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چکیده
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In present study, nonlinear vibrations of cracked microbeams are presented. Micro size characteristics of the beam is included in the model according to modified couple stress theory. The crack is introduced by modeling a torsional spring at the crack location, with the spring constant corresponds the severity of the crack. Approximate solutions are obtained through the application of the method of multiple scales, a perturbation technique. Results are validated by comparing them with existing literature and are presented in terms of both crack severity and micro size properties. Effects of crack are investigated on various aspects, including natural frequency, nonlinear frequency-response curves and nonlinear frequency responses. These effects are examined with respect to parameters such as crack severity, crack location, excitation, microbeam slenderness, all under differing boundary conditions. The predicted results reveal that as the crack severity increases, both natural frequency and nonlinear frequency decreases. Furthermore, the modified couple stress theory predicts an increase in natural frequencies as the size of the microbeams diminishes. Nonlinear hardening behavior of simply-supported microbeams undergoes a reduction as the crack severity increases. Conversely, in the case of clamped-clamped microbeams, changing from hardening to softening behavior is noted with increasing crack severity.
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