Transient response of a string on an elastic base

The transient response of a stretched string resting on an elastic base and subjected to impulsive end loading is treated herein. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variable and its derivatives. These discontinuities are determined from a recurrence relation which is in turn generated by using a time-harmonic asymptotic series solution to the equation of motion. Numerical examples are treated where the responses of the string to delta and step function boundary loads are obtained. The results confirm the influence of the base modulus on the transient displacement, velocity and slope distributions in the string. The distortion of the transients and the discontinuities in the velocity and slope are evident from the results presented. The transient response of the string due to other boundary conditions can be obtained by using the present results.     

Transient beam response in synchrotrons with a digital transverse feedback system

The transient beam response to an external impulse force in synchrotrons with a digital transverse feedback system is studied. The experimental data on damping coherent transverse oscillations of bunch excited by a discrete-time unit impulse in the Large Hadron Collider (LHC) are analyzed. Good agreement between the measured and theoretically predicted decrements has been obtained. A method of feedback fine tuning based on measurements of the bunch response to a harmonic excitation impulse is discussed.     

Dynamic analysis of a beam with an intermediate elastic support

A survey of the literature shows that the title problem has not been studied to a great extent. In the present paper an approximate solution is obtained in the case of a beam with ends elastically restrained against rotation and an intermediate elastic support. When dealing with the forced vibrations situation a sinusoidally varying excitation is assumed.     

Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries

An approach to express an incident shaped beam with respect to an arbitrarily oriented spheroidal particle having layers with non-confocal boundaries is presented. To overcome the difficulty of non-confocal boundary conditions connected with different spheroidal coordinate systems, a theoretical procedure is developed to deal with the non-confocal boundary conditions by virtue of a transformation for vector wave functions. The unknown coefficients of scattered and internal electromagnetic fields are determined by solving a system of linear equations derived from the boundary conditions and relations between the spheroidal vector wave functions and spherical ones. Numerical results of the normalized scattering cross section for a two-layered non-confocal prolate spheroid are evaluated. PACS 42.25.Fx; 42.25.Bs     

Transient sound radiated by spheres undergoing an elastic collision

An experimental and theoretical analysis of the sound field radiated by the collision of two elastic spheres is presented. The sound pressure measured at any point in space is the proper sum in time of the sound radiated independently by each sphere. It is shown that the combination of classical Hertzian impact theory and acoustical theory is sufficient to define the pressure time waveforms as measured in the experiments.     

Transition from normal to local modes in an elastic beam supported by nonlinear springs

The transient mode localization phenomenon is considered in a mechanical model combining a simply supported beam and transverse nonlinear springs with hardening characteristics. Two different approaches to the model reduction, such as normal and local mode representations for the beam's center line, are discussed. It is concluded that the local mode discretization brings advantages for the transient localization analysis. Based on the specific coordinate transformations and the idea of averaging, explicit equations describing the energy exchange between the local modes and the corresponding localization conditions are obtained. It was shown that when the energy is slowly pumped into the system then, at some point, the energy equipartition around the system suddenly breaks and one of the local modes becomes the dominant energy receiver. The phenomenon is interpreted in terms of the related phase-plane diagram which shows qualitative changes near the image of the out-of-phase mode as the total energy of the system has reached its critical level. A simple closed form expression is obtained for the corresponding critical time estimate.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.     

非近轴近似多高斯声束模型的相控阵换能器声场计算

针对近轴近似的多高斯声束模型无法准确计算离轴区域声场的问题,我们提出了一个矩形源的非近轴近似多高斯声束模型,用于计算偏转聚焦时线性相控阵换能器辐射的声场。利用该方法计算了由矩形阵元组成的相控线阵的辐射声场,并与瑞利积分、近轴近似方法及夫琅和费近似方法进行了分析和对比,计算结果表明该方法克服了常规近轴近似条件的限制,可以准确、快速地计算较大偏转范围内的换能器辐射声场,在计算相控阵换能器偏转聚焦声场中具有独特的优势。     

Transient response of an open resonator in the time domain

In the present paper a time response of a quasi-optical open resonator when exciting it by a pulse signal with a radiofrequency filling has been investigated using an inverse Fourier transformation. The radiofrequency filling corresponds to millimeter wavelengths region. Fourier image of the time response of the resonator is calculated from a product of two frequency’s functions. One of these functions is the Fourier image of a pulse signal at the resonator input, and the second is a calculated or measured amplitude — phase characteristic of the resonator. When calculating the amplitude- phase characteristic of the resonator (a complex transfer coefficient) a plane — layered model of the resonator was used. Experimental investigation has been conducted in millimeter wavelengths with Fabry-Perot type open resonator. Amplitude- phase characteristic of the resonator were measured in “on passage“ regime in wide frequency band. It was shown that presence of weakly absorbing layer in the resonator leads to changing of the time response of the resonator. The obtained results can be used in the dielectric measurements, defectoscopy of stratiform materials, relaxometry, non-destructive control of materials and structures, etc.     

