A Comprehensive Analysis on the Structural–Acoustic Aspects of Various Functionally Graded Plates

2015 ◽  
Vol 07 (05) ◽  
pp. 1550072 ◽  
Author(s):  
N. Chandra ◽  
S. Raja ◽  
K. V. N. Gopal
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Transmission Loss ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Radiation Efficiency ◽  
Sound Power ◽  
Acoustic Behavior ◽  
Acoustic Response ◽  
Plate Velocity

The vibration, sound radiation and transmission characteristics of plates with various functionally graded materials (FGM) are explored and a detailed investigation is presented on the influence of specific material properties on structural–acoustic behavior. An improved model based on a simplified first order shear deformation theory along with a near-field elemental radiator approach is used to predict the radiated acoustic field associated with a given vibration and acoustic excitation. Various ceramic materials suitable for engineering applications are considered with aluminum as the base metal. A power law is used for the volume fraction distribution of the two constitutive materials and the effective modulus is obtained using the Mori–Tanaka homogenization scheme. The structural–acoustic response of these FGM plates is presented in terms of the plate velocity, radiated sound power, sound radiation efficiency for point and uniformly distributed load cases. Increase in both vibration and acoustic response with increase in power law index is observed for the lower order modes. The vibro–acoustic metrics such as root-mean-squared plate velocity, overall sound power, frequency averaged radiation efficiency and transmission loss, are used to rank these materials for vibro–acoustically efficient combination. Detailed analysis has been made on the factors influencing the structural–acoustic behavior of various FGM plates and relative ranking of particular ceramic/metal combinations.

scholarly journals Optimization of Natural Frequencies and Sound Power of Beams Using Functionally Graded Material

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Nabeel T. Alshabatat ◽  
Koorosh Naghshineh
Keyword(s):  
Volume Fraction ◽  
Optimization Technique ◽  
Sound Radiation ◽  
Optimization Procedure ◽  
Functionally Graded ◽  
Lumped Parameter Model ◽  
Acoustic Properties ◽  
Sound Power ◽  
Material Distribution ◽  
Fgm Beam

This paper presents a design method to optimize the material distribution of functionally graded beams with respect to some vibration and acoustic properties. The change of the material distribution through the beam length alters the stiffness and the mass of the beam. This can be used to alter a specific beam natural frequency. It can also be used to reduce the sound power radiated from the vibrating beam. Two novel volume fraction laws are used to describe the material volume distributions through the length of the FGM beam. The proposed method couples the finite element method (for the modal and harmonic analysis), Lumped Parameter Model (for calculating the power of sound radiation), and an optimization technique based on Genetic Algorithm. As a demonstration of this technique, the optimization procedure is applied to maximize the fundamental frequency of FGM cantilever and clamped beams and to minimize the sound radiation from vibrating clamped FGM beam at a specific frequency.

scholarly journals A Comparison of Vibroacoustic Response of Isotropic Plate with Attached Discrete Patches and Point Masses Having Different Thickness Variation with Different Taper Ratios

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Bipin Kumar ◽  
Vinayak Ranjan ◽  
Mohammad Sikandar Azam ◽  
Piyush Pratap Singh ◽  
Pawan Mishra ◽  
...  
Keyword(s):  
Power Level ◽  
Low Frequency ◽  
Sound Radiation ◽  
Radiation Efficiency ◽  
Thickness Variation ◽  
Sound Power ◽  
Sound Power Level ◽  
Radiation Behavior ◽  
Thickness Variations ◽  
Different Thickness

A comparison of sound radiation behavior of plate in air medium with attached discrete patches/point masses having different thickness variations with different taper ratio of 0.3, 0.6, and 0.9 is analysed. Finite element method is used to find the vibration characteristics while Rayleigh integral is used to predict the sound radiation characteristics. Minimum peak sound power level obtained is at a taper ratio of 0.6 with parabolic increasing-decreasing thickness variation for plate with four discrete patches. At higher taper ratio, linearly increasing-decreasing thickness variation is another alternative for minimum peak sound power level suppression with discrete patches. It is found that, in low frequency range, average radiation efficiency remains almost the same, but near first peak, four patches or four point masses cause increase in average radiation efficiency; that is, redistribution of point masses/patches does have effect on average radiation efficiency at a given taper ratio.

