Wave propagation below the ring frequency on fluid‐loaded cylindrical shells

AbstractThe objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to study a certain long wave propagation problem related to micro-fluctuations of displacement field caused by a periodic structure of the shells. This micro-dynamic problem will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling applied here includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Both these procedures are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. It will be shown that the micro-periodic heterogeneity of the shells leads to exponential micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

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Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading

Journal of Sound and Vibration ◽

10.1016/j.jsv.2003.10.042 ◽

2004 ◽

Vol 278 (3) ◽

pp. 501-526 ◽

Cited By ~ 37

Author(s):

S.V. Sorokin ◽

O.A. Ershova

Keyword(s):

Wave Propagation ◽

Plane Wave ◽

Frequency Band ◽

Cylindrical Shells ◽

Band Gaps ◽

Fluid Loading ◽

Heavy Fluid ◽

Plane Wave Propagation

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Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406218802320 ◽

2018 ◽

Vol 232 (23) ◽

pp. 4342-4356 ◽

Cited By ~ 9

Author(s):

Muzammal Hussain ◽

M Nawaz Naeem ◽

Aamir Shahzad ◽

Mao-Gang He ◽

Siddra Habib

Keyword(s):

Wave Propagation ◽

Natural Frequencies ◽

Volume Fraction ◽

Cylindrical Shells ◽

Functionally Graded ◽

Wave Number ◽

Type I ◽

Rotating Speed ◽

Simply Supported ◽

Fundamental Frequencies

Fundamental natural frequencies of rotating functionally graded cylindrical shells have been calculated through the improved wave propagation approach using three different volume fraction laws. The governing shell equations are obtained from Love’s shell approximations using improved rotating terms and the new equations are obtained in standard eigenvalue problem with wave propagation approach and volume fraction laws. The effects of circumferential wave number, rotating speed, length-to-radius, and thickness-to-radius ratios have been computed with various combinations of axial wave numbers and volume fraction law exponent on the fundamental natural frequencies of nonrotating and rotating functionally graded cylindrical shells using wave propagation approach and volume fraction laws with simply supported edge. In this work, variation of material properties of functionally graded materials is controlled by three volume fraction laws. This process creates a variation in the results of shell frequency. MATLAB programming has been used to determine shell frequencies for traveling mode (backward and forward) rotating motions. New estimations show that the rotating forward and backward simply supported fundamental natural frequencies increases with an increase in circumferential wave number, for Type I and Type II of functionally graded cylindrical shells. The presented results of backward and forward simply supported fundamental natural frequencies corresponding to Law I are higher than Laws II and III for Type I and reverse effects are found for Type II, depending on rotating speed. Our investigations show that the decreasing and increasing behaviors are noted for rotating simply supported fundamental natural frequencies with increasing length-to-radius and thickness-to-radius ratios, respectively. It is found that the fundamental frequencies of the forward waves decrease with the increase in the rotating speed, and the fundamental frequencies of the backward waves increase with the increase in the rotating speed. This investigation has been made with three different volume fraction laws of polynomial (Law I), exponential (Law II), and trigonometric (Law III). The presented numerical results of nonrotating isotropic and rotating functionally graded simply supported are in fair agreement with parts of other earlier numerical results.

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