Ritz finite element approach to nonlinear vibrations of beams

DOI10.1002/nme.1620200213zbMath0525.73084OpenAlexW2129585680MaRDI QIDQ3038777

T. K. Varadan, B. S. Sarma

Publication date: 1984

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.1620200213

zbMATH Keywords

convergenceLagrange's equation of motionbeams with immovable endsdirect iteration techniquedisplacement norms on eigen-modeselement displacement vector chosen as combination of inplane and transverse displacementsfrequency norms for eigenvalueslarge amplitude free flexural vibrationsmodeshapes for transverse and longitudinal displacementsnonlinear frequenciesnonlinear stiffness as combination of bending-membrane interaction and bending stiffnessRitz finite element approachsimply-supported, clamped-clamped and simply- supported-clamped beams

Mathematics Subject Classification ID

Newton-type methods (49M15) Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05)

Related Items (4)

Nonlinear free vibration analysis of thin-walled curved beam with non-symmetric open cross section ⋮ Free vibration of structures with cubic nonlinearity -- remarks on amplitude equation and Rayleigh quotient. ⋮ On beam, membrane, and plate vibration backbone curves in cases of internal resonance ⋮ Analytical and Experimental Studies on the Large Amplitude Free Vibrations of Variable-Arc-Length Beams

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