Thermoelastic wave propagation in thin beams under thermal shock loading

• Published in: Applied Mathematical Modelling Vol. 105; pp. 584 - 614
• Main Authors: Kaur, Ramandeep, Kapuria, Santosh
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.05.2022; Elsevier BV
• Subjects: Beam theory (structures); Boundary conditions; Cantilever beams; Equations of motion; Euler-Bernoulli beams; Euler–Bernoulli beam; Exact solutions; Generalized thermoelasticity; Hamilton's principle; Homotopy perturbation method; Longitudinal waves; Perturbation methods; Propagation; Relaxation time; Shock loading; Shock wave propagation; Temperature distribution; Thermal shock; Thermoelasticity; Thickness; Wave propagation; Euler–Bernoulli beam; Homotopy perturbation method; Wave propagation; Thermal shock; Generalized thermoelasticity
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2022.01.004

•Analytical solution presented for thermoelastic wave propagation in thin beams under thermal shock loading.•Homotopy perturbation method used to solve the coupled thermoelastic equations in Laplace domain.•The solution accurately captures sharp jumps in temperature and stress profiles across the beam length.•Temperature distribution across thickness differs from applied load profile contrary to prevailing assumptions.•Nature of wavefronts and propagation depends on thermal boundary conditions and relaxation time. An analytical solution is presented for the thermoelastic longitudinal and flexural wave propagation in transversely isotropic thin beams subjected to a thermal shock loading using the Lord–Shulman generalized thermoelasticity theory. The formulation considers a general through-thickness profile of the applied thermal loading, does not assume the across-thickness distribution of the temperature field and considers a general convective boundary condition at the beam surfaces. The thin beam is modeled using the Euler–Bernoulli beam theory. The governing equations of motion and the variationally consistent boundary conditions are derived from the extended Hamilton’s principle. The coupled thermoelastic equations are solved in the Laplace domain satisfying the thermal and mechanical boundary conditions using the homotopy perturbation method. The Laplace inversion to obtain the final solution in the time domain is performed numerically by using Durbin’s method. The formulation is validated by comparing the results for longitudinal wave propagation response under uniform thermal loading with those available in the literature. The developed solution is then employed to study the longitudinal and flexural wave propagation behaviour of a cantilever beam subject to uniform and non-uniform symmetric, and linear and non-linear anti-symmetric thermal shock loading applied at the free end. The effects of thermal boundary conditions at the beam surfaces and the relaxation time parameter on the response of the beam are illustrated.