Free vibrations of thin rectangular nano-plates using wave propagation approach

Ilkhani, Mohammad Reza; Bahrami, Arian; Hosseini-Hashemi, Shahrokh

doi:10.1016/j.apm.2015.06.032

Cited by 28 publications

(12 citation statements)

References 43 publications

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“…Recently, due to the increased application of nanoscale structures like the nano-beam, 5 nano-bar, 6 and nano-plate 7 in technological systems, there has been an increase in demand for understanding the behavior of small-sized materials and structures. One of the procedures for studying the characteristics nano-sized materials and devices is "atomic simulation".…”

Section: Introductionmentioning

confidence: 99%

Exact Size-Dependent Elasticity Solution for Free Radial Vibration of Nano-Sphere

Mirzaei¹

2019

The International Journal of Acoustics and Vibration

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An exact size-dependent elasticity solution based on surface energy theory is used to investigate the free radial vibration behavior of a nanoscale sphere. The Gurtin-Murdoch surface elasticity model is employed to incorporate surface stress terms into pertinent boundary conditions. This leads to frequency equations involving spherical Bessel functions. Extensive numerical calculations have been carried out to illustrate the size effect of the nano-sphere on the first and second dimensionless breathing natural frequencies. The numerical results describe the imperative influence of surface energy and radii ratio on the vibrational characteristic frequency of the nano-sphere. In particular, the surface energy is much more important when the inner radius is smaller than 50 nm.

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Section: Introductionmentioning

confidence: 99%

Exact Size-Dependent Elasticity Solution for Free Radial Vibration of Nano-Sphere

Mirzaei¹

2019

The International Journal of Acoustics and Vibration

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“…Reviewing the above acknowledged literature provides us the clue that there is no research conducted on wave analysis and investigation of the effect of thickness of the plate on wave motion, conversion and reflection in thick plates. In all previously done researches in wave analysis of structures, there were at most two waves [27][28][29][30][31][32][33][34][35][36][37][38] while here there are three waves, and this makes the problem more complicated to analyze. In the present paper, a new analytical approach to analyze the free vibration and wave reflection in thick rectangular plates is presented using wave propagation method.…”

Section: Introductionmentioning

confidence: 99%

Free vibration and wave power reflection in Mindlin rectangular plates via exact wave propagation approach

Sarayi

Bahrami

2018

Composites Part B: Engineering

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Reflection, propagation and energy analysis are crucially important in designing structures, especially plates. A thick plate is considered based on first order shear deformation theory. Wave Propagation Method (WPM) is employed to exactly derive resonant frequencies and wave power reflection from different classical boundary conditions. Firstly, the frequency results are compared with other literatures to validate the exact proposed wave solution in the present work. Then, wave analysis and benchmark results for natural frequencies are presented for six different combinations of boundary conditions. The results indicate that the wave power reflection of thick rectangular plates is quite complicated and an incident wave of a specific type gives rise to other types of waves except for simply supported boundary conditions where the reflected wave power does not depend on the system parameters.

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“…A further discussion concerning the influence of geometric parameters on natural frequencies was also carried out. Ilkhani and Bahrami (2016) considered the free vibration of thin rectangular nano-plates. It can be found that, in the macro scale, the solutions obtained by the wave approach were exactly the same as those calculated by the classical method.…”

Section: Introductionmentioning

confidence: 99%

Transverse vibration analysis of composite thin annular plate by wave approach

Liu

Wang

2017

Journal of Vibration and Control

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In this paper, free vibration and transmission properties of single and composite thin annular plate (TAP) structures are presented by wave approach. The propagation matrix, continuity matrix and reflection matrix are introduced to carry out the analysis. Using the wave approach, natural frequencies of single and composite TAP are calculated theoretically. The results obtained by this method agree well with those calculated by the classical Bessel and Hankel methods. Additionally, transfer matrix is introduced and combined with the boundary conditions to obtain the transmission behaviors of composite multilayer TAP. To thoroughly understand the composite TAP, the influences of thickness, density ratio and radius ratio on natural frequencies are investigated. This study provides very useful information for transverse vibration suppression of TAP structure.

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Free vibrations of thin rectangular nano-plates using wave propagation approach

Cited by 28 publications

References 43 publications

Exact Size-Dependent Elasticity Solution for Free Radial Vibration of Nano-Sphere

Exact Size-Dependent Elasticity Solution for Free Radial Vibration of Nano-Sphere

Free vibration and wave power reflection in Mindlin rectangular plates via exact wave propagation approach

Transverse vibration analysis of composite thin annular plate by wave approach

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