Vibration Behavior of Nanobeams under Hyperbolic Two-Temperature Thermoelasticity Using Modified Couple Stress Theory

In this study, the vibration behavior of a nanobeam is analyzed within the framework of a modified couple stress (MCS) thermoelastic model under the hyperbolic two-temperature (HTT) theory. The governing equations are formulated using the Euler-Bernoulli beam theory and non-dimensional parameters for simplification. The Laplace transform, combined with an eigenvalue approach, is employed to solve the equations. Most of the problems studied so far in MCS thermoelastic media involve the use of potential functions; however, the eigenvalue approach has the advantage of determining the solution of the governing equations in matrix form. The nanobeam, assumed to be simply supported along its length (aligned with the x1-axis), is subjected to an exponentially decaying thermal source. The chosen boundary conditions are reflective of practical nanostructures experiencing localized laser heating or rapid transient effects. Key physical field quantities, including displacement, lateral deflection, temperature distribution, conductive temperature, and axial stress, are derived in the transformed domain. A general algorithm is developed for the numerical inversion of the Laplace transform, and results are computed and presented graphically. The study highlights the influence of single-temperature (1T), two-temperature (2T), HTT models, and characteristic time parameters on the system’s response. Some particular cases of interest are also reduced.