Thermoviscoelastic response of an axially loaded beam under laser excitation and resting on Winkler’s foundation

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

A review of Winkler's foundation and its profound influence on adhesion and soft matter applications

Few advanced mechanics of materials solutions have found broader and more enduring applications than Emil Winkler's beam on elastic foundation analysis, first published in 1867. Of particular note is its extensive use in adhesion mechanics, including modified forms for soft matter and viscous liquid interlayers.

Vibrations of thick plate resting on a deformable foundation under impulse load

The paper deals with vibrations of thick plate resting on generalized Winkler’s foundation. The plate is subjected to the impulse of force. Governing equations of the problem, analytical solution as well as numerical example are presented. Results of calculations are shownin the figures. Solution and diagrams are obtained by means of “Mathematica” code.