Analytical solutions of thermo-piezoelectric interactions in a solid fiber of polygonal cross-sections immersed in fluid

2018 ◽  
Vol 14 (3) ◽  
pp. 431-456
Author(s):  
Rajendran Selvamani
Keyword(s):  
Mathematical Model ◽  
Phase Velocity ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Fourier Expansion ◽  
Transversely Isotropic ◽  
Cross Sectional ◽  
Content Type ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

Purpose The purpose of this paper is to study the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid using the Fourier expansion collocation method. Design/methodology/approach A mathematical model is developed for the analytical study on a transversely isotropic thermo-piezoelectric polygonal cross-sectional fiber immersed in fluid using a linear form of three-dimensional piezothermoelasticity theories. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the Fourier expansion collocation method (FECM) at the irregular boundary surfaces of the polygonal cross-sectional fiber. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots. Findings From the literature survey, it is evident that the analytical formulation of thermo-piezoelectric interactions in a polygonal cross-sectional fiber contact with fluid is not discussed by any researchers. Also, in this study, a polygonal cross-section is used instead of the traditional circular cross-sections. So, the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid are studied using the FECM. The dispersion curves for non-dimensional frequency, phase velocity and attenuation coefficient are presented graphically for lead zirconate titanate (PZT-5A) material. The present analytical method obtained by the FECM is compared with the finite element method which shows a good agreement with present study. Originality/value This paper contributes the analytical model to find the solution of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid. The dispersion curves of the non-dimensional frequency, phase velocity and attenuation coefficient are more prominent in flexural modes. Also, the surrounding fluid on the various considered wave characteristics is more significant and dispersive in the hexagonal cross-sections. The aspect ratio (a/b) of polygonal cross-sections is critical to industry or other fields which require more flexibility in design of materials with arbitrary cross-sections.

Stress wave analysis of thermo-piezoelectric solid bar of polygonal cross-sections immersed in fluid

2014 ◽  
Vol 10 (4) ◽  
pp. 537-561
Author(s):  
Palaniyandi Ponnusamy
Keyword(s):  
Wave Propagation ◽  
Collocation Method ◽  
Cross Sections ◽  
Fourier Expansion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Dimensional Theory ◽  
Cross Sectional ◽  
Content Type ◽  
Piezoelectric Solid

Purpose – The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle, square, pentagon and hexagon) cross-section immersed in fluid is using Fourier expansion collocation method, with in the frame work of linearized, three-dimensional theory of thermo-piezoelectricity. Design/methodology/approach – A mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sections immersed in fluid is studied using the three-dimensional theory of elasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional bar immersed in fluid. Since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the curved surface of the polygonal bar directly. Hence, the Fourier expansion collocation method is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots. Findings – From the literature survey, it is clear that the free vibration of an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid. Research limitations/implications – Wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes of piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid. Originality/value – The researchers have discussed the wave propagation in thermo-piezoelectric circular cylinders using three-dimensional theory of thermo-piezoelectricity, but, the researchers did not analyzed the wave propagation in an arbitrary/polygonal cross-sectional bar immersed in fluid. So, the author has studied the free vibration analysis of thermo-piezoelectric polygonal (triangle, square, pentagon and hexagon) cross-sectional bar immersed in fluid using three-dimensional theory elasticity. The problem may be extended to any kinds of cross-sections by using the proper geometrical relations.

Influence of mechanical imperfection on the transference of Love-type waves in viscoelastic substrate overloaded by visco-micropolar composite structure

2020 ◽  
Vol 37 (9) ◽  
pp. 3407-3429
Author(s):  
Manisha Maity ◽  
Santimoy Kundu ◽  
Raju Kumhar ◽  
Shishir Gupta
Keyword(s):  
Phase Velocity ◽  
Soil Mechanics ◽  
Equations Of Motion ◽  
Vibrational Analysis ◽  
Content Type ◽  
Separation Of Variable ◽  
The Impact ◽  
Phase Velocity And Attenuation ◽  
Practical Implications ◽  
Stratified Model

