Coupled vibrations of beams—an exact dynamic element stiffness matrix
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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ABSTRACT: The governing field equations and boundary conditions based on a generalized Vlasov-Timoshenko beam the-ory are formulated using the principle of the stationary total potential energy. The formulation incorporates shear deformation effects due flexure and warping, and captures the flexural-torsional coupling in monosym-metric cross-sections. General closed-form solutions are obtained for cantilever boundary conditions. Numeri-cal examples for the flexural-torsional coupled analysis are presented and compared with Abaqus finite ele-ment solutions. Additional comparisons are performed against non-shear deformable beam theories and the ef-fect of transverse shear deformation is illustrated.SEMC 2013- The Fifth International Conference on Structural Engineering, Mechanics and Computation, 2-4 September 2013, Cape Town, South Africa; 09/2013
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ABSTRACT: The steady state response of thin-walled members with doubly symmetric cross-sections subjected to harmonic forces is investigated. Using the Hamiltonian functional, the governing differential equations and related boundary conditions are formulated based on the Vlasov thin walled beam theory. The formulation takes into account the effect of warping deformation and translational and rotary inertia. The resulting governing field equations are then exactly solved and closed form solutions for transverse and torsional responses are obtained for common boundary conditions. Numerical examples are then presented and comparisons are made against other established Abaqus beam and shell solutions to assess the accuracy of the present analytical solutions.CSCE 2013 - 3rd Specialty Conference on Engineering Mechanics and Materials in Montreal, Quebec, Montreal, Quebec, Canada; 05/2013
Article: Free vibration of thin walled beams[Show abstract] [Hide abstract]
ABSTRACT: Consistent and simple lumped mass matrices are formulated for the dynamic analysis of beams with arbitrary cross section. The development is based on a general beam theory which includes the effect of flexural-torsion coupling, the constrained torsion warping and the shear centre location. Numerical test are presented to demonstrate the importance of torsion warping constraints and the acceptable accuracy of the lumped mass matrix formulation.