Analytical investigation of the acoustic behavior of nanocomposite porous media by using modified nonlocal Biot’s equations

2017 ◽  
Vol 24 (13) ◽  
pp. 2701-2716 ◽  
Author(s):  
A Hasani Baferani ◽  
AR Ohadi
Keyword(s):  
Porous Media ◽  
Absorption Coefficient ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Analytical Investigation ◽  
Considerable Effect ◽  
Acoustical Properties ◽  
Coefficient Increase ◽  
Biot’S Equations ◽  
Good Agreement

In this paper, the modified Biot’s equations based on nonlocal elasticity theory are presented for modeling nanocomposite porous media. The analytical solution of modified Biot’s equations is obtained by using the recently developed potential function method. By doing some mathematical manipulation, the coupled modified Biot’s equations are converted to two decoupled equations. Consequently, the variations of field variables and acoustical properties of a considered nanocomposite foam are studied by changing the nonlocal parameter. The obtained results show that the local Biot’s results are in good agreement with the nonlocal modified Biot’s results for very small values of the nonlocal parameter. In addition, the values of field variables (i.e. pressure) in the thickness direction are decreased by increasing the nonlocal parameter for frequencies below 5000 Hz. Furthermore, by increasing the nonlocal parameter, the differences between local and nonlocal values of field variables and the absorption coefficient increase. Also, the nonlocal parameter has no considerable effect on the absorption coefficient for frequencies lower than 2000 Hz, whereas by increasing the nonlocal parameter the differences between corresponding results of local and nonlocal theories increase for frequencies above 2000 Hz.

Analytical Solution of Biot's Equations Based on Potential Functions Method

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Abolfazl Hasani Baferani ◽  
Abdolreza Ohadi
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Differential Equations ◽  
Porous Materials ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Potential Functions ◽  
Basic Field ◽  
Acoustical Properties ◽  
Biot’S Equations

In this paper, a new analytical solution for Biot's equations is presented based on potential functions method. The primary coupled Biot's equations have been considered based on fluid and solid displacements in three-dimensional (3D) space. By defining some potential functions, the governing equations have been improved to a simpler form. Then the coupled Biot's equations have been replaced with four-decoupled equations, by doing some mathematical manipulations. For a case study, it is assumed that the incident wave is in xy-plane and for specific boundary conditions; the partial differential equations are converted to ordinary differential equations and solved analytically. Then two foams with different properties have been considered, and acoustical properties of these foams due to the new developed method have been compared with the corresponding results presented by transfer-matrix method. Good agreement between results verifies the new presented solution. Based on the potential function method, not only the acoustical properties of porous materials are calculated, but also the analytical values of all basic field variables, such as pressure, fluid, and solid displacements, are obtained for all points in the porous media. Furthermore, fundamental features, such as damped and undamped natural frequencies, and damping coefficient of porous materials are calculated by considering presented results. The obtained results show that maximum values of field variables, such as pressure, fluid, and solid displacements, happen at the damped natural frequencies of the porous media, as expected. By increasing material thickness, the effect of damping of porous material on damped natural frequency decreases. Damping decreases the first natural frequency of the foam up to 8.5%.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

Chaotic vibrations of carbon nanotubes subjected to a traversing force considering nonlocal elasticity theory

2021 ◽  
pp. 239779142110633
Author(s):  
Reza Ebrahimi
Keyword(s):  
Nonlocal Parameter ◽  
Power Spectra ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Effective Control ◽  
Maximum Lyapunov Exponent ◽  
Harmonic Force ◽  
Spectra Analysis ◽  
Chaotic Vibrations ◽  
Euler Bernoulli Beam

