ASYMPTOTIC GOVERNING EQUATION FOR WAVE PROPAGATION ALONG WEAKLY NON-UNIFORM EULER–BERNOULLI BEAMS

✍ Scribed by K.P. BURR; M.S. TRIANTAFYLLOU; D.K.P. YUE

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 511 KB
• Volume: 247
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.3733

✦ Synopsis

Non-uniformity in beams arises either from manufacturing imperfections or by design, and can have a singular impact on the qualitative properties of the vibratory response of the beam. To describe the mechanism causing such large changes on the dynamics of the beam, we derived asymptotically a simpler equation, in the form

The coe$cient function Q(s) is given by equation ( 52) herein in terms of the beam #exural rigidity, the mass per unit length and the tensile force applied to the beam. The equation is asymptotic to the non-uniformity of the beam, but under certain restrictions, namely of having constant tension and a constant product of the beam mass per unit length and #exural rigidity, it is an exact governing equation for wave propagation along Bernoulli}Euler beams and it has a Helmholtz-like form. The behavior of the equation is systematically explored and illustrated through numerical results.