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Feb 2006

Volume 119, Issue 2, pp. 669-EL19

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A method for structural vibration characterization in the midfrequency region

W. Steve Shepard, Jr. and Yi Liu

J. Acoust. Soc. Am. Volume 119, Issue 2, pp. 897-908 (2006); (12 pages)

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The ability to characterize elastic structures at higher frequencies in a meaningful and convenient manner has been a topic of much interest. Many analytical or experimental approaches incorporate the use of lumped quantities to represent critical system characteristics at discrete locations. When the excitation frequency increases, the structural wavelength becomes comparable to the dimensions of that contact region and the point-quantity assumption is no longer valid. To provide a similar means for describing structures at higher frequencies, the work described here reformulates the traditional four-pole method in terms of quantities defined over planes. Spatial variations of the important response characteristics across the connecting regions can be considered. As for the four-pole method, the approach has the advantage of providing building blocks for simple structures in order to represent more complex structures. Three application examples are presented. One example involves modeling a simple vibration isolator. In another example, the impact of having spatial functions that extend over only a portion of the structure is studied. Finally, a two-dimensional structure is examined using a finite element approach. In using the approach, additional insight can be gained that cannot be easily found using typical finite element method analysis results.
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43.40.At Experimental and theoretical studies of vibrating systems
43.40.Cw Vibrations of strings, rods, and beams
43.40.Tm Vibration isolators, attenuators, and dampers

Longitudinal vibration frequencies of steadily whirling rods

W. S. Shum and R. D. Entwistle

J. Acoust. Soc. Am. Volume 119, Issue 2, pp. 909-916 (2006); (8 pages) | Cited 1 time

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Past researchers suggested that “static instabilities” exist at certain rotational speeds of whirling rods. This paper shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady-state equations of whirling rods are formulated in Lagrangian coordinates. Due to the nonlinear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred “static instabilities.” This approach first solves the “static” problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived.
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43.40.Cw Vibrations of strings, rods, and beams
43.40.Ga Nonlinear vibration

A closed form solution for the dynamic response of finite ribbed plates

Tian Ran Lin and Jie Pan

J. Acoust. Soc. Am. Volume 119, Issue 2, pp. 917-925 (2006); (9 pages) | Cited 10 times

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A simple and closed form solution for the vibration response of finite ribbed plates to point force/moment excitations is presented in this paper. This solution shows that input mobilities of finite ribbed plates are bounded by the input mobilities of the uncoupled plate and beam that form the ribbed plate. It is found that point force input mobilities of a finite ribbed plate are controlled by the plate bending stiffness when the excitation force is more than a quarter wavelength away from the beam. The input mobilities are mainly dominated by the beam flexural stiffness when the force acts on or very close to the beam, and when the beam flexural stiffness is far greater than the plate bending stiffness. A similar result is found in the moment excitation case when the moment axis is perpendicular to the beam neutral axis (bending moment excitation). In contrast, the input mobilities of the ribbed plate do not vary much from that of the corresponding uncoupled plate when the moment axis parallels to the beam’s neutral axis (torsional moment excitation) where the input mobilities are mainly dominated by the plate bending stiffness. The reductions in plate kinetic energy due to beam insertions are discussed.
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43.40.Dx Vibrations of membranes and plates
43.40.Cw Vibrations of strings, rods, and beams

Hybrid vibration isolator: Single axis control study

Peter C. Herdic, Robert D. Corsaro, Brian H. Houston, and Robert M. Baden

J. Acoust. Soc. Am. Volume 119, Issue 2, pp. 926-936 (2006); (11 pages)

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Results are presented for a laboratory study of a compact, single-axis hybrid (active-passive) vibration isolator. The passive system component demonstrates a very high level of vibration isolation at frequencies roughly a factor of 3 above the fundamental system resonance. The active component complements the system by significantly reducing the transmitted vibration levels at lower frequencies, where the passive-only system is ineffective. The device consists of three basic components, a passive compliant spring, force and velocity sensing, and a piezoelectric actuation layer. The experimental system is typically excited at 50 Hz with response characteristics measured over the band from ∼ 10 to 2000 Hz. The isolation performance is evaluated for an optimized passive stage as well as for all relevant hybrid layer configurations. The optimal physical control law is determined by identifying positions in the device stack where actuation and sensing are most effective at minimizing the downstream base velocity and power flow through the mount. Local force and velocity minimization are implemented via a least mean squared adaptive control filter. The role of harmonic distortion and actuator nonlinearity is examined by comparing the system performance and out-of-band enhancement obtained using PZT-4, PZT-5H, and single-crystal PMN-PT actuator materials.
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43.40.Tm Vibration isolators, attenuators, and dampers
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