Three-dimensional structural vibration analysis by the Dual Reciprocity BEM

Agnantiaris, J. P.; Polyzos, D.; Beskos, D.E.

doi:10.1007/s004660050314

Cited by 50 publications

(34 citation statements)

References 17 publications

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“…Various types of BEM are available in literature such as Domain-BEM (D-BEM) [8], Time Domain-BEM (TD-BEM), Dual Reciprocity-BEM (DR-BEM) [2,17], Frequency Domain-BEM (FD-BEM) [10], Convolution Quadrature-BEM (CQ-BEM) [1,24]. D-BEM and DR-BEM both discretize time and space separately, hence are not of interest here.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

Venkatesh

Thorin

Legrand

2017

Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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Finite elements in space with time-stepping numerical schemes, even though versatile, face theoretical and numerical difficulties when dealing with unilateral contact conditions. In most cases, an impact law has to be introduced to ensure the uniqueness of the solution: total energy is either not preserved or spurious high-frequency oscillations arise. In this work, the Time Domain Boundary Element Method (TD-BEM) is shown to overcome these issues on a one-dimensional system undergoing a unilateral Signorini contact condition. Unilateral contact is implemented by switching between free boundary conditions (open gap) and fixed boundary conditions (closed gap). The solution method does not numerically dissipate energy unlike the Finite Element Method and properly captures wave fronts, allowing for the search of periodic solutions. Indeed, TD-BEM relies on fundamental solutions which are travelling Heaviside functions in the considered one-dimensional setting. The proposed formulation is capable of capturing main, subharmonic as well as internal resonance backbone curves useful to the vibration analyst. For the system of interest, the nonlinear modeshapes are piecewise-linear unseparated functions of space and time, as opposed to the linear modeshapes that are separated half sine waves in space and full sine waves in time.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

Venkatesh

Thorin

Legrand

2017

Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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“…As mentioned before, the Houbolt method has been widely used with both D-BEM and DR-BEM formulations, see Carrer and Mansur [6] and [1].…”

Section: Time-marching Schemementioning

confidence: 99%

“…The acceleration is approximated by the Houbolt method [13], which has been extensively used, during the last years, not only in D-BEM formulations but also in the so-called DR-BEM formulations. In the DR formulations, DR meaning dual reciprocity, the domain integral is transformed into boundary integrals by suitable interpolation functions, see [1,14,15,25,26]. The Newmark method can be cited as well.…”

Section: Introductionmentioning

confidence: 99%

Boundary element method formulations for the solution of the scalar wave equation in one-dimensional problems

Carrer

Costa

2014

J Braz. Soc. Mech. Sci. Eng.

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“…On the other hand, by means of suitable interpolation functions the domain integral can be transformed into boundary integrals, generating the so-called DR-BEM formulations (DR meaning double reciprocity), e.g. Kontoni and Beskos [12], Partridge et al [13], Agnantiaris et al [14,15]. Although…”

Section: Introductionmentioning

confidence: 99%

Scalar wave equation by the boundary element method: a D-BEM approach with non-homogeneous initial conditions

2008

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This work is concerned with the development of a D-BEM approach to the solution of 2D scalar wave propagation problems. The time-marching process can be accomplished with the use of the Houbolt method, as usual, or with the use of the Newmark method. Special attention was devoted to the development of a procedure that allows for the computation of the initial conditions contributions. In order to verify the applicability of the Newmark method and also the correctness of the expressions concerned with the computation of the initial conditions contributions, four examples are presented and the D-BEM results are compared with the corresponding analytical solutions.

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Three-dimensional structural vibration analysis by the Dual Reciprocity BEM

Cited by 50 publications

References 17 publications

Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

Boundary element method formulations for the solution of the scalar wave equation in one-dimensional problems

Scalar wave equation by the boundary element method: a D-BEM approach with non-homogeneous initial conditions

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