Natural Frequencies and Mode Shapes of a Free–free Beam With Large End Masses

Kirk, C.L.; Wiedemann, Simon

doi:10.1006/jsvi.2001.4138

Cited by 33 publications

(27 citation statements)

References 14 publications

(4 reference statements)

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“…This research, however, assumes no payload mass center offset and therefore does not take torsional deformations into account. In [12], the free vibration of an Euler-Bernoulli beam with offset payload has been investigated. The exact closed-form expressions, however, have not been presented and the torsional deformation has been ignored.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

Salarieh

Ghorashi

2006

International Journal of Mechanical Sciences

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Section: Introductionmentioning

confidence: 99%

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

Salarieh

Ghorashi

2006

International Journal of Mechanical Sciences

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“…This displacement will in turn be sensed at the output electrodes, generating an output current. From these relationships, two important electromechanical coupling coefficients are defined: (5) From this we can define the following electromechanical LCR equivalents that represents the two input/output ports of the FFSFR:…”

Section: B Electromechanical Mixer-filter Modelmentioning

confidence: 99%

“…The bending equation for a free-free beam can be shown to be cosh(β n )cos(β n )=1 [5]. The first two mode constants (β n ) that satisfy this equation is 4.73 and 7.85 which dictates the first two mode shapes where the resonator will vibrate with maximum displacement (e.g.…”

Section: Introductionmentioning

confidence: 97%

Higher order FFSFR coupled micromechanical mixer-filters integrated in CMOS

Ramstad

Soeraasen

2010

Norchip 2010

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This paper demonstrates how micromechanical on-chip MEMS resonators can be used as higher-order mixer-filters in RF front-end WSN nodes. Vibrating FFSFRs (Free-free Square Frame Resonator) connected together can create 4th and 6th order mixer-filter responses. The output is further enhanced by an on-chip amplifier, thus reducing stray capacitances. These mixer-filters are fabricated utilizing a CMOS-MEMS approach where the movable MEMS structure is defined by the metal layers offered by the CMOS foundry and released using a few simple etch steps. The system is implemented in TSMC 0.35µm CMOS and was post-CMOS processed at NTHU in Taiwan. Detailed modeling, simulation and implementation of the system show the performance of these higher order MEMS resonator mixer-filters as a potential candidate to replace bulky offchip transceiver components.

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“…Vibration analysis of a system, shown in Figure , was carried out in paper . The system is composed of a free‐free Euler‐Bernoulli beam of the cross section with two axes of symmetry ( y and z axes) with end rigid bodies ( V 1 ) and ( V 2 ) of masses M 1 and M 2 , respectively.…”

Section: Introductionmentioning

confidence: 99%

Contribution to the free vibration problem of a free‐free beam with large end masses

et al. 2018

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Free vibration of an Euler‐Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.

show abstract

Natural Frequencies and Mode Shapes of a Free–free Beam With Large End Masses

Cited by 33 publications

References 14 publications

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

Free vibration of Timoshenko beam with finite mass rigid tip load and flexural–torsional coupling

Higher order FFSFR coupled micromechanical mixer-filters integrated in CMOS

Contribution to the free vibration problem of a free‐free beam with large end masses

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