scholarly journals Optimum response of functionally graded piezoelectric plates in thermal environments

2017 ◽  
Vol 35 (3) ◽  
pp. 606-617 ◽  
Author(s):  
Hossein Nourmohammadi ◽  
Bashir Behjat
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Sensors And Actuators ◽  
Thermal Environments ◽  
Functionally Graded Piezoelectric ◽  
Power Law Index

AbstractIn this article, the static response of the functionally graded piezoelectric (FGP) plates with piezoelectric layers (sandwich FGPM) is studied based on the first order shear deformation plate theory. The plate is under mechanical, electrical and thermal loadings and finite element method is employed to obtain the solution of the equation. All mechanical, thermal and piezoelectric properties, except Poisson ratio, obey the power law distribution through the thickness. By solving the governing equation, optimum value of power law index is investigated in each type of loading. The effects of different volume fraction index, layer arrangements, various boundary conditions and different loading types, are studied on the deflection of FGPM plate. It is inferred that, the correlations between the deflection, power law index and layer arrangement are completely different in the mechanical and thermal loading and the optimum value of the power law index should be selected in each case separately. This optimum values can be used as a design criterion to build a reliable sensors and actuators in thermal environments.

Sound Radiation Characteristics of Lightweight Roof Constructions Excited by Rain

1994 ◽  
Vol 1 (4) ◽  
pp. 249-270 ◽  
Author(s):  
Hiromi Suga ◽  
Hideki Tachibana
Keyword(s):  
Transmission Loss ◽  
Power Level ◽  
Sound Radiation ◽  
Sound Intensity ◽  
Sound Power ◽  
Radiation Characteristics ◽  
Natural Rainfall ◽  
Artificial Rainfall ◽  
Sound Power Level ◽  
Measurement Results

In order to investigate the sound radiation characteristics of lightweight roof constructions when excited by rainfall, an artificial rainfall apparatus was constructed to simulate natural rainfall conditions. From the measurement results, it can be seen that the facility developed is practically applicable for the examination of the sound radiation characteristics of rain noise. It was therefore used in the measurement of sound power of 20 lightweight roofs. In addition, the relationship between sound power level and sound transmission loss measured by the sound intensity method was investigated statistically. As a result, it has been shown that a linear relationship exists between them and there is a possibility of estimating the sound power level from the transmission loss.

scholarly journals Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

2020 ◽  
Vol 10 (22) ◽  
pp. 8197
Author(s):  
Prabhakar Sathujoda ◽  
Aneesh Batchu ◽  
Bharath Obalareddy ◽  
Giacomo Canale ◽  
Angelo Maligno ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Power Law ◽  
Inner Core ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Linear Temperature ◽  
Volume Fractions ◽  
Rotor Bearing ◽  
Bearing System

The present work deals with natural and whirl frequency analysis of a porous functionally graded (FG) rotor–bearing system using the finite element method (FEM). Stiffness, mass and gyroscopic matrices are derived for porous and non-porous FG shafts by developing a novel two-noded porous FG shaft element using Timoshenko beam theory (TBT), considering the effects of translational inertia, rotatory inertia, gyroscopic moments and shear deformation. A functionally graded shaft whose inner core is comprised of stainless steel (SS) and an outer layer made of ceramic (ZrO2) is considered. The effects of porosity on the volume fractions and the material properties are modelled using a porosity index. The non-linear temperature distribution (NLTD) method based on the Fourier law of heat conduction is used for the temperature distribution in the radial direction. The natural and whirl frequencies of the porous and non-porous FG rotor systems have been computed for different power law indices, volume fractions of porosity and thermal gradients to investigate the influence of porosity on fundamental frequencies. It has been found that the power law index, volume fraction of porosity and thermal gradient have a significant influence on the natural and whirl frequencies of the FG rotor–bearing system.

