IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

The coupled wavenumbers of a fluid-filled flexible cylindrical shell vibrating in the axisymmetric mode are studied. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter e due to the coupling. Using the smallness of Poisson's ratio (v), a double-asymptotic expansion involving e and v2 is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (for large and small values of e). Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. The wavenumber solutions are continuously tracked as e varies from small to large values. A general trend observed is that a given wavenumber branch transits from a rigidwalled solution to a pressure-release solution with increasing e. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. Only the axisymmetric mode is considered. However, the method can be extended to the higher order modes. Copyright © 2007 Tech Science Press.

Department of Mechanical Engineering

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CMES - Computer Modeling in Engineering and Sciences

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The axisymmetric mode

The coupled wavenumbers in the axisymmetric mode of a fluid-filled cylindrical shell are studied. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic domain, with an added fluid-loading term (e) due to the coupling. Using the smallness of poisson's ratio, a double-asymptotic solution to this equation is found for large and small values of e. Analytical expressions are derived for the coupled wavenumbers. Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. The wavenumber solutions are continuously tracked as e varies from small to large values. A general trend observed is that a given wavenumber branch transits from a rigid-walled solution to a pressure-release solution with increasing e. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. Only the axisymmetric mode is considered, however the findings can be extended to the higher order modes.

14th International Congress on Sound and Vibration 2007, ICSV 2007

An asymptotic approach for the coupled dispersion characteristics of a fluid-filled cylindrical shell

A rectangular plate, point supported at four corners, is irradiated with a normally incident acoustic wave. The plate has an inclusion embedded in it supposedly at an unknown location. A structural-acoustic coupled formulation using FEM and BEM is developed and the inclusion is imaged (located) from the surface displacement response of the plate. The efficacy of the formulation is demonstrated by varying the location, size, geometry, and material properties. For variations in location, size, and geometry of the inclusion, the method is seen to give satisfactory results. The frequency of the incident wave is limited to 4775 Hz due to the available computing power. This limits the smallest size and clarity of the image for certain cases. For some cases where the material properties are widely different, and where one would expect the results to distinguish the two materials clearly, the image clarity is less than satisfactory. A list of factors is presented for possible future work.

International Journal of Acoustics and Vibrations

A coupled FEM-BEM formulation in structural acoustics for imaging a material inclusion

The dynamics of an Euler–Bernoulli beam, with multiple spring/mass attachments, is investigated in this paper. A novel analytical approach for determining the natural frequencies and mode shapes of the system is presented. The formulation is applicable for any parameter value of the attached mass or spring stiffness. The calculation is performed using a minimal binary set of admissible functions for each spring/mass connection, with extremal values (zero or infinity) of the parameter. For example, to study a beam with n intermediate spring/mass connections, only 2n admissible functions are required. These functions are used in a Rayleigh–Ritz-based energy formulation. The small number of functions used in the formulation leads to an efficient computational procedure. The results from the proposed formulation are compared with those from a finite element simulation, for different boundary conditions. The results obtained by the two methods are in excellent agreement for all boundary conditions as well as for different parameter ranges. Detailed design studies, on the effect of spring stiffness and lumped mass values, as well as their locations, on the natural frequencies and mode shapes, have been carried out. Design charts have also been generated to aid the designer of such structures.