The existence of chaos in the lateral vibration of the carbon nanotube (CNT) can contribute to source of instability and inaccuracy within the nano mechanical systems. So, chaotic vibrations of a simply supported CNT which is subjected to a traversing harmonic force are studied in this paper. The model of the system is formulated by using nonlocal Euler–Bernoulli beam theory. The equation of motion is solved using the Rung–Kutta method. The effects of the nonlocal parameter, velocity and amplitude of the traversing harmonic force on the nonlinear dynamic response of the system are analyzed by the bifurcation diagrams, phase plane portrait, power spectra analysis, Poincaré map and the maximum Lyapunov exponent. The results indicate that the nonlocal parameter, velocity and amplitude of the traversing harmonic force have considerable effects on the bifurcation behavior and can be used as effective control parameters for avoiding chaos.

scholarly journals Study on the sound absorption behavior of multi-component polyester nonwovens: experimental and numerical methods

2018 ◽  
Vol 89 (16) ◽  
pp. 3342-3361 ◽  
Author(s):  
Tao Yang ◽  
Ferina Saati ◽  
Kirill V Horoshenkov ◽  
Xiaoman Xiong ◽  
Kai Yang ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Absorption Coefficient ◽  
Empirical Model ◽  
Surface Impedance ◽  
Sound Absorption ◽  
Low Frequency ◽  
Accurate Method ◽  
Small Error ◽  
Sound Absorption Coefficient ◽  
Acoustical Properties

This study presents an investigation of the acoustical properties of multi-component polyester nonwovens with experimental and numerical methods. Fifteen types of nonwoven samples made with staple, hollow and bi-component polyester fibers were chosen to carry out this study. The AFD300 AcoustiFlow device was employed to measure airflow resistivity. Several models were grouped in theoretical and empirical model categories and used to predict the airflow resistivity. A simple empirical model based on fiber diameter and fabric bulk density was obtained through the power-fitting method. The difference between measured and predicted airflow resistivity was analyzed. The surface impedance and sound absorption coefficient were determined by using a 45 mm Materiacustica impedance tube. Some widely used impedance models were used to predict the acoustical properties. A comparison between measured and predicted values was carried out to determine the most accurate model for multi-component polyester nonwovens. The results show that one of the Tarnow model provides the closest prediction to the measured value, with an error of 12%. The proposed power-fitted empirical model exhibits a very small error of 6.8%. It is shown that the Delany–Bazley and Miki models can accurately predict surface impedance of multi-component polyester nonwovens, but the Komatsu model is less accurate, especially at the low-frequency range. The results indicate that the Miki model is the most accurate method to predict the sound absorption coefficient, with a mean error of 8.39%.

scholarly journals A Meshfree Method for Heat Explosion Problems with Natural Convection in Inclined Porous Media

2018 ◽  
Vol 241 ◽  
pp. 01019 ◽  
Author(s):  
Abdoulhafar Halassi ◽  
Youssef Joundy ◽  
Loubna Salhi ◽  
Ahmed Taik
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Vertical Direction ◽  
Meshfree Method ◽  
Boussinesq Approximation ◽  
Complex Behaviour ◽  
Meshless Collocation ◽  
Darcy Equations ◽  
Small Inclination ◽  
Good Agreement

This paper investigates the interaction between natural convection and heat explosion in porous media. A meshless collocation method based on multiquadric radial basis functions has been applied to study the problem in an inclined two-dimensional porous media. The governing equations consist of coupling the Darcy equations in the Boussinesq approximation of low density variations to the heat equation with a nonlinear chemical source term. The numerical results obtained are in good agreement with some previous studies that consider the vertical direction. A complex behaviour of solutions is observed, including periodic and aperiodic oscillations. We have shown that a small inclination of the container stabilizes the reactive fluid and can prevent thermal explosion.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

A three-parameter analytical model for the acoustical properties of porous media

2019 ◽  
Vol 145 (4) ◽  
pp. 2512-2517 ◽  
Author(s):  
Kirill V. Horoshenkov ◽  
Alistair Hurrell ◽  
Jean-Philippe Groby
Keyword(s):  
Porous Media ◽  
Analytical Model ◽  
Acoustical Properties
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