Displacement fields of a Cuboid crystal in a Photoacoustic Cell: Mathematical aspects

2021 ◽  
Vol 101 (1) ◽  
pp. 6-11
Author(s):  
A.P. Sarode ◽  
◽  
O.H. Mahajan ◽  
Keyword(s):  
Displacement Field ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Solid State Physics ◽  
Photoacoustic Cell ◽  
Displacement Fields ◽  
Transform Method ◽  
Premature Failure ◽  
Acoustic Effect ◽  
Photoacoustic Effect

Photo acoustic effect is popular due to a minimal sample preparation during execution, the ability to examine scattering and opaque sample along with the capability to access depth profile. These features enable Photoacoustic spectroscopy to be used in depth-resolved characterization of solids. Thermal interaction is a basic perspective in solid state physics research regarding industrial devices and components. It is a key factor of fabrication and performance of such devices and components. Today, crystalline solids are widely studied due to their wide scientific and industrial applications. Displacement field resulting in thermal stresses is one of the important aspects of premature failure of industrial components and devices. In this paper, displacement fields in photoacoustic effect with solid cuboid crystal are mathematically presented. According to our opinion, displacement fields in photoacoustic effect in three dimensional analysis are not reported earlier. Hence that will be a major contribution of this paper. For a simple cuboid homogeneous crystal kept in a photoacoustic cell, an airy stress function is determined based on laser interaction with surface of the crystal. By applying the finite Marchi-Fasulo integral transform method within the crystal size limitations, displacement field is exactly determined.

scholarly journals Theoretical aspects of transient temperature on cubic crystal surface in a photoacoustic effect

2020 ◽  
Vol 99 (3) ◽  
pp. 73-79
Author(s):  
A.P. Sarode ◽  
◽  
O.H. Mahajan ◽  
Keyword(s):  
Integral Transform ◽  
Crystal Surface ◽  
Solid Sample ◽  
Transient Temperature ◽  
Relaxation Processes ◽  
Photoacoustic Cell ◽  
Radiative Relaxation ◽  
Cubic Crystal ◽  
Photoacoustic Effect ◽  
Translational Temperature

In photoacoustic effect, the solid sample absorbs a fraction of the radiation falling upon it and excitation process occurs. The type of excitation depends on the energy of the incident radiation. The relaxation processes, which are also popularly known as non-radiative de-excitation processes generally take place. The light – matter interaction is responsible for the generation of heat within the solid sample. The temperature of the sample changes due to absorption and non-radiative relaxation by the atoms. The pressure fluctuations will be generated due to the heating and cooling of the sample. Today, crystalline solids are widely studied due to their wide scientific and industrial applications. Temperature is one of the important parameter to be studied regarding artificial preparation of large crystals. In this paper, transient translational temperature on the surface of a homogeneous isotropic cubic crystal kept in a photoacoustic cell is calculated theoretically. For a simple cubic homogeneous crystal kept in a photoacoustic cell, an airy stress function is determined based on laser interaction with surface of the crystal. By applying the finite Marchi-Fasulo integral transform method within the crystal size limitations, transient translational temperature is exactly determined.

On some steady state thermoelastic stress distributions in a slab

1965 ◽  
Vol 14 (4) ◽  
pp. 303-310 ◽  
Author(s):  
R. Shail
Keyword(s):  
Steady State ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Displacement Vector ◽  
Scalar Potential ◽  
Thermoelastic Stress ◽  
Fourier Integral ◽  
Elastic Half Space ◽  
Transform Method ◽  
Plane State

The calculation of the steady state thermal stresses in an isotropic elastic half space or slab with traction free faces has been the subject of several investigations. Steinberg and McDowell (1), using an extension of the Bousinesq-Papkowitch method of isothermal elasticity, first derived the now well-known result that in such a body which contains no heat sources there exists a plane state of stress parallel to the boundary planes. Sneddon and Lockett (2) approached this class of problems by direct solution of the equations of thermoelasticity using a double Fourier integral transform method, the results being transformed to Hankel type integrals in the case of axial symmetry. A further approach due to Nowinski (3) exploits the fact that in steady state thermoelasticity each component of the displacement vector is a biharmonic function which can be expressed as a combination of harmonics. However, possibly the most economical method of solution of this type of problem is that of Williams (4) who expressed the displacement vector in terms of two scalar potential functions, one of which is directly related to the temperature field. The same principle has also been used by Fox (5) in treating thermoelastic distributions in a slab containing a spherical cavity.