scholarly journals Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

Semi-Analytical Approach in Buckling Analysis of Functionally Graded Shells of Revolution Subjected to Displacement Dependent Pressure

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Majid Khayat ◽  
Davood Poorveis ◽  
Shapour Moradi
Keyword(s):  
Power Law ◽  
Stiffness Matrix ◽  
Lateral Pressure ◽  
Volume Fraction ◽  
Numerical Study ◽  
Middle Surface ◽  
Reduction Factor ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Shells Of Revolution

Linearized buckling analysis of functionally graded shells of revolution subjected to displacement-dependent pressure, which remains normal to the shell's middle surface throughout the deformation process, is described in this work. Material properties are assumed to be varied continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of a ceramic and a metal. The governing equations are derived based on the first-order shear deformation theory, which accounts for through the thickness shear flexibility with Sanders type of kinematic nonlinearity. Displacements and rotations in the shell's middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, also known as the pressure stiffness matrix, which accounts for the variation of load direction, is derived for each strip and after assembling resulted in the global load stiffness matrix of the shell, which may be unsymmetric. The load stiffness matrix can be divided into two unsymmetric parts (i.e., load nonuniformity and unconstrained boundary effects) and a symmetric part. The main part of this research is to quantify the effects of these unsymmetries on the follower action of lateral pressure. A detailed numerical study is carried out to assess the influence of various parameters such as power law index of functionally graded material (FGM) and shell geometry interaction with load distribution, and shell boundary conditions on the follower buckling pressure reduction factor. The results indicate that, when applied individually, unconstrained boundary effect and longitudinal nonuniformity of lateral pressure have little effect on the follower buckling reduction factor, but when combined with each other and with circumferentially loading nonuniformity, intensify this effect.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

Characteristics of Power Law and Sigmoid FGMs Models in Thermal Effect

2016 ◽  
Vol 829 ◽  
pp. 90-94
Author(s):  
Seok Hyeon Kang ◽  
Ji Hwan Kim
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Virtual Work Principle ◽  
Temperature Dependent Properties

In thermal environment, vibration behavior of Functionally Graded Materials (FGMs) plates is investigated, and the materials are developed with mixing ceramic and metal. Present study is based on the first-order shear deformation theory of plate. Then, mixture methods such as Power law (P-) and Sigmoid (S-) models are chosen. According to a volume fraction, the material properties are assumed to vary continuously through the thickness direction and to be temperature dependent properties. Further, thermal effects are considered as uniform temperature rise and one dimensional heat transfer. For the structure analysis, FEM is used to obtain the natural frequencies based on the virtual work principle.

Mechanical buckling of cylindrical shells with varying material properties

2010 ◽  
Vol 224 (8) ◽  
pp. 1551-1557 ◽  
Author(s):  
P Khazaeinejad ◽  
M M Najafizadeh
Keyword(s):  
Exponential Function ◽  
Power Law ◽  
Material Properties ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Buckling Loads ◽  
Young’S Moduli ◽  
Wave Numbers

The analytical solutions of the first-order shear deformation theory are developed to study the buckling behaviour of functionally graded (FG) cylindrical shells under three types of mechanical loads. The Poisson's ratios of the FG cylindrical shells are assumed to be constant, while the Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents given by power-law or exponential function. The stability equations are employed to obtain the closed-form solutions for critical buckling loads of each loading case. The dependence of the critical buckling loads on the variations of the material properties with a power-law or exponential function is studied. It is observed that these effects change appreciably the critical buckling loads. Results for critical loads are tabulated for thin and moderately thick shells. Although the critical buckling load of FG cylindrical shells decreases as the circumferential wave numbers increase, it rises for axially compressed long shells as the longitudinal wave numbers increase.

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