## Analysis of Azimuthal Shear Wave in an Incompressible Hollow Cylindrical Mooney Rivlin Material Using Monge’s Methods

Published: 2023-04-28

Page: 134-144

Nwagwu Isaac Ogazie *

Department of Mathematics, Federal University of Technology, Owerri, Nigeria.

Bassey Julius Effiong

Department of Mathematics, Federal University of Technology, Owerri, Nigeria.

Panle Augustine Bwan

Department of Mathematics, Federal University of Technology, Owerri, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

The investigation was on analysis of Azimuthal shear wave in an incompressible hollow cylindrical Mooney Rivlin material with nine parameter constants using Monge’s method. The model from the strain energy function was analyzed and reduced to nonlinear second order partial differential equation for the determination of angular displacement and stresses in the cylindrical solid of Mooney-Rivlin material. The method of solution reduced the nonlinear second order partial differential equation into a nonlinear ordinary differential equation and boundary conditions were applied in solving the governing equations in order to eliminate the arbitrary constants. The Angular displacement and stresses were determined.

Keywords: Angular displacement, deformed radius, shear stress, displacement gradient and shear stresses

#### How to Cite

Ogazie, N. I., Effiong, B. J., & Bwan, P. A. (2023). Analysis of Azimuthal Shear Wave in an Incompressible Hollow Cylindrical Mooney Rivlin Material Using Monge’s Methods. Asian Journal of Pure and Applied Mathematics, 5(1), 134–144. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1803

### References

Haddow JB, Erbay HA. Some aspects of finite amplitude transverse waves in a compressible hyperelastic solid. Q J Mech Appl Math. 2002;55(1):17-28. DOI: 10.1093/qjmam/55.1.17

Abo-El-Nou NA, Fatimah A. The dispersion relation of flexural waves in a magnetoelastic anisotropic circular cylinder. Adv Phys Theor Appl. 2013;13:20-33.

Horgan CO, Saccomandi G. Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility. J Elast. 1999;56(2):159-70. DOI: 10.1023/A:1007606909163

Simmonds JG, Warne P. Azimuthal shear of compressible or incompressible Nonlinearly elasticpolar orthotropic tubes of infinite extent. Int J Non Linear Mech. 1992;27(3):447-64. DOI: 10.1016/0020-7462(92)90012-V

Haddow JB. Nonlinear waves in hyperelastic solids. Appl Mech Rev. 1993;46(12):527-39. DOI: 10.1115/1.3120314

Erumaka EN. Finite deformation of a class of Ogden solid under anti-plane shear. J Math Sci. 2003;18:19-24.

Ogden RW. Non-Linear elastic deformations. chichester: Ellis Horwood; 1984.

Haddow JB, Jiang X. Finite amplitude azimuthal shear waves in an incompressible hyperelastic solids, ibid. 2002;68:145-52.

Erumaka EN, Onugha EE, Nwagwu IO. Axial shear wave in an incompressible cylindrical solid. J Niger Assoc Math Math Phys. 2017;42:137-42.

Erumaka EN, Onugha EE, Nwagwu IO. Combined axial and azimuthal shear wave in an incompressible hollow circular cylinder. Trans Niger Math Phys. 2018;7:41-6.

M. and Darijani H. J Appl Polym Sci. New polynomial strain energy function; application to rubbery circular cylinders under finite extension and torsion. 2015;132.

Mangan R, Destrade M, Saccomandi G. Strain energy function for isotropic non-linear elastic incompressible solids with linear finite strain response in shear and torsion. Extreme Mech Lett. 2016;9:204-6.

DOI: 10.1016/j.eml.2016.07.004

Merodio J, Ogden RW. Extension, inflation and torsion of a residually stressed circular cylindrical tube, continnum mechanics thermodynamics 28. Stress analysis of thick pressure vessel composed of incompressible hyperelastic materials; International Journal of Recent advances in Mechanical Engineering (IJMECH). 2015;4(3):157-74.

Anani Y, Gholamhosein R. Stress analysis of thick pressure vessel composed of incompressible hyperelastic materials. IJMECH. 2015;4(3):19-37. DOI: 10.14810/ijmech.2015.4303