Axially Moving Microscale Panel Model Based on Modified Couple Stress Theory

Abstract

The problem of the axially moving microscale panel based on the modified couple stress theory and the principle of minimum total potential energy is analyzed. The mathematical model of the considered system contains the internal material length parameter and can capture the size effect. The equation of equilibrium states of the axially moving panel tensioned with the constant longitudinal load is derived. As a direct application of the model, an axially moving microscale panel with two simply supported and two free longitudinal edges is solved. The effects of the transport speed, the length scale parameter, and the geometry of the microscale panel on the dynamic behavior of the axially moving system are presented. The investigation results show that the dynamic behavior of the panel in the overcritical range of transport speed is mostly affected by time histories of lowest frequencies of free flexural vibrations.