Asymptotic and variational methods in non-linear problems of the interaction of surface waves with acoustic fields

Lukovskii, I. A.; Timokha, Alexander

doi:10.1016/s0021-8928(01)00052-1

Cited by 19 publications

(5 citation statements)

References 7 publications

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“…The slow time variable is τ = 3/2 t and the lowest-order terms are governed by (22). In this section, we separate slow and fast time variables in the variational formulations from section (4) to derive the quasi-potential energy of the drop vibroequilibrium governed by (23). …”

Section: Quasipotential Energy Of the Drop Vibroequilibriummentioning

confidence: 99%

“…Appearance of the acoustic radiation pressure in this empirical model can be interpreted as the so-called vibrational force well-known from the vibrational mechanics [18]. The papers [19,20,21,22,23] considered the vibrational hydrodynamic problems of compressible liquids partly filling a container as an object of the applied functional analysis. They introduced the so-called vibroequilibria, the time-averaged liquid shapes occurring due to high-frequency vibrational loads.…”

Section: Introductionmentioning

confidence: 99%

“…The present paper follows the applied mathematical studies in [19,20,23] to construct a new, mathematically-justified model which describes slow-time motions of an acoustically levitating drop. The analysis starts with the "ulage gasliquid drop" interface problem formulated within the framework of ideal compressible fluids with irrotational flows.…”

Section: Introductionmentioning

confidence: 99%

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Differential and Variational Formalism for an Acoustically Levitating Drop

2016

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Starting with a most general problem on interface waves between two ideal compressible fluids, treated here as an ullage gas and a liquid, respectively, and separating fast and slow time scales, differential and variational formalism for an acoustically levitating drop and its time-averaged shape (the drop vibroequilibrium) is developed. The drop vibroequilibria can differ from spherical shape; stable vibroequilibria are associated with local minima of the quasipotential energy whose analytical form is also derived in the present paper.

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Section: Quasipotential Energy Of the Drop Vibroequilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Differential and Variational Formalism for an Acoustically Levitating Drop

2016

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“…The nonlinear FEM steps utilised to compute the large amplitude free vibration frequency responses of the doubly curved laminated composite shell panels using the HSDT kinematics model by Singh and Panda 22 and Mahapatra 23 , et al including the effect of the environmental effect. Also, a large volume of the research articles on the dynamic behaviour of the laminated composite plate and shell structure reported using variational asymptotic method (VAM) [24][25][26][27][28][29][30][31] . Studies indicate that the VAM approach is capable of analysing the geometrical nonlinearity including geometries effect with adequate accuracy.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Free Vibration Analysis of Laminated Carbon/Epoxy Curved Panels

Hirwani¹,

Mahapatra²,

Panda³

et al. 2017

Def. Sc. Jl.

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Nonlinear frequency responses of the laminated carbon/epoxy composite curved shell panels have been investigated numerically and validated with in-house experimentation. The nonlinear responses have been computed numerically via customised computer code developed in MATLAB environment with the help of current mathematical model in conjunction with the direct iterative method. The mathematical model of the layered composite structure derived using various shear deformable kinematic models (two higher-order theories) in association with GreenLagrange nonlinear strains. The current model includes all the nonlinear higher-order strain terms in the formulation to achieve generality. Further, the modal test has been conducted experimentally to evaluate the desired frequency values and are extracted via the transformed signals using fast Fourier transform technique. In addition, the results are computed using the simulation model developed in commercial finite element package (ANSYS) via batch input technique. Finally, numerical examples are solved for different geometrical configurations and discussed the effects of other design parameters (thickness ratio, curvature ratio and constraint condition) on the fundamental linear and nonlinear frequency responses in details.

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“…), where the fluid has a disconnected free surface (see [15,16]). In the solution of these problems, the crucial point is the development of methods of their study, in particular, of variational and functional-operator methods (see, e.g., [6][7][8][11][12][13]). …”

Section: Introductionmentioning

confidence: 99%

On the spectral criterion of stability in the problem of small motions of an ideal capillary fluid with disconnected free surface

Kopachevsky

Sitshayeva

2015

J Math Sci

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This paper deals with the problem of static stability of the equilibrium state and the problem of stability of small (linear) movements of an ideal incompressible fluid in the open vessel with holes in the bottom. The gravitational forces and the surface tension are taken into account. We consider a case where the equilibrium surface of the fluid is curvilinear and corresponds to an arbitrary contact angle. Using the operator approach, we obtain the sufficient conditions for static and dynamic stabilities and propose a method of determination of the equilibrium surface.

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Asymptotic and variational methods in non-linear problems of the interaction of surface waves with acoustic fields

Cited by 19 publications

References 7 publications

Differential and Variational Formalism for an Acoustically Levitating Drop

Differential and Variational Formalism for an Acoustically Levitating Drop

Nonlinear Free Vibration Analysis of Laminated Carbon/Epoxy Curved Panels

On the spectral criterion of stability in the problem of small motions of an ideal capillary fluid with disconnected free surface

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