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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 literature 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. [ABSTRACT FROM AUTHOR]

In this paper, the wave propagation method and the differential constitutive law consequent (not equivalent) to the Eringen strain-driven integral nonlocal elasticity model are utilized to analyze the free vibration, wave power transmission and reflection in multi-cracked nanorods. This aim is pursued by deriving the propagation, reflection and transmission matrices and comparing the natural frequencies obtained by these matrices with the available results in the literature. Then, the nonlocal, crack-severity, and crack location effects on the natural frequencies are presented for two combinations of the boundary conditions. Finally, the paper presents the effects that the reflected and transmitted power of a wave incident on a crack location receive from the nonlocal and crack-severity parameters. The results obtained via the reflection and transmission matrices will provide valuable insights into the subject of wave power reflection and transmission analysis in nanoscale structures for the future. The computer coding of the proposed method is much easier than the classical vibration analysis methods which makes it more appropriate in implementation. [ABSTRACT FROM AUTHOR]

In this paper, the wave propagation method and the nonlocal elasticity theory are utilized to analyze the vibration, wave power transmission and reflection in multi-cracked Euler-Bernoulli nanobeams. This aim is pursued by deriving the propagation, reflection and transmission matrices and comparing the natural frequencies obtained by these matrices with the available results in the literature. Then, the nonlocal and crack-severity effects on the natural frequencies are presented for some combinations of the boundary conditions. Finally, the effects of nonlocal and crack-severity parameters on the reflected and transmitted power of a wave incident upon a crack location are studied in details for cracked nanobeams. The results obtained via the reflection and transmission matrices will provide valuable insights into the subject of wave power reflection and transmission analysis in nanoscale structures for the future. The computer coding of the proposed method is much easier than the classical vibration analysis methods for similar analyses which makes it more appropriate in implementation. [ABSTRACT FROM AUTHOR]

In this paper, the wave propagation technique is developed for analyzing the wave power reflection in circular annular nanoplates. Firstly, the propagation and reflection matrices are derived for circular annular nanoplates. Then, the obtained natural frequencies by these matrices are compared with the available literature. A set of natural frequency results is provided in a practical range of small scale for all nine possible combinations of classical boundary conditions. Finally, the effect of small scale on the reflected power of an incident wave upon different boundary conditions is investigated in details for circular annular nanoplates. The obtained hints via these matrices are valuable for future works correlated with wave power reflection and transmission in nanoscale structures. [ABSTRACT FROM AUTHOR]

This paper presents the wave propagation approach for analyzing the free vibration and wave reflection in carbon nanotubes. The propagation and reflection matrices obtained by the wave propagation method are useful for the analysis of mechanical energy transmission and reflection in micro/nano devices. These matrices can also be used for obtaining the natural frequencies of carbon nanotubes. Firstly, the obtained natural frequencies by this method are compared with the results in the literature. Then, the effect of small scale on the reflected power of an incident wave upon different boundary conditions is studied in details. It was found that the reflected power of an incident wave upon a simply supported boundary is independent of the small scale, incident wave frequency, material and geometrical parameters of the carbon nanotubes while the reflected power of a wave upon clamped and free boundary conditions depends on the small scale, incident wave frequency, material and geometrical parameters. [ABSTRACT FROM AUTHOR]

In this paper, the wave propagation approach is combined with nonlocal elasticity theory to analyze the buckling and free vibrations of Euler–Bernoulli nanobeams. This method gives the propagation and reflection matrices which are useful for the analysis of mechanical energy transmission and reflection in micro/nano devices. Firstly, the propagation and reflection matrices for nanobeams are derived. Then, these matrices are combined to provide a concise and exact approach for obtaining the natural frequencies of the nanobeams for any possible combination of boundary conditions. Then, the natural frequencies obtained by this method are compared with the results in the literature and a set of benchmark results is presented for any combination of boundary conditions in a practical range of nonlocal parameter and axial preload parameter. Finally, the effect of nonlocal and preload parameters on the reflected power of an incident wave upon different boundary conditions is studied in details for the first time. [ABSTRACT FROM AUTHOR]

Wave propagation is one of the famous approaches for analyzing the vibration of solid structures. Literature reviews show that most bodies analyzed with this approach are one-dimensional waveguide structures. In this paper, the free vibration of annular circular and sectorial membranes are analyzed using the wave propagation approach. Firstly, the propagation and reflection matrices are derived. Then, a concise and systematic approach for obtaining the natural frequencies is presented which can be a reference for future studies. The solution obtained by this method is exactly the same as those derived by the classical method. [ABSTRACT FROM AUTHOR]