a quartic potential and the slowing down of dynamic processes in finite autocatalytic systems near first and second order transitions.     

A numerical study of double-leaf microperforated panel absorbers

Microperforated panel (MPP) absorbers are promising as a basis for the next-generation of sound absorbing materials. Typically, they are backed by an air-cavity in front of a rigid wall such as a ceiling or another interior surface of a room. Indeed, to be effective, MPP absorbers require the Helmholtz-type resonance formed with the backing cavity. Towards the creation of an efficient sound-absorbing structure with MPPs alone, the acoustical properties of a structure composed of two parallel MPPs with an air-cavity between them and no rigid backing is studied numerically. In this double-leaf MPP (DLMPP) structure, the rear leaf (i.e., the MPP remote from the incident sound) plays the role of the backing wall in the conventional setting and causes resonance-type absorption. Moreover, since a DLMPP can work efficiently as an absorber for sound incidence from both sides, it can be used efficiently as a space absorber, e.g., as a suspended absorber or as a sound absorbing panel. The sound absorption characteristics of the double-leaf MPP are analysed theoretically for a normally incident plane wave. The effects of various control parameters are discussed through a numerical parametric study. The absorption mechanisms and a possible design principle are discussed also. It is predicted that: (1) that a resonance absorption, similar to that in conventional type MPP absorbers, appears at medium-to-high frequencies and (2) that considerable “additional” absorption can be obtained at low frequencies. This low-frequency absorption is similar to that of a double-leaf permeable membrane and can be an advantage compared with the conventional type of MPP arrangement.     

Range compensation for backscattering measurements in the difference-frequency nearfield of a parametric sonar

Measurement of acoustic backscattering properties of targets requires removal of the range dependence of echoes. This process is called range compensation. For conventional sonars making measurements in the transducer farfield, the compensation removes effects of geometrical spreading and absorption. For parametric sonars consisting of a parametric acoustic transmitter and a conventional-sonar receiver, two additional range dependences require compensation when making measurements in the nonlinearly generated difference-frequency nearfield: an apparently increasing source level and a changing beamwidth. General expressions are derived for range compensation functions in the difference-frequency nearfield of parametric sonars. These are evaluated numerically for a parametric sonar whose difference-frequency band, effectively 1-6?kHz, is being used to observe Atlantic herring (Clupea harengus) in situ. Range compensation functions for this sonar are compared with corresponding functions for conventional sonars for the cases of single and multiple scatterers. Dependences of these range compensation functions on the parametric sonar transducer shape, size, acoustic power density, and hydrography are investigated. Parametric range compensation functions, when applied with calibration data, will enable difference-frequency echoes to be expressed in physical units of volume backscattering, and backscattering spectra, including fish-swimbladder-resonances, to be analyzed.     

Contrast-enhanced photothermal imaging for the evaluation of thermal transport parameters of liquids

In this article, we discuss the application of a baseline-suppressed, contrast-enhanced laser photothermal imager as a sensitive effusivity sensor for liquids, for the first time. We analyze the sources of errors associated with a conventional phase-comparison technique for evaluating the thermal transport parameters of liquids as a function of the pump power. Weak signal at lower powers and convection currents at higher powers are found to be the principal agencies deteriorating the sensitivity. Enhanced sensitivity has been achieved by using lower pump power and a signal baseline-suppressing common-mode-rejection-demodulation technique. The strength of thermoelastic vibration is small due to the low linear thermal expansion coefficient of the silicon nitride plate, which is the optical absorber. The approach has been extended for analyzing the effusivity modification of a water–methanol mixture as a function of methanol volume. The method is capable of detecting less than 1% change in effusivity for the mixture, which is 300–400% enhancement compared to the capability of conventional phase comparison. PACS 78.20.Nv; 81.70.Cv