Sergey Sorokin

On analysis and optimization in structural acoustics - Part I: Problem formulation and solution techniques

This paper is devoted to problems of structuralacoustic coupling with emphasis on analysis, design sensitivity analysis and optimization. The paper is divided into two parts, and it is the aim of Part I to (i) give a brief survey of recent developments in sensitivity analysis and sound emission and NVH (Noise, Vibration and Harshness) design of acoustically loaded structures, and (ii) discuss alternative objective functions and optimization formulations for structural acoustics. The aims of Part II are to (i) present consistent numerical techniques commonly used for treatment of coupled structural and acoustic dynamics, (ii) use the structural optimization tool ODESSY for solution of several coupled problems, and (iii) compare the numerical efficiency of alternative techniques and the relevance of selected objective functions.

Green's matrix and the boundary integral equation method for the analysis of vibration and energy flow in cylindrical shells with and without internal fluid loading

Abstract This paper presents several aspects of the dynamics of a cylindrical shell with and without heavy internal fluid loading, which have not been studied before in detail. Firstly, a consistent formulation of boundary integral equations for a shell of finite length is derived based on the energy conservation principle and the reciprocity theorem. This derivation naturally leads to identification of principal components of the energy flux through an arbitrary cross-section of a shell and to formulation of Greens matrix for an infinitely long shell at each individual circumferential wave number. Secondly, an inspection into the energy re-distribution between several transmission paths in a near field (in a boundary layer at the vicinity of a loaded cross-section) is performed, which sheds light on the role of evanescent waves in motions of a driven shell. Thirdly, the influence of excitation conditions on steady fluctuations of the overall energy flow between transmission paths in a far field is explored for the case, when several propagating waves exist in a shell both with and without internal fluid loading. Besides, a systematic verification of the solution offered by the boundary equations method is given through comparison of eigenfrequencies with those computed in finite element modelling for various boundary conditions. Analysis of dispersion curves and input mobilities is also presented.

On analysis and optimization in structural acoustics — Part II: Exemplifications for axisymmetric structures

This two-part paper is devoted to problems of structural-acoustic coupling with emphasis on analysis, design sensitivity analysis and optimization. Part II of the paper aims to (i) present consistent numerical techniques commonly used for treatment of coupled structural and acoustic dynamics, (ii) use the structural optimization tool ODESSY for solution of several coupled problems, and (iii) compare the numerical efficiency of alternative techniques and the relevance of selected objective functions.

The finite-product method in the theory of waves and stability

This paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental. The method involves replacing each transcendental term in the dispersion relation by a finite-product polynomial. The finite products chosen must be consistent with the low-frequency, low-wavenumber limit; but the method is nevertheless accurate up to high frequencies and high wavenumbers. Full details of the method are presented for a non-trivial example, that of anti-symmetric elastic waves in a layer; the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers. It is proved that the method is accurate because certain gamma-function expressions, which occur as ratios of transcendental terms to finite products, largely cancel out, nullifying Runge’s phenomenon. The polynomial approximations, which are unrelated to Taylor series, introduce no spurious branches into the dispersion relation, and are ideal for numerical computation. The method is potentially useful for a very wide range of problems in wave theory and stability theory.

Isogeometric analysis of free vibration of simple shaped elastic samples

The paper is devoted to numerical solution of free vibration problems for elastic bodies of canonical shapes by means of a spline based finite element method (FEM), called Isogeometric Analysis (IGA). It has an advantage that the geometry is described exactly and the approximation of unknown quantities is smooth due to higher-order continuous shape functions. IGA exhibits very convenient convergence rates and small frequency errors for higher frequency spectrum. In this paper, the IGA strategy is used in computation of eigen-frequencies of a block and cylinder as benchmark tests. Results are compared with the standard FEM, the Rayleigh-Ritz method, and available experimental data. The main attention is paid to the comparison of convergence rate, accuracy, and time-consumption of IGA against FEM and also to show a spline order and parameterization effects. In addition, the potential of IGA in Resonant Ultrasound Spectroscopy measurements of elastic properties of general anisotropy solids is discussed.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Greens matrix, of the Somiglianas identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Greens matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis.

The active control of vibrations of composite beams by parametric stiffness modulation

Abstract The paper addresses an active control of the resonant vibrations of composite beams performed by a parametric stiffness modulation. A sandwich beam composition with the continuous core is considered. The stiffness modulation is introduced by some fairly small changes in an orientation of elements of the microstructure of a core ply. The controlled vibrations are those of the dominantly flexural type excited by a transverse force acting at a low resonant frequency, whereas the stiffness modulation is performed at a comparatively high frequency identified by the resonance of a mode of the dominantly shear type. This difference in time scales of the controlled vibrations and the input signal facilitates a use of the method of direct partition of motion that predicts an existence of the modal interaction between the low-frequency and the high-frequency motions due to so-called vibrational forces. It is shown that such a parametric control can provide a significant favourable shift of the first eigenfrequency of a controlled beam (the one subjected to the stiffness modulation) from its nominal value for an uncontrolled beam. Heavy fluid loading conditions are accounted for as well as material losses in a structure. Then instead of analysis of eigenfrequencies, a problem of forced vibrations is posed and the forced frequency–amplitude response is analysed. It is demonstrated that although heavy fluid loading reduces resonant frequencies of forced vibrations, the suggested mechanism of control remains valid in these cases.

A SIMPLE EXAMPLE OF A TRAPPED MODE IN AN UNBOUNDED WAVEGUIDE

This letter presents concerns on analysis of a trapped mode in a simple one‐dimensional waveguide. The chosen system is an unbounded elastic string lying on a Winkler elastic foundation. It is shown that in such a system there is the single eigenfrequency corresponding to a trapped mode.

Linear dynamics of elastic helical springs: asymptotic analysis of wave propagation

Helical springs serve as vibration isolators in virtually any suspension system. A variety of theories to describe the dynamic behaviour of these structural elements, which involves interaction of flexural, torsion and longitudinal waves, can be found in the literature. Alongside this, various approximate methods are employed to determine the eigenfrequencies of vibrations of springs. In this paper, the validity ranges of alternative theories are assessed by comparison of the location of the dispersion curves. This paper also contains a rigorous asymptotic analysis of the exact dispersion equation with two small parameters being employed. It allows for the identification of significant regimes of linear wave motion in a helical spring. In each of these regimes, simple formulae for wavenumbers are obtained by the dominant balance method and their validity ranges are checked against direct numerical solution. Mode shapes associated with each wavenumber are also analysed.

A nonlinear model of the dynamics of a large elastic plate with heavy fluid loading

In this paper, we derive weakly nonlinear equations for the dynamics of a thin elastic plate of large extent under conditions of heavy fluid loading. Two situations are then considered. First, we consider the case in which transverse motion of the plate generates a weaker in-plane motion, which is in turn coupled back to the evolution of the transverse motion. This results in the familiar nonlinear Schrödinger equation for the amplitude of a transverse plane wave, and we show that solitary-wave solutions are possible over the range of (non-dimensional) frequencies ω>ωc, which depends on the material properties. Dimensional values of ωc are physically realizable for a typical composite material underwater. Second, we consider the case in which the amplitudes of the transverse and in-plane motion are of the same order of magnitude, possible at a single resonant frequency, which leads to an evolution equation of rather novel type. We find a range of travelling-wave solutions, including cases in which incident in-plane waves can generate localized regions of transverse displacement.