Research Papers

Analytical and Experimental Investigation of Buckled Beams as Negative Stiffness Elements for Passive Vibration and Shock Isolation Systems

[+] Author and Article Information
Benjamin A. Fulcher

Harvest Technologies,
Belton, TX 76513
e-mail: bfulcher@harvest-tech.com

David W. Shahan

HRL Laboratories,
Malibu, CA 90265
e-mail: dwshahan@hrl.com

Michael R. Haberman

Mechanical Engineering Department
and Applied Research Laboratories,
The University of Texas at Austin,
Austin, TX 78712
e-mail: haberman@arlut.utexas.edu

Carolyn Conner Seepersad

Mechanical Engineering Department,
The University of Texas at Austin,
Austin, TX 78712
e-mail: ccseepersad@mail.utexas.edu

Preston S. Wilson

Mechanical Engineering Department
and Applied Research Laboratories,
The University of Texas at Austin,
Austin, TX 78712
e-mail: pswilson@mail.utexas.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 8, 2013; final manuscript received February 4, 2014; published online April 1, 2014. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 136(3), 031009 (Apr 01, 2014) (12 pages) Paper No: VIB-13-1102; doi: 10.1115/1.4026888 History: Received April 08, 2013; Revised February 04, 2014

The behavior of a buckled beam mechanism, which exhibits both bistability and negative stiffness, is investigated for the purposes of passive shock and vibration isolation. The vibration and shock isolation systems investigated in this research include linear, positive stiffness springs in parallel with the transverse motion of buckled beams, resulting in quasizero stiffness behavior. For vibration isolation systems, quasizero stiffness lowers the resonance frequency of the system, thereby reducing its transmissibility at frequencies greater than resonance. For shock isolation systems, quasizero stiffness provides constant-force shock isolation at tailored force levels, thereby enabling increased capacity for absorbing shock energy relative to a comparable positive stiffness system. Single- and double-beam configurations that exhibit first-mode buckling are utilized for vibration isolation, and a single beam that exhibits first- and third-mode buckling is used for shock isolation. For all cases, the static and dynamic behavior of each configuration is modeled analytically. The models are then used to design prototype vibration and shock isolation systems that are fabricated using selective laser sintering (SLS). The dynamic behavior of the systems in response to base excitations is determined experimentally, and the results are compared to model-based predictions. The vibration isolation prototypes display isolation levels that are tunable by varying the axial compression of the beams. Double-beam systems are shown to provide greater reductions in resonance frequency than single-beam systems for comparable levels of axial compression. However, low-frequency isolation capabilities are sensitive to the high levels of precision required to obtain low levels of system stiffness. The shock isolation prototype provides isolation at prespecified threshold levels of force or acceleration. In the prototype system, an input shock with a peak acceleration of approximately 7 g is reduced to a peak acceleration of the isolated mass of approximately 1 g. High levels of negative acceleration are observed in models and prototype systems when the buckled beam snaps back to its original position; however, models indicate that large negative accelerations can be mitigated using one-way dampers.

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Fig. 1

First-mode buckled beam transitioning from one stable state to another under transverse loading, Ft

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Fig. 2

Transverse constitutive relationship of an axially compressed, buckled beam, relative to that of an unbuckled beam

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Fig. 3

Computer-aided design models for vibration isolation systems including the single beam (top), uncoupled double beam (middle), and coupled double beam (bottom)

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Fig. 4

(top) Vibration isolation system schematic, (middle) reduced schematic, and (bottom) bond graph, where vin is input velocity; vout is output velocity; Ft is transverse beam force as a function of δs, the compression of the spring; Fs is spring force; Fc is damper force; m is the isolated mass; ks is the linear spring constant; cs is the damping coefficient for the system; Pm is the momentum of the system mass; and δ·s and P·m are derivatives with respect to time

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Fig. 5

(a) Compressed beam and (b) compressed beam experiencing transverse force

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Fig. 6

Configurations of interest for a bistable first-mode buckled beam that transits the third-mode buckled state upon transverse loading

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Fig. 7

Piecewise constitutive relationship of a third-mode buckled beam, where uy0+ and uy0– represent the stable, first-mode buckled positions of the center of the beam

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Fig. 8

Force versus displacement of a third-mode buckled beam and spring in parallel

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Fig. 9

Photographs of vibration isolation systems: single-beam system (upper), coupled double-beam system (middle), and uncoupled double-beam system (bottom)

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Fig. 10

Photograph of shock isolation system

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Fig. 14

Single-beam system sensitivity to imperfection

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Fig. 13

Coupled double-beam system transmissibility

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Fig. 12

Uncoupled double-beam system transmissibility

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Fig. 16

Beam constitutive curve fit, based on Eq. (21), for an axial compression of 4.76 mm

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Fig. 17

Experimental hysteresis plot

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Fig. 15

Experimental and simulated shock response

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Fig. 18

Experimental and updated simulated shock responses

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Fig. 11

Single-beam system transmissibility




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