Large free vibration of thin plates: Hierarchic finite Element Method and asymptotic linearization

European Journal of Mechanics, A/Solids

Volumn 28, Issue 1, 2009, Pages 155-165

  Taazount, M ^a   Zinai, A ^a   Bouazzouni, A ^b  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b UNIVERSITÉ MOULOUD MAMMERI   (Algeria)

Author keywords

Asymptotic linearization; Equivalent linear dynamical system; Equivalent linearization; HFEM; Nonlinear dynamics

Indexed keywords

ASYMPTOTIC ANALYSIS; BOUNDARY VALUE PROBLEMS; DAMPING; DEGREES OF FREEDOM (MECHANICS); DYNAMIC RESPONSE; DYNAMICAL SYSTEMS; DYNAMICS; EQUATIONS OF MOTION; EQUIVALENCE CLASSES; FINITE ELEMENT METHOD; FUNCTION EVALUATION; IMAGE SEGMENTATION; LATTICE VIBRATIONS; LINEAR CONTROL SYSTEMS; LINEARIZATION; PLATES (STRUCTURAL COMPONENTS); STIFFNESS MATRIX; UNCERTAIN SYSTEMS;

ASYMPTOTIC LINEARIZATION; EQUIVALENT LINEAR DYNAMICAL SYSTEM; EQUIVALENT LINEARIZATION; HFEM; NONLINEAR DYNAMICS;

SCHRODINGER EQUATION;

EID: 56949093184     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2008.04.002     Document Type: Article

References (15)

1. Arquier R., Bellizzi S., Bouc R., and Cochelin B. Two methods for the computation of non linear modes of vibrating systems at large amplitudes. Computers and Structures 84 (2006) 1565-1576
2. Azrar L., Benamar R., and Potier-Ferry M. An asymptotic-numerical method for large-amplitude free vibrations of thin elastic plates. Journal of Sound and Vibration 220 4 (1999) 695-727
3. Bardell N.S. Free vibration analysis of flat plate using the hierarchical finite element method. Journal of Sound and Vibration 151 2 (1991) 263-289
4. Bathe K.-J., and Wilson E.L. Numerical Methods in Finite Element Analysis (1976), Prentice-Hall Inc., Englewood Cliffs, NJ
5. Bellizzi S., and Bouc R. Analysis of multi-degree of freedom strongly non linear mechanical systems with random input - Part I: Non-linear modes and stochastic averaging. Journal of Probabilistic Engineering Mechanics 14 (1999) 229-244
6. Bellizzi S., and Bouc R. Analysis of multi-degree of freedom strongly non linear mechanical systems with random input - Part II: Equivalent linear system with random matrices and power spectral density matrix. Journal of Probabilistic Engineering Mechanics 14 (1999) 245-256
7. Bellizzi S., and Bouc R. A new formulation for the existence and calculation of non linear normal modes. Journal of Sound and Vibration 287 (2005) 545-569
8. Han W., and Petyt M. Geometrically non linear vibration analysis of thin, rectangular plates using the hierarchical finite element method I: The fundamental mode of isoparametric plates. Journal of Computers and Structures 63 2 (1997) 295-308
9. Han W., and Petyt M. Geometrically non linear vibration analysis of thin, rectangular plates using the hierarchical finite element method II: 1st mode of laminated plates and higher modes of isoparametric and laminated plates. Journal of Computers & Structures 63 2 (1997) 309-318
10. Houmat A. An alternative hierarchical finite element formulation applied to plate vibrations. Journal of Sound and Vibration 206 2 (1997) 201-215
11. Lau S.L., Cheung Y.K., and Wu S.Y. Non-linear linear vibration of thin elastic plates - Part I: generalised incremental Hamilton's principle and element formulation. Journal of Applied Mechanics 51 (1984) 837-844
12. Mei C. Finite element displacement method for large amplitude free flexural vibrations of beams and plates. Journal of Computers and Structures 3 (1973) 163-174
13. Ribeiro P. Nonlinear linear vibrations of simply-supported plates by the p-version finite element method. Finite Elements in Analysis and Design 41 (2005) 911-924
14. Ribeiro P., and Petyt M. Non-linear vibration of beams with internal resonance by the hierarchical finite-element method. Journal of Sound and Vibration 224 4 (1999) 591-624
15. Shi Y., and Mei C. A finite element time domain modal formulation for large amplitude free vibrations of beams and plates. Journal of Sound and Vibration 193 2 (1996) 453-464