Coupled vibrations of beams—an exact dynamic element stiffness matrix

Division of Solid Mechanics, Chalmers University of Technology, Gothenburg, Sweden
International Journal for Numerical Methods in Engineering (Impact Factor: 2.06). 07/2005; 19(4):479 - 493. DOI: 10.1002/nme.1620190403

ABSTRACT A uniform linearly elastic beam element with non-coinciding centres of geometry, shear and mass is studied under stationary harmonic end excitation. The Euler-Bernoulli-Saint Venant theory is applied. Thus the effect of warping is not taken into account. The frequency-dependent 12 × 12 element stiffness matrix is established by use of an exact method. The translational and rotational displacement functions are represented as sums (real) of complex exponential terms where the complex exponents are numerically found. Built-up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines.

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