Thin Beams: Natural Frequencies and Mode Shapes

TheBeams, Euler-Bernoullivariable cross section natural frequencies and mode shapesBeams, Timoshenkomode shape of thin beams of constantSingle degree-of-freedom systemconstant force cross section, continuouslyBeams, Euler-Bernoullimode shape variable cross sectionBeams, Timoshenkovariable cross section, and cross sections with step changes in properties for numerous combinations of boundary conditionsBeams, Euler-Bernoulliboundary conditions and boundary and in-span attachments are obtained. The in-span and boundary attachments include springs, concentratedBeams, Euler-Bernoulliconcentrated mass masses, single andBeams, Euler-Bernoullitwo degree-of-freedom system two degree-of-freedom systemsTwo degree-of-freedom system, and inertersBeams, Euler-Bernoullisingle degree-of-freedom system. Single degree-of-freedom systemsBeams, Timoshenkosingle degree-of-freedom system and inerters are examined in their role as tuned mass dampers. The effects of a mass on the natural frequencies of a beam are illustrated by considering a cantileverBeams, Euler-Bernoullicantilever beam in which the center of gravity of the attached mass is a finite distance from the end of the beam and by considering a rigid mass of finite length supported by a beam at each of its ends. The natural frequencies of pre-twisted beams, of beams on an elastic foundation and subject to anForceaxial axial forceAxial force, and beams that are elastically connectedBeams, Euler-Bernoullielastically connected to other beams are also determined.