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The purpose of this paper is to investigate the response of viscoelastic beam resting on a Winkler’s foundation and subjected to an axial initial stress, thermal load and an ultra-fast laser heating.

In this introduced model, the authors considered the interaction design between the vertical springs only. The beam is considered as an Euler–Bernoulli beam exposed to sinusoidal varying heat.

The deflection and the temperature response of the beam are obtained using Laplace transform and its numerical inversion method. In the numerical example, the effect of the laser pulse duration and viscous damping coefficient on the transverse displacement response of the beam is discussed. The thermoelastic interactions of the beam due to the axial load are also illustrated.

Physical views of this paper may be useful for the design and vibration analysis of micro-resonators and micro-sensors applications. In addition, the utilization of laser-ultrasonic technology has found wide applications in lab environments, and in an expanding number of cases, it is extending to the industrial field and realm application.

The thermo-diffusion analysis of an isotropic cylinder under thermal flux and chemical potential impacts has been discussed. Improvements of Green and Naghdi generalized thermoelasticity theory have been proposed.

Some models with and without energy dissipation have been presented as well as the simple forms of Green–Naghdi (G–N) theories. These novel multi- and single-/dual-phase-lag models are presented to investigate the thermo-diffusion of the solid cylinder. The closed-form solution of thermo-diffusion governing equations of solid cylinder has been obtained to deduce all field variables.

A comparison study between the simple G–N II and III models and their improved models has been presented. The validations of outcomes are acceptable and so benchmarks are reported to help other investigators in their future comparisons.

The modified Green and Naghdi theories of types II and III are presented to get novel and accurate models of single- and dual-phase-lag of multiterms. The heat of mass diffusion equation as well as the constitutive equations for the stresses and chemical potential of a solid cylinder is added to the present formulation. The system of three differential coupled equations is solved, and all field variables are obtained for the thermal diffusion of the solid cylinder. Some validation examples and applications are presented to compare the simple and modified Green and Naghdi theories of types II and III. Sample plots are illustrated along the radial direction of the solid cylinder. Some results are tabulated to serve as benchmark results for future comparisons with other investigators. The reported and illustrated results show that the simple G–N II and III models yield the largest values of all field quantities. The single-phase-lag models give the smallest values. However, the dual-phase-lag model yields results that are intermediate between those of the simple and single-phase-lag G–N models.