Natural Frequency of Plates and Shells

Blevins, Robert D.

doi:10.1002/9781119038122.ch5

Cited by 3 publications

(1 citation statement)

References 118 publications

(92 reference statements)

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“…Comparison with previous authors shows some minor difference, for example, the differences for first 4 frequencies with classic work of Leissa A.W. [10], Blevins recent handbook [22], where old results of Durvasula S. [23] are used there, Gorman D. [24] is confined withing 0.03%. Of course, this is not a big difference, but it is interesting to know which results are more exact.…”

Section: Static Centric Loadingmentioning

confidence: 64%

Application of exponential functions in weighted residuals method in structural mechanics. Part II: static and vibration analysis of rectangular plate

Bai¹,

Оrynyak²

2021

M&AT

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The paper is continuation of our efforts on application of the properly constructed sets of exponential functions as the trial (basic) functions in weighted residuals method, WRM, on example of classical tasks of structural mechanics. The purpose of this paper is justification of new method’s efficiency as opposed to getting new results. So, static deformation and free vibration of isotropic thin – walled plate are considered here. Another peculiarity of paper is choice of weight (test) functions, where three options are investigated: it is the same as trial one (Galerkin method); it is taken as results of application of differential operator to trial function (least square method); it equals to the second derivative of trial function with respect to both x and y coordinate (moment method). Solution is considered as product of two independent sets of functions with respect to x or y coordinates. Each set is the combination of five consequent exponential functions, where coefficient at first function is equal to one, and four other coefficients are to satisfy two boundary conditions at each opposite boundary. The only arbitrary value in this method is the scaling factor at exponents, the reasonable range of which was carefully investigated and was shown to have a negligible impact on results. Static deformation was investigated on example of simple supported plate when outer loading is either symmetrical and concentrated near the center or is shifted to any corner point. It was demonstrated that results converge to correct solution much quickly than in classical Navier method, while moment method seems to be a best choice. Then method was applied to free vibration analysis, and again the accuracy of results on frequencies and mode shape were excellent even at small number of terms. At last the vibration of relatively complicated case of clamped – clamped plate was analyzed and very encouraged results as to efficiency and accuracy were achieved.

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Section: Static Centric Loadingmentioning

confidence: 64%

Application of exponential functions in weighted residuals method in structural mechanics. Part II: static and vibration analysis of rectangular plate

Bai¹,

Оrynyak²

2021

M&AT

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Influence of the plate thickness on the frequency of its natural vibration

Leontiev

Balandina

2021

IOP Conf. Ser.: Mater. Sci. Eng.

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Effectiveness of nonporous windscreens for infrasonic measurements

Lanfranchi¹,

Hayot²,

Denis³

2016

The Journal of the Acoustical Society of America

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This paper deals with nonporous windscreens used for reducing noise in infrasonic measurements. A model of sound transmission using a modal approach is derived. The system is a square plate coupled with a cavity. The model agrees with finite element simulations and measurements performed on two windscreens: a cubic windscreen using a material recommended by Shams, Zuckerwar, and Sealey [J. Acoust. Soc. Am. 118, 1335-1340 (2005)] and an optimized flat windscreen made out of aluminum. Only the latter was found to couple acoustical waves below 10 Hz without any attenuation. Moreover, wind noise reduction measurements show that nonporous windscreens perform similarly as a pipe array by averaging the pressure fluctuations. These results question the assumptions of Shams et al. and Zuckerwar [J. Acoust. Soc. Am. 127, 3327-3334 (2010)] about compact nonporous windscreens design and effectiveness.

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Natural Frequency of Plates and Shells

Cited by 3 publications

References 118 publications

Application of exponential functions in weighted residuals method in structural mechanics. Part II: static and vibration analysis of rectangular plate

Application of exponential functions in weighted residuals method in structural mechanics. Part II: static and vibration analysis of rectangular plate

Influence of the plate thickness on the frequency of its natural vibration

Effectiveness of nonporous windscreens for infrasonic measurements

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