Mode analysis of realistic optical waveguide structures and microstructured holey fibers by modal field evolution

In this article, we describe a useful technique for calculating modes of practical optical waveguides having two-dimensional arbitrary transverse refractive index profile. The method uses a finite difference platform for evaluating Helmholtz's equation in scalar and semivectorial forms through a field evolution algorithm. The method is straightforward, easy to handle and does not involve any complex analysis or matrix formulation. We tested the accuracy of our analysis approach by applying it on a large number of realistic waveguide problems having known results or results available in the literature. The formulation has facilitated us to study the modal properties, viz., field distribution, birefringence, dispersion and mode effective area, of a variety of practical two-dimensional structures namely, planar structure, coupler, semiconductor optical waveguides, optical fibers and arbitrary profile microstructured fibers which are uniquely important in photonics and guided-wave devices. The algorithm will therefore be very useful in designing and studying any arbitrary-structure waveguides, and to explore new geometry and properties.     

ITER聚变装置重力支撑有限元模态分析

运用有限元分析软件ANSYS建立了ITER装置重力支撑结构环向20°的三维有限元模型,采用子空间法对ITER重力支撑结构系统进行了有限元模态分析,求出了重力支撑系统的前10阶固有频率和振型,并对振型特点进行了分析。     

Vibration of complex structures: The modal constraint method

A method is described for establishing the natural frequencies of an arbitrary structure with arbitrary supports. The method is based on the modal constraint technique described in a previous paper [1]. As shown in the present paper Weinstein's theory for the intermediate problem can be regarded as equivalent to the Lagrangian multiplier method: i.e., both methods result in the same eigenvalue equations. Weinstein's theory deals with modifications of base differential operators whereas the Lagrangian multiplier method deals with modifications of base energy functionals. The modal constraint technique is an extension of Weinstein's theory, or in energy terms the generalized Fourier expansion of the Lagrangian multiplier. The merits of this method lie in the fact that the eigenvalues and eigenfunctions of structures are used as base structures. The coupling of these structures are taken into account by Lagrangian generalized forces of the constraint acting on the base structures. Some examples are given and the results compared with known solutions.     

Use of speckle interferometry and modal assurance criterion for identification of component modes

One of the problems encountered in performing modal analysis is the identification of different modes occurring at close natural frequencies. This paper proposes to face such a problem by an original application of the modal assurance criterion (MAC) that is typically used to verify the reliability of numerical structural models by evaluating the correspondence between numerical and experimental mode shapes. To properly apply the MAC, experimental mode shapes must be retrieved acquiring data at a high number of experimental points suitably distributed on the surface of the structure. Using usual modal analysis techniques based on pointwise transducers, difficulties can be encountered to retrieve mode shapes with the required spatial resolution. In order to overcome such difficulties, Speckle interferometry techniques can be used. This paperproposes a procedure based on the application of a highly reliable MAC evaluated by time average Speckle interferometry for recognising the modes contributing to the stationary vibration patterns. The results obtained from the modal analysis of a thin square plate have shown that the proposed procedure is capable of pointing out the component modes.     

A method for modal identification of lightly damped structures

In many cases modal tests are conducted on individual components of complex engineering structures where interest is confined to deriving an undamped model of the structure. A method is proposed for this task which demands a minimum of input data and which, in particular, does not require accurate measurements around resonance. The method is simple to program and its application to various practical structures is described.     

Measurement of modal damping by electronic speckle shearing interferometry

A time-average electronic speckle shearing interferometer (ESSI) has been used for modal damping measurement. This is effected by a new fringe enhancement technique. The damping factor of a cantilever measured by using this technique agrees well with the value measured by using the accelerometer method. The study shows that time-average speckle interferometry can be used as a convenient tool for modal damping measurement.     

A novel method for crack detection in beam-like structures by measurements of natural frequencies

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.     

Prediction of the sound reduction index: a modal approach

Different methods for the calculation of the sound reduction index using modal analysis are described. The calculations use two steps: a vibratory study to determine the transverse displacement of the plate and a study of radiation. Orthotropic plates are studied in particular and the resulting calculation algorithm has been programmed. Initial hypotheses are indicated, as well as results obtained for various plates or partitions. Modal analysis calculation results are then compared to results of the Cremer-Sewell approach.     

Response of periodic structures by modal analysis

A periodic structure is a structure consisting of identical substructures, coupled together in identical ways to form the complete system. The undamped response of such a system is derived by using a modal analysis technique. The procedure allows for arbitrary loads and takes full advantage of the periodic properties of the structure. The algorithm is based on a technique previously developed by the authors.     

Influence of refractive profile shape on the distribution of modal attenuation in planar structures with absorption cover

The paper illustrates the influence of refractive profile shape in a sensor planar structure on the distribution of modal attenuation. Depending on the shape of refractive profile, the dependence of modes attenuation on their order can be an increasing function, decreasing function or non-monotonic one. The problem is discussed basing on the example of parabolic, exponential, Gaussian and linear profiles of refractive index. For the linear refractive profile, we present the influence of the gradient of waveguide’s refractive index and the influence of the thickness and refractive index of sensitive layer on the distribution of modal attenuation. Theoretical predictions are experimentally verified for two different refractive profiles. Theoretical predictions are excellent agreement with experimental results.