Purpose This mathematical analysis has been accomplished for the purpose of understanding the propagation behaviour like phase velocity and attenuation of Love-type waves through visco-micropolar composite Earth’s structure. Design/methodology/approach The considered geometry of this problem involves a micropolar Voigt-type viscoelastic stratum imperfectly bonded to a heterogeneous Voigt-type viscoelastic substratum. With the aid of governing equations of motion of each individual medium and method of separation of variable, the components of micro-rotation and displacement have been obtained. Findings The boundary conditions of the presumed geometry at the free surface and at the interface, together with the obtained components of micro-rotation, displacement and mechanical stresses give rise to the determinant form of the dispersion relation. Moreover, some noteworthy cases have also been extrapolated in detail. Graphical interpretation irradiating the impact of viscoelasticity, micropolarity, heterogeneity and imperfectness on the phase velocity and attenuation of Love-type waves is the principal highlight of the present study. Practical implications In this study, the influence of the considered parameters such as micropolarity, viscoelasticity, heterogeneity, and imperfectness has been elucidated graphically on the phase velocity and attenuation of Love-type waves. It has been noticed from the graphs that with the rising magnitude of micropolarity and heterogeneity, the attenuation curves shift upwards, that is the loss of energy of these waves takes place in a rapid way. Hence, from the outcomes of the present analysis, it can be concluded that heterogeneous micropolar stratified media can serve as a helpful tool in increasing the attenuation or in other words, loss of energy of Love-type waves, thus reducing the devastating behaviour of these waves. Originality/value Till date, the mathematical modelling as well as vibrational analysis of Love-type waves in a viscoelastic substrate overloaded by visco-micropolar composite Earth’s structure with mechanical interfacial imperfection remain unattempted by researchers round the globe. The current analysis is an approach for studying the traversal traits of surface waves (here, Love-type waves) in a realistic stratified model of the Earth’s crust and may thus, serves as a dynamic paraphernalia in various domains like earthquake and geotechnical engineering; exploration geology and soil mechanics and many more, both in a conceptual as well as pragmatic manner.

scholarly journals Effect of Rotation on Wave Propagation in Hollow Poroelastic Circular Cylinder

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
A. M. Abd-Alla ◽  
S. Alqosami
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Phase Velocity ◽  
Frequency Equation ◽  
Wave Number ◽  
Elastic Behavior ◽  
Hollow Circular Cylinder ◽  
Poroelastic Material ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

The objective of this paper is to study the effect of rotation on the wave propagation in an infinite poroelastic hollow circular cylinder. The frequency equation for poroelastic hollow circular cylinder is obtained when the boundaries are stress free and is examined numerically. The frequency, phase velocity, and attenuation coefficient are calculated for a pervious surface for various values of rotation, wave number, and thickness of the cylinder which are presented for nonaxial symmetric vibrations for a pervious surface. The dispersion curves are plotted for the poroelastic elastic behavior of the poroelastic material. Results are discussed for poroelastic material. The results indicate that the effect of rotation, wave number, and thickness on the wave propagation in the hollow poroelastic circular cylinder is very pronounced.

Dispersion study of plane-strain vibrations in poroelastic solid bars with polygonal cross-section

2016 ◽  
Vol 22 (1) ◽  
pp. 38-52 ◽  
Author(s):  
Sandhya Rani Bandari ◽  
Malla Reddy Perati ◽  
Gangadhar Reddy Gangu
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Plane Strain ◽  
Cross Section ◽  
Cross Sections ◽  
Fourier Expansion ◽  
Data Phase ◽  
Base Curve ◽  
Symmetric And Antisymmetric Modes ◽  
Relevant Material

This paper studies wave propagation in a poroelastic solid bar with polygonal cross-section under plane-strain conditions. The boundary conditions on the surface of the cylinder whose base curve is polygon are satisfied by means of the Fourier expansion collocation method. The frequency equations are discussed for both symmetric and antisymmetric modes in the framework of Biot’s theory of poroelastic solids. For illustration purposes, sandstone saturated materials and bony material are considered. The numerical results were computed as the basis of relevant material data . Phase velocity is computed against the wavenumber for various cross-sections and results are presented graphically.

scholarly journals Phase Velocity and Attenuation of Longitudinal Shear Vibrations of Hollow Poroelastic Cylinders

