Coupled vibrations of beams—an exact dynamic element stiffness matrix

✍ Scribed by P. O. Friberg

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 691 KB
• Volume: 19
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620190403

✦ Synopsis

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 12x 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. P. 0. FRIBERG ZI, w = Translations of cross-section at shear centre axis in y-and z-directions. C $ = Rotation of cross-section about x-axis. YG, Z G = Co-ordinates of geometric centre G. yw, zM = Co-ordinates of mass centre M.