Free and forced vibrations of a segmented bar by a Meshless Local Petrov-Galerkin (MLPG) formulation

R. C. Batra, Maurizio Porfiri, D. Spinello

Research output: Contribution to journalArticle

Abstract

We use the meshless local Bubnov-Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential boundary conditions are satisfied in all cases by the method of Lagrange multipliers. The related mixed semidiscrete formulations are shown to be stable, and optimal in the sense that the ellipticity and the inf-sup (Babuška-Brezzi) conditions are satisfied. Numerical results obtained for a bimaterial bar are compared with those from the analytical, and the finite element methods. The monotonic convergence of first two natural frequencies, first three mode shapes, and a static solution in the L 2, and H 1 norms is shown. The relative error in the numerical solution for a transient problem is also very small.

Original languageEnglish (US)
Pages (from-to)473-491
Number of pages19
JournalComputational Mechanics
Volume41
Issue number4
DOIs
StatePublished - Mar 2008

Fingerprint

Forced Vibration
Petrov-Galerkin
Lagrange multipliers
Meshless
Free Vibration
Bimaterial
Moving Least Squares
Square Functions
Mixed Formulation
Mode Shape
Formulation
Ellipticity
Relative Error
Natural Frequency
Galerkin
Monotonic
Basis Functions
Natural frequencies
Jump
Finite Element Method

Keywords

  • Convergence analysis
  • Inf-sup condition
  • Material discontinuities
  • MLPG method
  • Segmented bar

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality

Cite this

Free and forced vibrations of a segmented bar by a Meshless Local Petrov-Galerkin (MLPG) formulation. / Batra, R. C.; Porfiri, Maurizio; Spinello, D.

In: Computational Mechanics, Vol. 41, No. 4, 03.2008, p. 473-491.

Research output: Contribution to journalArticle

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