Free Vibrations of Timoshenko Beams Carrying Elastically Mounted, Concentrated Masses

Free vibration analysis of a Timoshenko beam carrying multiple spring-mass systems by using the numerical assembly technique

“…The location of the attaching point is at 1 = x 1 =L = 0:5, while the non-dimensional sprung mass m * 1 and spring constant k * 1 are given by m * 1 = m 1 =m b = 0:2 and k * 1 = k 1 =k b = 1:0, respectively. From Table I one sees that the lowest six eigenvalue coe cients j (j = 1; : : : ; 6) for the three boundary conditions of the Timoshenko beam (SS, CC and CS) obtained from the present approach are very close to those obtained from Reference [5]. It is noted that the eigenvalue coe cients j and the actual natural frequencies !…”

“…To check the reliability of the theory presented and the computer programs developed for this paper, the lowest six natural frequencies of Timoshenko beam carrying a single spring-mass system as illustrated in Reference [5] were studied ÿrst. The location of the attaching point is at 1 = x 1 =L = 0:5, while the non-dimensional sprung mass m * 1 and spring constant k * 1 are given by m * 1 = m 1 =m b = 0:2 and k * 1 = k 1 =k b = 1:0, respectively.…”

“…Thereafter, similar research work was done by Abramovich and Hamburger [3; 4] and Rossi et al [5]. In Reference [3], the in uence of shear deformation and rotatory inertia on the natural frequencies of the Timoshenko beam studied in Reference [2] was investigated.…”

“…In Reference [4], the same work was repeated, but a translational spring and a rotational spring located intermediately were also considered in addition to a tip mass with lumped mass moment of inertia. In Reference [5], the exact solutions for the natural frequencies and mode shapes of a Timoshenko beam carrying a single elastically mounted concentrated mass with three types of boundary conditions were presented. In theory, all the foregoing approaches may be extended to do the free vibration analysis of a Timoshenko beam carrying multiple concentrated elements.…”

Simple models for natural frequencies and mode shapes of towers supporting utilities

“…Similar studies involving beams with concentrated mass have been carried out by Rossi et al [9], Posiadala [10], Auciello [11] and Uscilowska and Kolodziej [12]. Tomski et al [13] considered a model of a cantilever beam under a prestressing force along with a concentrated mass and investigated the effects of the prestressing force and the concentrated mass of the beams natural frequency.…”