Mathematical Models for the Propagation of Stress Waves in Elastic Rods: Exact Solutions and Numerical Simulation. Issue 2 (27th January 2016)

• Record Type: Journal Article
• Authors: Tenkam, H. M.; Shatalov, M.; Fedotov, I.; Anguelov, R.
• Is Part Of: Advances in applied mathematics and mechanics. Volume 8:Issue 2(2016)
• Page Start: 257
• Page End: 270
• Publication Date: 2016-01-27
• Subjects: 33C90, -- 35Q74, -- 35L35; Longitudinal vibration of rods, -- variable cross-section, -- exact solution, -- method of lines, -- hypergeometric functions; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2013.m383
• Languages: English
• ISSNs: 2070-0733

Abstract

Abstract: In this work, the Bishop and Love models for longitudinal vibrations are adopted to study the dynamics of isotropic rods with conical and exponential cross-sections. Exact solutions of both models are derived, using appropriate transformations. The analytical solutions of these two models are obtained in terms of generalised hypergeometric functions and Legendre spherical functions respectively. The exact solution of Love model for a rod with exponential cross-section is expressed as a sum of Gauss hypergeometric functions. The models are solved numerically by using the method of lines to reduce the original PDE to a system of ODEs. The accuracy of the numerical approximations is studied in the case of special solutions.