Vibration Analysis of a Cantilevered Beam with Spring Loading at the Tip as a Generic Elastic Structure

Abstract

Although fundamental, vibration of a cantilevered Euler-Bernoulli beam with spring attached at the tip is not found in literatures and is here solved analytically and numerically using finite element approach. The equation of motion of the beam is obtained by using Hamilton’s principle. Finite element method is utilized to write in-house program for the free vibration of the beam. Results show plausible agreements.

Active Vibration Suppression of an elastic piezoelectric sensor and actuator fitted cantilevered beam configurations as a generic smart composite structure

“…Similarly, the next two modes exhibit similar accuracy. The result thus obtained agrees with the work of Maurizi, Rossi and Reyes [30] for a degenerate case, as elaborated in references [21,22].…”

“…(13) for the eigen-frequencies and eigen-modes for the beam considered is elaborated in [21,22]. The natural frequencies of the numerical approach are determined by Eq.…”

“…Following a series of previous investigation on the analysis of impact resilient structure [17][18][19][20], and vibration analysis of an elastically clamped cantilever beam [21,22], the main aim of this investigation is to design a straightforward and convenient controller for suppressing the transverse vibration in a cantilever aluminum flexible beam through the use of sensing and actuating transducers. The Euler-Bernoulli beam theory is utilized to model the flexible beam with piezoelectric patches.…”

“…(8)-(11) for a cantilever beam with spring loading at the free end as appropriate [21,22], the natural frequencies and vibration modes of the system may be obtained.…”