Vibration Characteristics of Functionally Graded Micro-Beam Carrying an Attached Mass

Abstract

In this article, in reference to the modified couple stress theory and Euler-Bernoulli beam theory, the free lateral vibration response of a micro-beam carrying a moveable attached mass is investigated. This is a decent model for biological and biomedical applications beneficial to the early-stage diagnosis 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 supposed to show variations through-thickness of the beam in consonance to the power of law. Rayleigh-Ritz method is applied in order to explore the natural frequencies of the first three vibration modes. In order to manifest the accuracy of the proposed method, the results are established and juxtaposed with technical literature. Influences of the material length-scale parameter that captures the size-dependency, ratio of the mass of the beam to the mass of the attached mass and power index of the graded material consequent to the vibrational behavior of the system are contemplated. This technical research denotes the value of the material gradation besides to the inertia of an attached mass in the dynamic behavior of the bio-micro-systems. As a result, the adoption of suitable power index, mass ratio and position of the attached mass lead to the superior design of bio-micro-systems persuading early-stage diagnostics.