Transient response of an electrically addressable nonlinear bistable optical device

A study has been made of the transient response of a Fabry-Perot cavity exhibiting bistability of the optical output with applied voltage. In this system the electro-optic and optical nonlinear effects act cooperatively to produce the switch, and the transient response was shown to have characteristics associated with both mechanisms. The switch was found to be composed of three distinct regions, a purely electro-optic part, followed by a slow change in the cavity intensity brought about by the electro-optic and nonlinear effects, with a final fast switch up to the high transmission state. The relative magnitude of the time duration of regions 1 and 2 was found to be dependent upon the applied voltage, initial dc biasing and optical input power. In particular, critical slowing down was evident in region 2 of the switch for values of applied voltage close to the critical value. In this case region 2 was the dominant part of the switching time. Overdriving the system resulted in the time duration of region 2 decreasing and region 1 becoming more dominant. Qualitative agreement was achieved between the experimental results and theoretical predictions of the transient response of a cavity undergoing a slow change in some external parameter.     

Characterization of elastic parameters of acoustical porous materials from beam bending vibrations

Dynamic visco-elastic characterization of porous material parameters shows a revival of interest since a few years. In this article, a methodology for the assessment of the visco-elastic parameters of soft, highly damped porous materials is presented. This method uses a frequency response function of a free-free bending beam. The global method is based on an inversion procedure. It consists of fitting the experimental data to the GLM computation model. In the experimental part of this work, it is explained how to take the attachment system and sensor mass into account and how to measure it. The assessment of the visco-elastic parameters needs a discrete laminae analytic model. The GLM model is described and used for a sensitivity study in relation to the visco-elastic parameters. This study gives indications for the beam dimensions design. The results, bending modulus and loss factor in the beam's main direction for various frequencies, obtained for two polymeric foams are shown and compared to results obtained with other techniques. The originality can be found in the experimental developments but also on technical developments of parameters assessment.     

Resonance elastic scattering of light by a quantum well with statistically uneven boundaries

A theory is formulated for the elastic scattering of light through quasi-two-dimensional exciton states in a quantum well with randomly uneven walls. The nonlocal exciton susceptibility is expressed in terms of random functions describing the shape of the quantum well boundaries up to and including linear terms in the unevenness height. The resonance elastic scattering cross sections in the presence of arbitrary statistical unevenness are calculated in the Born approximation for all channels in which the initial and final states are represented by an electromagnetic TM or TE mode. The spectral and angular dependences of the scattering probability are calculated with the unevenness characterized by Gaussian correlation functions. It follows from numerical estimates that elastic scattering in quantum wells should be observed for unevenness having an rms height of the order of the thickness of an atomic monolayer. Fiz. Tverd. Tela (St. Petersburg) 41, 330–336 (February 1999)     

Transient response of an acoustic medium by an excited submerged spherical shell.

An exact closed-form solution is obtained for the transient response of an acoustic fluid due to an excited submerged spherical shell. Step axisymmetric stress acting on the inner surface of the shell is expanded into modal Fourier components in which for each modal stress systematic exact expressions for modal radial displacement of the shell, fluid pressure, fluid particle velocity and displacement are presented. The superiority of the formulations herein is its applicability to any time and spatial distance in the fluid as well as on the shell. The formulation also does not require additional numerical computations associated with other methods.     

Transient response in flexure to general uni-directional loads of variable cross-section beam with concentrated tip inertias immersed in a fluid

This paper presents a method for solving problems of transient response in flexure due to general unidirectional dynamic loads of beams of variable cross section with tip inertias. An elastodynamic theory which includes effects of continuous mass and rigidity of the beam has been applied. In the analysis the general dynamic load is expanded into a Fourier series and the beam is divided into many small uniform thickness segments. The equation of motion of each segment is mapped onto the complex domain by use of the Laplace transform method. The solutions of each set of adjoining segments are related to each other at the boundaries by the use of the transfer matrix method. The displacement, the bending slope, the bending moment and the shearing force at each boundary and at arbitrary time are obtained from the Laplace transform inversion integral by using the residue theorem. The theoretical results given in this paper are applicable to problems of dynamic response due to arbitrary loads varying with time of beams of arbitrary shape with concentrated tip inertias. As applications of the present theoretical results, numerical calculations have been carried out for two cases: a uniform beam with a tip inertia and a non-uniform beam (a truncated cone) with a tip inertia. Both are immersed in a fluid and subjected to large waves such as cnoidal waves.