Nonlinear vibrations of cracked microbeams based on modified couple stress theory

Abstract

In this study, nonlinear vibrations of cracked microbeams have been investigated. The micro size characteristics of the beam have been involved in the model by utilizing the modified couple stress theory. Longitudinal elongation of the microbeam during transverse vibrations have been considered to capture the nonlinear behavior. To model the crack, a torsional spring has been introduced at the crack location and the spring constant corresponds to the severity of the crack. Approximate solutions have been obtained by using the method of multiple scales, a perturbation technique. The results have been validated by comparing them with existing literature and have been presented in terms of both crack severity and micro scale properties. The effects of the crack have been examined on various aspects, including natural frequency, nonlinear frequency-response curves and nonlinear frequency responses. These effects have been investigated with respect to parameters such as crack severity, crack location, amplitude of excitation, slenderness of the beam, all under differing boundary conditions. The predicted results reveal that as the crack severity increases, both natural frequency and nonlinear frequency decrease. Furthermore, the modified couple stress theory predicts an increase in natural frequencies as the size scale of the microbeams reduces. The frequency-response curves with varying crack severity and crack locations have indicated the significant effects of the presence of the crack in microbeams.