Vibration analysis of EFGM beam using GDQ method

• Published in: International journal on interactive design and manufacturing 2024-05, Vol.18 (4), p.2215-2223
• Main Authors: Sharma, Pankaj, Gautam, Mrinal, Chaturvedi, Manish
• Format: Article
• Language: English
• Subjects: Boundary conditions; CAE) and Design; Clamping; Computer-Aided Engineering (CAD; Electronics and Microelectronics; Engineering; Engineering Design; Exponential functions; Functionally gradient materials; Generalized differential quadrature method; Industrial Design; Instrumentation; Mechanical Engineering; Nonuniformity; Original Paper; Parameters; Quadratures; Resonant frequencies; Shear strain; Vibration analysis
• ISSN: 1955-2513; 1955-2505
• DOI: 10.1007/s12008-022-01063-0

This work deals with vibration analysis of exponentially functionally graded material (EFGM) beams. The width of the beam is varied along the axial direction in accordance with an exponential function. An approximate solution technique called the generalized differential quadrature method is used to obtain the desired solution. MATLAB code is developed to compute the natural frequencies. A detailed parametric study is given. This investigation will be useful in the design of the EFGM beam. It is revealed that the increase of the non-uniformity parameter up to the value of − 0.2 leads to decrease in frequency while after that the natural frequency increases under clamped–clamped boundary condition. The same phenomenon can be observed for next higher frequency (mode-II). In the case of clamped-supported (C–S) boundary condition, the fundamental frequency continuously decreases with the increase of the non-uniformity parameter. The same phenomenon can be seen for next higher frequency (mode-II). It can be seen that the increase of the non-uniformity parameter up to the value of zero leads to increase in frequency while after that the natural frequency decreases under simply-supported boundary condition. For next higher mode, increase of the non-uniformity parameter up to the value of zero leads to increase in frequency while after that the natural frequency decreases. It can be found that the increase of the parameter h/L up to the value of 40 leads to decrease in natural frequency while after that the natural frequency increases for both the convergent and divergent beams under all considered boundary conditions.