Vibration characteristics of functionally graded micro-beam carrying an attached mass

Document Type: Research Paper


1 Mechanic, Urmia University

2 Department of Mechanical Engineering, University of North Dakota, Grand Forks, ND, USA

3 Urmia university of technology


In this paper based on the modified couple stress theory and Euler-Bernoulli beam theory, free lateral vibration response of a micro-beam carrying a moveable attached mass is report-ed. This is a decent model for biological and biomedical applications helping early-stage diag-nosis of diseases and malfunctions of human body organs and enzymes. The micro-cantilever beam is composed of functionally graded materials (FGMs). The material properties are sup-posed to have variations through thickness of the beam in accordance with the power of law. Rayleigh-Ritz method is employeed to find natural frequencies of the first three vibration modes. To demonstrate the accuracy of the proposed method, the results are established and compared with technical literature. Influences of the material length-scale parameter that captures the size-dependency, ratio of mass of the beam to mass of the attached mass and power index of the graded material upon the vibrational behaviour of the system are consid-ered. This technical research denotes the importance of the material gradation besides to the inertia of an attached mass in the dynamic behaviour of the bio-micro-systems. As a result, adoption of suitable power index, mass ratio and position of the attached mass leads to a bet-ter design of bio-micro-systems leading to early-stage diagnostics.