Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

Abstract

The frequency parameters of an Axially Functionally Graded (AFG) bar for viscoelastic and point mass boundary conditions are studied in this paper. The structures with functionally graded materials under axial loads can be modelled as AFG bars. Those may be considered as support elements with spring and dashpot in the vibration isolation. Keeping the ratio of force frequency and natural frequency at a certain level is ensured to control the natural frequency therefore dynamic amplification factor with different material combinations. Various boundary conditions are attained by changing the spring and damping coefficients of viscoelastic support elements and the ratio of rod mass to tip mass. Researchers assume that the beam material properties in directions of length and thickness change exponentially, individually, or both in their studies. There are a few studies on the AFG rods in the existing studies. Analysis is carried out via the finite element method for the non-dimensional frequency parameters of the bar in MATLAB. The energy equations of the motion are obtained in the frame of axial bar theory considering the material properties of the bar vary longitudinally according to the power-law distribution. The effects of material distribution, spring, damping and tip mass values on the bar's frequency parameters and structural behaviour have been extensively investigated.