Review Articles

Saint-Venant’s Principle in Dynamics of Structures

[+] Author and Article Information
B. Karp1

Department of Mechanical Engineering,  Ben-Gurion University of the Negev, P.O.B., 653, Beer-Sheva 84105, Israelbkarp@bgu.ac.il

D. Durban

Faculty of Aerospace Engineering, Technion,  Israel Institute of Technology, Haifa, 32000, Israel


Corresponding author.

Appl. Mech. Rev 64(2), 020801 (Oct 27, 2011) (20 pages) doi:10.1115/1.4004930 History: Received February 11, 2011; Revised August 11, 2011; Published October 27, 2011; Online October 27, 2011

Research studies aiming at examination and formulation of a dynamic analog to Saint-Venant’s principle (DSVP) are critically reviewed. Article concentrates on isotropic homogeneous linear elastic response over a range of structural geometries including waveguides, with either free or constrained lateral surfaces, half space, wedges and cones. Nearly 140 DSVP related references are covered starting with early ideas by Boley. A special chapter is dedicated to available experimental work on end effects and decay rate in dynamically excited structures. Current thinking on possible versions of DSVP is classified into several categories, one of which, the dynamic equivalence, is compatible with much of known experimental data and has been tacitly applied at various engineering situations. That observation provides inspiring ground for renewed interest in both practical and theoretical aspects of DSVP.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Photoelastic photographs of experiment with rectangular blocks loaded by a concentrated load [35], p. 30

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Figure 2

Axial (a) and deflective (b) beam combinations investigated by Boley [36-37]

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Figure 3

Attenuation patterns of the maximal stress along the axis of the combined strip imposed by moments with different rise time t0 , 0 – for step function and ∞ – for quasi-static case [37]

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Figure 4

Configuration of the impacted bar with the attached strain gauges [52]

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Figure 5

Surface strain for flat and round strikers of length 100 cm (upper) and 2.54 cm (lower) at impact velocity of 0.7 m/s 24 diameters from the end [53]

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Figure 6

Configuration of the impacted bar with an embedded strain gauge No. 1 and the surface strain gauges Nos. 2-5 [68]

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Figure 7

Experimental and numerical results for center (a) and surface (b) strain at a distance of 3 diameters from impact [68]

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Figure 8

A fringe pattern in a plate impacted by two different materials with different surface irregularities [72]

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Figure 9

A fringe pattern in a plate impacted at the center of the upper end of a strip at two instants [73]

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Figure 10

Surface strain recording within the near-field (station 1) for three beam fixation conditions excited by transversal excitation at the free end of a cantilever beam. Baseline is the recording of excitation when all screws are tight in (see Ref. [164]).

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Figure 11

A standard striker and four modified strikers (three hollow and one solid) used to examine the sensitivity of the surface strain in impact loading to the form of the excitation [76]

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Figure 12

Surface strain recording (in Volts) within the near field for four strikers with identical contact area and different form (Fig. 1). Small oscillations are notable for certain strikers [76].

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Figure 13

Surface strain recording (normalized by far field strain) in experiment and finite element calculation of a rod, versus distance from the excited end, with different strikers (P1 and P4 pin type, B1 and B4 bore type) [75]

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Figure 14

Mixed boundary conditions used by DeVault and Curtis [80]

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Figure 15

Frequency map (wave number k versus frequency Ω) for symmetric fields in a strip with clamped surfaces made of elastic material with Poisson’s ratio ν = 0.25 (Blatz-Ko material without prestretch). Thin lines (composed of black dots) indicate real and purely imaginary branches. Thick lines (composed of hollow circles) indicate complex branches (two curves for each eigenvalue). Purely real wave numbers are associated with propagating waves (from Karp and Durban [113]).

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Figure 16

Variation of SVR for five excitation forms S (resembling damaged joint) with frequency Ω = 0.5 (below first cut-off) and S2-in excitation also with frequency Ω = 1.5 (close to first cut-off). Four Si-in excitations represent damaged joint at the center line of the strip while S5-out excitation represent damage at the outer edges (See Karp [114]).

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Figure 17

Axial surface strain recording in the close vicinity to clamped end of a beam, with three different “clamping” condition subjected to transversal excitation at the far end of the beam (from Karp [164])




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