Generalized Thermoelastic Waves Propagation in Non-uniform Rational B-spline Rods Under Quadratic Thermal Shock Loading
- PDF / 2,134,822 Bytes
- 17 Pages / 595.276 x 790.866 pts Page_size
- 93 Downloads / 203 Views
RESEARCH PAPER
Generalized Thermoelastic Waves Propagation in Non‑uniform Rational B‑spline Rods Under Quadratic Thermal Shock Loading Using Isogeometric Approach Ahmad Yavari1 · Mohammad Hossein Abolbashari1 Received: 20 April 2020 / Accepted: 15 September 2020 © Shiraz University 2020
Abstract Generalized thermoelasticity based on Lord–Shulman theory that admits the second sound effect is developed for continuumbased modeling of the thermoelastic wave propagation in functionally graded material (FGM) rods with a variable crosssectional area under quadratic thermal shock loading. The geometry of the problem, as well as the distribution of material properties, is defined continuously with Non-uniform rational B-spline. To assure the exact modeling of geometry, the problem is analyzed using the isogeometric approach. The effects of geometry and material distribution on thermoelastic waves are discussed in detail. Also, propagation, reflections, and propagation speed along the rod axis are investigated. It is shown that the amplitudes and speed of thermoelastic waves can be desirably controlled by the cross-sectional area and the material distribution of the rod, respectively. Keywords Lord–Shulman coupled thermoelasticity · Isogeometric analysis · Wave propagation · NURBS rods · Shock loading
1 Introduction From the experimental results, it is found that the motion of a body is characterized by the mutual interaction of the deformation and temperature fields. Duhamel (1837) was the first who realized the existence of coupling between deformation and temperature fields, and later, Biot (1956) gave the full justification of the thermal conductivity equation. In the classical linear thermoelastic theory, when a thermal disturbance is applied to an elastic solid, its effect is propagated in the body far distant from the source instantaneously. This phenomenon shows an infinity velocity for the propagation of the thermal wave, and it is physically an unreasonable result. According to this phenomenon, some generalized thermoelastic theories were introduced to eliminate this paradox in classical theory. Chester (1963) used macroscopic equations for energy conservation and heat current to discuss the possibility of second sound (thermal wave * Mohammad Hossein Abolbashari [email protected] 1
Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O. Box 91775‑1111, Mashhad, Iran
with finite velocity) in solid. Also, Ackerman et al. (1966) and Ackerman and Overton (1969) observed the phenomenon of second sound in experiments for temperature pulse propagation in solid helium. Lord and Shulman (1967) introduced a generalized thermoelastic theory, which is called Lord–Shulman (L–G) thermoelastic theory. The main challenge in the modeling of thermoelastic wave propagation by continuous models is for complex geometry and FGM. The continuous models consider the data, such as material properties and geometry, to be continuous within the domain. As an example, Nariboli and Nyayadhish (1963) worked on one-di
Data Loading...