2014 ◽  
Vol 19 (2) ◽  
pp. 337-346
Author(s):  
S. Ahmed Shah ◽  
S. Javvad Hussaini
Keyword(s):  
Cylindrical Shell ◽  
Phase Velocity ◽  
Longitudinal Shear ◽  
Frequency Equation ◽  
Circular Cylinders ◽  
Physical Parameters ◽  
Flexural Mode ◽  
Second Mode ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

Abstract The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

Vulnerability of different nerves to intrafascicular injection by different needle types and at different approach angles: a mathematical model

2020 ◽  
Vol 45 (4) ◽  
pp. 306-310
Author(s):  
Margarita Sanromán-Junquera ◽  
Andre Boezaart ◽  
Yury Zasimovich ◽  
Olga C Nin ◽  
Xavier Sala-Blanch ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cross Sections ◽  
Longitudinal Axis ◽  
Needle Insertion ◽  
Nerve Roots ◽  
Nerve Blocks ◽  
Cross Sectional ◽  
Peripheral Nerve Blocks ◽  
Microscopic Images ◽  
Insertion Angle

Background and objectivesWe assume that intrafascicular spread of a solution can only occur if a large enough portion of the distal needle orifice is placed inside the fascicle. Our aim is to present and evaluate a mathematical model that can calculate the theoretical vulnerability of fascicles, analyzing the degree of occupancy of the needle orifice in fascicular tissue by performing simulations of multiple positions that a needle orifice can take inside a cross-sectional nerve area.MethodsWe superimposed microscopic images of two routinely used nerve block needles (22-gauge, 15° needle and 22-gauge, 30° needle) over the microscopic images of cross-sections of four nerve types photographed at the same magnification. Fascicular tissue that was overlapped between 80% and 100% by a needle orifice was considered at risk to possible intrafascicular injection. The effect of three angular approaches was evaluated.ResultsThere were statistical differences between the vulnerability of fascicular tissue depending on nerve type, the bevel angle of the needle and the angle approach. Fascicular vulnerability was greater in nerve roots of the brachial plexus after using a 22-gauge 30° needle, as was choosing a 45° angle approach to the longitudinal axis of the nerve.ConclusionsOur results suggest that clinicians may want to consider needle insertion angle and bevel type as they perform peripheral nerve blocks. Furthermore, researchers may want to consider this mathematical model when estimating vulnerabilities of various nerves, needle types and angles of approach of needles to nerves.

Tensile strength of partially filled FFF printed parts: meta modelling

2017 ◽  
Vol 23 (3) ◽  
pp. 524-533 ◽  
Author(s):  
Shahrain Mahmood ◽  
A.J. Qureshi ◽  
Kheng Lim Goh ◽  
Didier Talamona
Keyword(s):  
Mathematical Model ◽  
Tensile Strength ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Fused Filament Fabrication ◽  
Cross Sectional ◽  
Content Type ◽  
Test Pieces ◽  
Solid Part ◽  
The Cross

Purpose This paper aims to investigate the tensile strength of partially filled fused filament fabrication (FFF) printed parts with respect of cross-sectional geometry of partially filled test pieces. It was reported in the authors’ earlier work that the ultimate tensile strength (UTS) is inversely proportional to the cross-sectional area of a specimen, whereas the number of shells and infill density are directly proportional to the UTS with all other parameters being held constant. Here, the authors present an in-depth evaluation of the phenomenon and a parametric model that can provide useful estimates of the UTS of the printed part by accounting for the dimensions of the solid floor/roof layers, shells and infills. Design/methodology/approach It was found that partially filled FFF printed parts consist of hollow sections. Because of these voids, the conventional method of determining the UTS via the gross cross-sectional area given by A = b × h, where b and h are the width and thickness of the printed part, respectively, cannot be used. A mathematical model of a more accurate representation of the cross-sectional area of a partially filled part was formulated. Additionally, the model was extended to predict the dimensions as well as the lateral distortion of the respective features within a printed part using input values from the experimental data. Findings The result from this investigation shows that to calculate the UTS of a partially filled FFF part, the calculation based on the conventional approach is not sufficient. A new meta-model is proposed which takes into account the geometry of the internal features to give an estimate of the strength of a partially filled printed part that is closer to the value of the strength of the material that is used for fabricating the part. Originality/value This paper investigates the tensile strength of a partially filled FFF printed part. The results have shown that the tensile strength of a partially filled part can be similar to that of a solid part, at a lower cost: shorter printing time and lower material usage. By taking into account the geometries within a printed part, the cross-sectional area can be accurately represented. The mathematical model which was developed would aid end-users to predict the tensile strength for a given set of input values of the process parameters.

