Free Vibration of Beams With Two Sections of Distributed Mass

Abstract

The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

Free Vibrations of a Rectangular Plate Carrying a Distributed Mass

“…To apply the Galerkin discretization procedure to equation (1), the true solution of this equation is approximated with the following series:…”

The Effects of Distributed Mass Loading on Plate Vibration Behavior

“…While there are several reports on plate vibrations with added point masses [3}6], very few reports on plate vibrations with distributed mass loading can be found in the literature. It has been proved that distributed mass loading can induce signi"cant changes of modal frequencies and shapes in beam vibrations [7,8]. In this paper, the free bending vibration of a simply supported rectangular plate carrying distributed mass loading is analyzed by the Rayleigh}Ritz method.…”

On the Eigenfrequencies of a Two-Part Beam–mass System

“…Chan et al [6], and Chan and Wang [7] investigated the free vibration of simply supported and cantilever beams with distributed mass, using Euler}Bernoulli and Timoshenko beam models respectively. Chan et al [8] treated the free vibration of a beam with two distributed masses in-span. Low [9] derived the frequency equations of a beam with a concentrated mass in-span under classical boundary conditions.…”