Comment on “Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young's modulus” [J. Acoust. Soc. Am. 132, 2887–2895 (2012)]

2014 ◽  
Vol 135 (3) ◽  
pp. 1031-1033 ◽  
Author(s):  
Philip L. Marston
Keyword(s):  
Wave Propagation ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Mass Density ◽  
Negative Mass ◽  
One Dimensional ◽  
Acoustic Metamaterial ◽  
Anomalous Wave

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

2019 ◽  
Vol 19 (08) ◽  
pp. 1950084 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Young's Modulus ◽  
Mass Density ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Governing Equations ◽  
Direct Integral

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

Characterization of metal-containing amorphous hydrogenated carbon films

1992 ◽  
Vol 7 (3) ◽  
pp. 667-676 ◽  
Author(s):  
M. Wang ◽  
K. Schmidt ◽  
K. Reichelt ◽  
H. Dimigen ◽  
H. Hübsch
Keyword(s):  
Mechanical Properties ◽  
Critical Load ◽  
Young’S Modulus ◽  
Metal Concentration ◽  
Young's Modulus ◽  
Protective Coatings ◽  
Mass Density ◽  
Carbon Films ◽  
Elastic Recoil ◽  
Amorphous Hydrogenated Carbon

Metal-containing amorphous hydrogenated carbon (Me–C: H) films were prepared on silicon substrates. Two kinds of metals (Ti, Ta) were incorporated in the process of reactive rf diode— (13.56 MHz) and DC-magnetron sputtering, respectively. Elastic recoil detection (ERD) and Rutherford backscattering (RBS) of MeV He+ ions were used to determine the hydrogen content and mass density of Me–C: H films. The mechanical properties, i.e., microhardness, Young's modulus, and adhesion, were measured with the help of a nanoindenter and scratch tester. Results show that (1) the mechanical properties of Me–C: H films depend mainly on metal concentrations. At a certain metal concentration, optimal hardness, Young's modulus, and critical load were obtained; (2) the M–C: H films with an optimal metal concentration possess similar hardness, Young's modulus, and higher critical load compared with the corresponding values of diamond-like carbon (a–C: H) films, due to the improvement of the toughness of the films by the incorporation of metals. Therefore, Me–C: H films show high promise of being wear-resistant protective coatings.

Investigation into the Dynamic Fracture Properties of Large Scale Functionally Graded Materials

2006 ◽  
Vol 324-325 ◽  
pp. 239-242 ◽  
Author(s):  
Xiao Bin Yang ◽  
Zhuo Zhuang ◽  
Xue Feng Yao
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Large Scale ◽  
Young's Modulus ◽  
Mass Density ◽  
Poisson's Ratio ◽  
Constant Mass ◽  
Functionally Gradient Materials ◽  
Gradient Materials ◽  
Functionally Gradient

A crack propagation perpendicular to gradient in a large scale functionally gradient materials, which has (1) a linear variation of Young’s modulus with a constant mass density and Poisson’s ratio, and (2) a exponential variation of Young’s modulus with a constant mass density and Poisson’s ratio, is modelled by finite element methods. Based on the experimental result of large scale functionally gradient materials, the dynamic propagation process of the FGMs is modelled and the dynamic parameters, like the energy release rate and crack tip opening angle, are calculated through a generation phase.

scholarly journals Inverse Doppler effect of acoustic metamaterial with negative mass density

2017 ◽  
Vol 66 (2) ◽  
pp. 024301
Author(s):  
Liu Song ◽  
Luo Chun-Rong ◽  
Zhai Shi-Long ◽  
Chen Huai-Jun ◽  
Zhao Xiao-Peng
Keyword(s):  
Doppler Effect ◽  
Mass Density ◽  
Negative Mass ◽  
Acoustic Metamaterial
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