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  • 1
    Electronic Resource
    Electronic Resource
    Three-dimensional nonlinear vibrations of composite beams — I. Equations of motion (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 477-502 
    Details
    ISSN: 1573-269X
    Keywords: Composite beams ; flexural-flexural-torsional-extensional vibrations ; nonlinear equations of motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Newton's second law is used to develop the nonlinear equations describing the extensional-flexural-flexural-torsional vibrations of slewing or rotating metallic and composite beams. Three consecutive Euler angles are used to relate the deformed and undeformed states. Because the twisting-related Euler angle ϕ is not an independent Lagrangian coordinate, twisting curvature is used to define the twist angle, and the resulting equations of motion are symmetric and independent of the rotation sequence of the Euler angles. The equations of motion are valid for extensional, inextensional, uniform and nonuniform, metallic and composite beams. The equations contain structural coupling terms and quadratic and cubic nonlinearities due to curvature and inertia. Some comparisons with other derivations are made, and the characteristics of the modeling are addressed. The second part of the paper will present a nonlinear analysis of a symmetric angle-ply graphite-epoxy beam exhibiting bending-twisting coupling and a two-to-one internal resonance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01856950
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  • 2
    Electronic Resource
    Electronic Resource
    A nonlinear composite beam theory (1992)
    Springer
    Nonlinear dynamics 3 (1992), S. 273-303 
    Details
    ISSN: 1573-269X
    Keywords: Composite beams ; geometric nonlinearity ; third-order shear deformation theory ; extensional-flexural-flexuraltorsional-shearing-shearing vibrations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Presented here is a general theory for the three-dimensional nonlinear dynamics of elastic anisotropic initially straight beams undergoing moderate displacements and rotations. The theory fully accounts for geometric nonlinearities (large rotations and displacements) by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvature and strain-displacement expressions that contain the von Karman strains as a special case. Extensionality is included in the formulation, and transverse shear deformations are accounted for by using a third-order theory. Six third-order nonlinear partial-differential equations are derived for describing one extension, two bending, one torsion, and two shearing vibrations of composite beams. They show that laminated beams display linear elastic and nonlinear geometric couplings among all motions. The theory contains, as special cases, the Euler-Bernoulli theory, Timoshenko's beam theory, the third-order shear theory, and the von Karman type nonlinear theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045486
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    Paper (German National Licenses)
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