COMMENT ON “FREE VIBRATIONS OF A FREE-FREE PARTIALLY STRESSED STEPPED BEAM”

✍ Scribed by M.A. De Rosa

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 225 KB
• Volume: 187
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1995.0540

✦ Synopsis

In reference [1] an elegant and effective finite element formulation for a stepped beam with a follower force at the step has been developed, in order to simulate the internal pressures developed in rocket motors. The analysis is performed by using (a) a Galerkin finite element formulation [2], and a powerful high order finite element, and (b) the method proposed by Kikuchi [3]. In this comment the exact equation of motion is solved, and the numerical results of the paper are confirmed.

In fact, the equation is a particular case of the general frequency equation given in reference [4] for a stepped beam as in Figure 1, with flexible ends.

After zeroing the stiffnesses of the constraints it is possible to arrive at the equation -V 22 V' 21 V0 12 V1 11 +V 21 V' 22 V0 12 V1 11 +V 22 V' 21 V0 11 V1 12 -V 21 V' 22 V0 11 V1 12