1950
DOI: 10.1121/1.1906592
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The Velocity of Compressional Waves in Rods of Rectangular Cross Section

Abstract: Solutions for compressional waves in an isotropic rod of rectangular cross section are formulated from the general elastic equations of motion. Two general modes of propagation are constructed which satisfy the boundary conditions for the free vibrations of a long rod for which the width 2d is considerably greater than the thickness 2a. The thickness mode is shown to have an infinite phase velocity (cut-off frequency) at that frequency for which the half wave-length in an infinitely wide rod would be equal to … Show more

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Cited by 64 publications
(21 citation statements)
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“…This point of view has been developed by LeCorre [91] and by Joel Further discussion of the Laval-Raman approach can be found in Huntington's review paper [7]. The propagation of elastic compressional waves in rectangular bars [103], in impulsively loaded cylindrical rods [104], and in explosively loaded plates [105] has also been studied. Truesdell [106] has discussed the propagation of waves in an isotropic elastic material subject to a finite static strain.…”
Section: Thermal Gradient Problemsmentioning
confidence: 99%
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“…This point of view has been developed by LeCorre [91] and by Joel Further discussion of the Laval-Raman approach can be found in Huntington's review paper [7]. The propagation of elastic compressional waves in rectangular bars [103], in impulsively loaded cylindrical rods [104], and in explosively loaded plates [105] has also been studied. Truesdell [106] has discussed the propagation of waves in an isotropic elastic material subject to a finite static strain.…”
Section: Thermal Gradient Problemsmentioning
confidence: 99%
“…The apparatuses described so far can be used when there is Probably the largest uncertainty in comparative methods arises from failure to meet the basic underlying requirements of eqs (106) and (107) By analogy with the development of eqs (98) to (100) (103) and (104) + errors due to failure to meet requirements of equation (112) where the terms are analogous to those following eq (105 [71] and Moore, McElroy, and Graves [72].…”
Section: Interferometersmentioning
confidence: 99%
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“…Therefore other techniques must be used to more accurately model the propagation of ultrasound in such finite width strips. several techniques have been used previously to study the propagation of ultrasonic waves in such narrow strips including semi-analytical finite element modeling [14] and various analytical models [15], [16]. These earlier works have shown that such strips can support lamb-like modes.…”
Section: A Lamb Waves and Guided Waves In Finite Width Stripsmentioning
confidence: 99%
“…Speci"cally, Chree [3] in 1889 discussed an approximate dispersion relation for long wavelength modes in an in"nitely long body with an arbitrary cross-section. Later, Morse [4,5] and Kynch and Green [6] examined this problem for rectangular cross-sections. Most of their results pertain to large wavelength vibrations.…”
Section: Introductionmentioning
confidence: 98%