Free Vibrations of Viscoelastic Timoshenko Beams

Huang, T. C.; Huang, C. C.

doi:10.1115/1.3408805

Cited by 20 publications

(9 citation statements)

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“…10 For example, some researchers only consider damping associated with the mass operator with no spatial derivatives -i.e., deflection or rotation alone. 11,12,13,14 Others consider only strain-or shear-based damping, perhaps through a viscoelastic formulation of the constitutive equations. 15,16,17 As with structural damping, the concept of proportional damping can be extended to apply to the boundary conditions to model their associated dissipative mechanisms.…”

Section: Damping Model Backgroundmentioning

confidence: 99%

Damping Models for Shear Beams with Applications to Spacecraft Wiring Harnesses

Kauffman

Lesieutre²

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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7
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Spacecraft wiring harnesses can fundamentally alter a spacecraft's structural dynamics, necessitating a model to predict the coupled dynamic response of the structure and attached cabling. While a beam model including first-order transverse shear can accurately predict vibration resonance frequencies, current time-domain damping models are inadequate. For example, the common proportional damping model results in modal damping that depends unrealistically on the frequency. Inspired by a geometric rotation-based viscous damping model that provides frequency-independent modal damping in an Euler-Bernoulli formulation, a time-domain viscous damping model with terms associated with the shear and bending angles is presented. This model demonstrates a much weaker dependence on frequency than proportional damping models. Specifically, the model provides modal damping that is approximately constant in the bending-dominated regime (low mode numbers), increasing by at most 6% for a particular selection of bending and shear angle-based damping coefficients. In the shear-dominated regime (high mode numbers), damping values increase linearly with mode number and are proportional to the shear angle-based damping coefficient. A key feature of this model is its ready implementation in a finite element analysis, requiring only the typical mass, stiffness, and geometric stiffness (associated with axial loads) matrices as developed for an Euler-Bernoulli beam. Such an analysis using empirically determined damping coefficients generates damping values that agree well with existing spacecraft cable bundle data. Nomenclature α viscous damping coefficient β shear angle nondimensional shear parameter, EIπ 2 κAGL 2 κ shear coefficient [M ], [K], and [K G ] beam finite element mass, stiffness, and geometric stiffness matrices ω m natural frequency of vibration ρ density ϕ rotation of beam centerline associated with bending ζ m modal damping ratio A cross-sectional area a m modal coordinate E Young's modulus G shear modulus I moment of inertia

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Section: Damping Model Backgroundmentioning
confidence: 99%

Damping Models for Shear Beams with Applications to Spacecraft Wiring Harnesses
Kauffman
¹
,
Lesieutre²
2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
5
0
7
0
View full text Add to dashboard Cite

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“…The second common approach is through the inclusion of proportional damping terms. Here damping terms result as some combination of terms proportional to the mass and stiffness terms [12][13][14][15][16][17][18][19]. This technique is mathematically convenient; however, it fails to provide modal damping that is physically realistic.…”

Section: Damping Model Backgroundmentioning
confidence: 99%

“…Several such approaches exist; the solution employed here is to interpolate the displacement, w, using cubic shape functions and the centerline slope associated with bending, φ, using quadratic shape functions [20]. The coordinates can thus be written in terms of the shape functions (9) where (10) The shape functions are (11) (12) Where ϕ is an elemental shear stiffness parameter: (13) Inserting these shape functions in Equation (8) ultimately leads to the mass, damping, and stiffness matrices for each element. The elemental mass matrix comes from terms involving the second time derivative of the displacements and rotations: (14) where…”

Section: Discretization Of Equation Of Motion With Damping Termsmentioning
confidence: 99%

Damping Models for Shear-Deformable Beam with Applications to Spacecraft Wiring Harness
Lesieutre¹,
Kauffman²
2014
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Using Government drawings, specifications, or other data included in this document for any purpose other than Government procurement does not in any way obligate the U.S. Government. The fact that the Government formulated or supplied the drawings, specifications, or other data does not license the holder or any other person or corporation; or convey any rights or permission to manufacture, use, or sell any patented invention that may relate to them. This report is the result of contracted fundamental research deemed exempt from public affairs security and policy review in accordance with SAF/AQR memorandum dated 10 Dec 08 and AFRL/CA policy clarification memorandum dated 16 Jan 09. This report is available to the general public, including foreign nationals. Copies may be obtained from the Defense Technical Information Center (DTIC) (http://www.dtic.mil).

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“…In order to investigate the vibration fatigue characteristics of the viscoelastic structures, the modal analysis method can be used to derive the analytical solutions. By using the complex modal method and Laplace transform, Huang and Huang [3] studied the free vibration of Timoshenko viscoelastic beams satisfying the standard linear solid constitutive equations. Considering the axial forces, Chen et al [4] studied the vibration characteristics of clamped-clamped Timoshenko viscoelastic beams constituted by the Kelvin-Voigt model.…”

Section: Introductionmentioning
confidence: 99%

Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models
Fu
2023
Journal of Applied Mathematics
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Based on the equivalent bending stiffness of the viscoelastic cracked beam with open cracks, the corresponding complex frequency characteristic equations of a Timoshenko viscoelastic cracked beam are obtained by using the method of separation of variables and the Laplace transform. The vibration characteristics of a viscoelastic Timoshenko cracked beams with the standard linear solid model and Kelvin-Voigt model are investigated. By numerical examples, the effects of the crack location, crack number, crack depth, and slenderness ratio on the vibration characteristics of the viscoelastic cracked beams are revealed.

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Free Vibrations of Viscoelastic Timoshenko Beams

Cited by 20 publications

References 0 publications

Damping Models for Shear Beams with Applications to Spacecraft Wiring Harnesses

Damping Models for Shear Beams with Applications to Spacecraft Wiring Harnesses

Damping Models for Shear-Deformable Beam with Applications to Spacecraft Wiring Harness

Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models

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