Vibrations of Beams Carrying Mass

Vibration Analysis of Beams Using the Generalized Differential Quadrature Rule and Domain Decomposition

“…Note: Data in &&( )'' from reference [28], in &&+ ,'' from reference [29]. Domain decomposition must be employed in the DQ technique if the solution function is not continuously di!erentiable in the solution domain, since the weighting coe$cients are obtained using continuously di!erentiable trial functions.…”

“…References [28,29] considered the concentrated mass at an intermediate point (x"¸/3 or¸/2) of single-span uniform beam. The mass will apply a dynamic concentrated force in vibration problems.…”

“…The Laplace transform was employed to obtain a characteristic equation in paper [28]. An analytic characteristic equation was obtained in paper [29].…”

Eigenfrequency Shift of Micro-sensor with the Concentrated Mass and Spring

“…However, in FMTM when the concentrated mass/spring is small or around the node, the FMTM formulation of Eq. (19) or (20) matrix. The formulation of Galerkin method on the eigenfrequency computation is relatively easy and can be done in systematic way.…”

“…Three formulations on the eigenfrequency shift of an EulerBernoulli beam carrying arbitrary number of concentrated mass and (translational) spring are presented and compared. The three formulations are the analytical method [17][18][19][20], Galerkin method [21] and finite mode transform method (FMTM). FMTM is a new method presented in this paper and it adopts the similar approach of Amba-Rao's formulation [22] on the plate carrying a concentrated mass.…”