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Research Papers

Response of Viscoelastic Plate to Impact

[+] Author and Article Information
D. Ingman

QA&R,  Technion-I.I.T., Technion City, Haifa 32000, Israelqadov@tx.technion.ac.il

J. Suzdalnitsky1

QA&R,  Technion-I.I.T., Technion City, Haifa 32000, Israeliosef@tx.technion.ac.il

1

Corresponding author.

J. Vib. Acoust 130(1), 011010 (Nov 15, 2007) (8 pages) doi:10.1115/1.2731416 History: Received February 22, 2006; Revised February 07, 2007; Published November 15, 2007

Organization of product tests in the microelectronic and optical-electronic industries by the impact method is considered. Two mathematical models: a circular plate under dynamic loading with predetermined initial conditions, and contact interaction of a falling mass and a barrier, are examined. The deflection function, curvature, and acceleration are determined. As the series for these characteristics may prove divergent, the problem is to secure sufficiently reliable results. The method of impact mechanics permits determination of the duration and force of the impact, estimation of the total energy of each mode in the expansion of the deflection function and preclusion of divergent series when determining the plate acceleration and curvature during the vibration process. In parallel, viscoelasticity is simulated with the aid of a fractional-differentiation operator, certain features of which are discussed. Representation of this operator with time-dependent order by ones with constant orders is considered. Three alternative approaches for determination of the eigenfrequency and damping decrement of a vibration process are examined. In particular, a method for calculating these characteristics under conditions of time-dependence and servo control of the order function is proposed.

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Figures

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Figure 5

Damping decrement δ(a) for η=0.05, (b) for η=0.2

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Figure 1

Function y(t)=Dα(t)x(t), α(t)=1−e−t, x(t)=t and its approximations

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Figure 2

(a) Dependence of the acceleration factor a* on ηω2, (b) dependence of the curvature factor κ* on ηω2 for indicated orders of α

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Figure 3

Contact force and deflections under the central transverse impact

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Figure 4

Dependencies of maximal deflection w1,max: (a) on initial velocity v0, (b) on ratio of masses m2∕m1

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