The Study in the Displacement Field near Crack of the Plexiglass by Frequency Domination Method of the White Speckle

2006 ◽  
Vol 306-308 ◽  
pp. 357-362 ◽  
Author(s):  
Xin Hua Ji ◽  
Fang Yu Xu ◽  
Jin Long Chen ◽  
Yu Wen Qin
Keyword(s):  
Light Source ◽  
Displacement Field ◽  
Vibration Isolation ◽  
Laser Speckle ◽  
Displacement Fields ◽  
Fracture Properties ◽  
Normal Environment

The fracture properties of Plexiglass bright the attentions of the researchers as it is the import material used in aero-planes industry The white speckle technique could obtain displacement fields nondestructively under the normal environment. Compare to the laser speckle method there are no interference light source and the vibration isolation needed. In the paper the principle of the technique is described and the displacement field near crack and SIF are measured. The results show that the technique is very suitable to the application in industry.

Reflection of an Acoustic Step Wave From an Elastic Cylinder

1958 ◽  
Vol 25 (1) ◽  
pp. 103-108
Author(s):  
Richard Skalak ◽  
M. B. Friedman
Keyword(s):  
Integral Transform ◽  
Formal Solution ◽  
Elastic Cylinder ◽  
Transform Method ◽  
Pressure Fields ◽  
Plane Step ◽  
Single Integral ◽  
Short Time ◽  
Acoustic Fluid

Abstract An elastic cylinder, circular in section and infinite in length, is considered in an infinite acoustic fluid. The object of this paper is the determination of the reflected and diffracted pressure fields at large distances resulting from a plane step wave of pressure impinging on the cylinder and moving in a direction normal to the axis of the cylinder. A formal solution is obtained for the general case of an elastic cylinder. Numerical results are computed for rigid, fixed cylinders, and for rigid, floating cylinders. Two different methods are used to achieve results in the different ranges of time which are of interest. A short time approximation is developed by the use of a double integral-transform method. A mode approach and a single integral transform are used for later times. The results show that the reflected pulse decays quickly, within a time on the order of the transit time of the original wave across the cylinder.

Comprehending Occurrence of Premature Failure in Compressor Turbine (CT) Blades for Short-Haul Aircraft Fleet

2019 ◽  
Vol 42 ◽  
pp. 10-23
Author(s):  
Joshua Kimtai Ngoret ◽  
Venkata Parasuram Kommula
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
High Pressure ◽  
Thermal Stresses ◽  
Geometrical Model ◽  
Mechanical Stresses ◽  
Element Analysis ◽  
Premature Failure ◽  
Structural Stresses ◽  
Transient Thermal

This paper presents results from modeling of Compressor Turbine (CT) blades for short-haul aircraft fleet occasioned by thermo-mechanical stresses in order to comprehend the occurrence of premature failure. A 3D PT6A-114A engine high pressure (HP) CT blade geometrical model was developed in commercial CAD-SolidWorks, then imported to ANSYS 15.0 environment for finite element analysis (FEA). The CT blade was investigated for transient thermal stresses from heat generated by the combustors and static structural stresses from rotational velocities of the engine which account for 80% of inertial field during flight. The results revealed that the blades could have served for another 1.44% of the time they were in service.

Acceleration of the Convergence of the Integral Transform Method

1976 ◽  
Vol 61 (3) ◽  
pp. 431-434 ◽  
Author(s):  
V. C. Boffi ◽  
V. G. Molinari ◽  
G. Spiga
Keyword(s):  
Integral Transform ◽  
Transform Method ◽  
Integral Transform Method
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