Rayleigh waves in generalized thermoelastic medium with mass diffusion

2015 ◽  
Vol 93 (10) ◽  
pp. 1039-1049 ◽  
Author(s):  
Rajneesh Kumar ◽  
Vandana Gupta
Keyword(s):  
Mathematical Model ◽  
Phase Velocity ◽  
Rayleigh Waves ◽  
Polynomial Equation ◽  
Mass Diffusion ◽  
Thermoelastic Medium ◽  
Special Cases ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Phase Velocity And Attenuation

This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic generalized thermoelastic solid half space with mass diffusion in the context of the Lord–Shulman (Lord and Shulman. J. Mech. Phys. Solids. 15, 299 (1967)) and Green–Lindsay (Green and Lindsay. J. Elasticity. 2, 1 (1972)) theories of thermoelasticity. The medium is subjected to stress-free, isothermal, isoconcentrated boundary. After developing a mathematical model, the dispersion curve in the form of a polynomial equation is obtained. The roots of this polynomial equation are verified for not satisfying the original dispersion equation and therefore are filtered out and the remaining roots are checked with the property of decay with depth. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. The behavior of the particle motion is studied for the propagation of Rayleigh waves under Lord–Shulman model. Some special cases are also deduced from the present investigation.

Performance investigation of micro-pocketed textured pad thrust bearing

2018 ◽  
Vol 70 (8) ◽  
pp. 1388-1395 ◽  
Author(s):  
Shipra Aggarwal ◽  
R.K. Pandey
Keyword(s):  
Coefficient Of Friction ◽  
Cross Sections ◽  
Carrying Capacity ◽  
Thrust Bearing ◽  
Load Carrying Capacity ◽  
Temperature Relation ◽  
Cross Sectional ◽  
Content Type ◽  
Load Carrying ◽  
Coupled Solution

Purpose The purpose of this paper is to conceive a new surface texture incorporating a tiny shape among the micro-pockets (with circular, rectangular, trapezoidal and triangular cross-sections) and dimples (cylindrical, hemispherical and ellipsoidal) for exploring to enhance the maximum possible performance behaviors of sector shape pad thrust bearing. Design/methodology/approach Numerical simulation of hydrodynamically lubricated sector shape textured pad thrust bearing has been presented incorporating thermal and cavitation effects. The coupled solution of governing equations (Reynolds equation, film thickness expression, viscosity–temperature relation, energy equation and Laplace equation) has been achieved using finite difference method and Gauss–Seidel iterative scheme. Findings With new textured pads, higher load-carrying capacity and lower coefficient of friction are obtained in comparison to plain sector shape pad. Texture pattern comprising square cross-sectional pockets yields higher load-carrying capacity and lower coefficient of friction in comparison to other cross-sectional shapes (circular, trapezoidal and triangular) of pockets considered herein. Originality/value This study reports a new texture, which involves micro-pockets of square cross-sectional shapes to improve the performance behavior of sector shape pad thrust bearing. About 75 per cent increase in load carrying capacity and 42 per cent reduction in coefficient of friction have been achieved with pad having new texture in comparison to conventional pad.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Latha Madhuri Poonem ◽  
Rajitha Gurijala ◽  
Sindhuja Ala ◽  
Malla Reddy Perati
Keyword(s):  
Phase Velocity ◽  
Initial Stress ◽  
Half Space ◽  
Frequency Equation ◽  
Poroelastic Medium ◽  
Content Type ◽  
Torsional Waves ◽  
Reinforcement Parameter ◽  
Dry Sand ◽  
Phase Velocity And Attenuation

PurposeThe purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.Design/methodology/approachTorsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.FindingsPhase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.Originality/valueInitial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

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