Nonlinear resonance oscillations of bodies with a liquid

Ганиев, Р. Ф.

doi:10.1007/bf00883177

Cited by 19 publications

(4 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The kinematic conditions are the requirement of continuity of liquid in the domain τ Αφ = 0, ΔΩ = 0 in τ, (1) the non flux condition on the tank -liquid contact boundary Σ with unit normal η dip TP = ε · η, on on dn = r χ η (2) and the conditions of no flux through the liquid free surface Ξξ…”

Section: Mathematical Model Of the Systemmentioning

confidence: 99%

“…The system of motion equations in parameters a,i, ai is completed by generalized dissipative forces following results of the work [2,9]. The variables ε, supposed to have a finite magnitude and variables a* and a t are held including the values of the third order smallness.…”

mentioning

confidence: 99%

“…There are also other algorithms for obtaining finite dimensional models for tanks with liquid, for example the Narimanov model [2,12] and models of J. There are also other algorithms for obtaining finite dimensional models for tanks with liquid, for example the Narimanov model [2,12] and models of J.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Properties for Dynamic Behavior of Liquid with a Free Surface in a Rigid Moving Tank

Limarchenko¹

2000

International Journal of Nonlinear Sciences and Numerical Simulation

View full text Add to dashboard Cite

Mechanical and mathematical aspects of nonlinear properties for dynamical behavior of liquid with a free surface in tanks are described. Basic principles for dynamical simulation of the mentioned systems in the range of manifestation of nonlinear properties are proposed. Criteria for construction of lowdimensional models are developed. Some properties of such models for certain examples demonstrate the potential of the suggested approach.

show abstract

Section: Mathematical Model Of the Systemmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Properties for Dynamic Behavior of Liquid with a Free Surface in a Rigid Moving Tank

Limarchenko¹

2000

International Journal of Nonlinear Sciences and Numerical Simulation

View full text Add to dashboard Cite

show abstract

“…The constraints taken, which are related to shortening the system of differential equations and the degree of taking account of the nonlinear properties of the mechanical system, are based on the results of theoretical [2,8] and experimental research [3,7], as well as on the fact that the results obtained on the basis of the truncated system with the additional constraints on the nature of the appearance of the nonlinearities taken into account, are in good agreement with the data of experiments and theoretical researches without relying on such hypotheses. Let us note that the selection of the degree of system truncation and the nature of taking account of its nonlinear properties should be determined from an analysis of the physical crux of the problem for every specific case.…”

mentioning

confidence: 99%

Application of a variational method to the solution of nonlinear problems of the dynamics of combined motions of a tank with fluid

Limarchenko¹

1983

Soviet Applied Mechanics

View full text Add to dashboard Cite

Investigation of dynamics problems of a fluid with a free surface is fraught with significant difficulties caused both by the need to satisfy the boundary condition on a previously unknown boundary, and the substantial nonlinearity of the problem which appears principally in the boundary conditions and the fluid interaction with the elastic or solid walls of the tank.Special complexities are observed in quantitative investigations of problems of this kind, especially problems of the dynamics of joint motion of bodies with a fluid. Despite the urgency of such problems, as is noted in [7,9], say, there is just an insignificant number of papers on this problem.In particular, it is shown [i, 4-6, i0] that the application of variational and numerical methods permits reduction of the investigation of such problems to the investigation of a system of ordinary differential equations and to problems of linear algebra, for whose solution powerful computational methods have been developed that predetermined the success of applying numerical and variational methods to the investigation of dynamics problems of a fluid with a free surface.i. A variational method of investigating nonlinear dynamics problems of the combined motion of a tank and a fluid partially filling it, based on the application of the Hamilton--Ostrogradskii principle to the system of tank-fluid with free surface, is elucidated in [4,5]. The direct method of L. V. Kantorovich, generalized to the particular case of nonlinear problems of mathematical physics with a free boundary, is used for the solution of the variational problem.Its distinguishing feature is the construction of a series expansion of the velocity potential ~ and the perturbations of the liquid free surface ~ that satisfy the kinematic boundary conditions on the tank walls identically (because of the selection of the coordinate functions), and on the free surface to the accuracy of fourth-order quantities in ~ (this is achieved by substituting the expansions for ~ and ~ in the kinematic boundary condition on the free surface with the subsequent determination of the interrelation of the coefficients of their series expansions).Let us note that the method to be applied to determine the dependences of the coefficients of the series expansions of ~ and ~ is analogous to the known method [ii] ; however, it is constructed on the basis of the kinematic boundary condition on the liquid free surface written in differential form, is used for the case of a moving tank, and eliminates the need for approximate inversion of the matrix with variable elements, Realization of the proposed modification of the direct method results in a nonlinear system of ordinary differential equations that allows for a simple numerical solution for arbitrary methods of dynamical excitation.In contrast to the method of Narimanov [8,9], the need to solve sequences of linear boundary-value problems of mathematical physics is eliminated here.The system equations of motion obtained on the basis of the proposed method have the fol...

show abstract

Liquid Sloshing Dynamics

Ibrahim

2005

658

235

View full text Add to dashboard Cite

Nonlinear resonance oscillations of bodies with a liquid

Cited by 19 publications

References 1 publication

Nonlinear Properties for Dynamic Behavior of Liquid with a Free Surface in a Rigid Moving Tank

Nonlinear Properties for Dynamic Behavior of Liquid with a Free Surface in a Rigid Moving Tank

Application of a variational method to the solution of nonlinear problems of the dynamics of combined motions of a tank with fluid

Liquid Sloshing Dynamics

Contact Info

Product

Resources

About