000003634 001__ 3634
000003634 005__ 20141118153352.0
000003634 04107 $$acze
000003634 046__ $$k2013-05-13
000003634 100__ $$aSobotka, J.
000003634 24500 $$aFREE VIBRATION ANALYSIS OF EULER-BERNOULLI BEAM WITH DISCONTINUITIES BY MEANS OF DISTRIBUTIONS

000003634 24630 $$n19.$$pEngineering Mechanics 2013
000003634 260__ $$bInstitute of Thermomechanics AS CR, v.v.i., Praha
000003634 506__ $$arestricted
000003634 520__ $$2eng$$aThe general equation for the transverse vibration of Euler-Bernoulli beam has been used since it was derived by means of classical derivatives of the shear force, the bending moment, the slope and the deflection of the beam. However these derivatives are not defined at such points of center-line between ends of the beam in which there is a concentrated support or a concentrated mass or a concentrated moment of inertia or an internal hinge connecting beam segments. We have applied the distributional derivative for a discontinuous shear force, a discontinuous bending moment, and a discontinuous slope of the beam in order to derive generalized mathematical model for free transverse vibration as a system of partial differential equations. We have computed a general solution to the generalized mathematical model for prismatic beam by means of a symbolic programming approach via Maple. As a result of this approach, computing natural frequencies and modal shapes of a slender beam, it is not necessary for continuity conditions to be put together at discontinuity points mentioned. As an example we have used this approach to obtain a frequency equation of a beam on three pin rigid supports, which would be more complicated if we tried to apply the transfer matrix method.

000003634 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000003634 653__ $$aEuler-Bernoulli beam, transverse vibration, discontinuities, Dirac distribution.

000003634 7112_ $$aEngineering Mechanics 2013$$cSvratka (CZ)$$d2013-05-13 / 2013-05-16$$gEM2013
000003634 720__ $$aSobotka, J.
000003634 8560_ $$ffischerc@itam.cas.cz
000003634 8564_ $$s102915$$uhttp://invenio.itam.cas.cz/record/3634/files/003_Sobotka_J-FT.pdf$$y
             Original version of the author's contribution as presented on CD, DYN.
            
000003634 962__ $$r3632
000003634 980__ $$aPAPER