Axisymmetric Vibrations of Variable Thickness Functionally Graded Clamped Circular Plate
The axisymmetric vibrations of functionally graded clamped circular plate have been analysed on the basis of classical plate theory. The material properties, i.e. Young’s modulus and density vary continuously through the thickness of the plate, and obey a
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Abstract The axisymmetric vibrations of functionally graded clamped circular plate have been analysed on the basis of classical plate theory. The material properties, i.e. Young’s modulus and density vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituent materials. A semi-analytical technique, i.e. differential transform method has been employed to solve the differential equation governing the equation of motion. The effect of various plate parameters, i.e. volume fraction index g and taper parameter γ have been studied on the first three modes of vibration. Three-dimensional mode shapes for the first three modes of vibration have been presented. A comparison of results with those available in the literature has been given. Keywords Functionally graded circular plates Axisymmetric vibrations
Differential transform method
1 Introduction The wide applications of functionally graded materials (FGMs) in space vehicles, nuclear reactor, defence industries and chemical plants have attracted many researchers throughout the world. FGMs are microscopically inhomogeneous materials whose mechanical properties vary continuously in one or more directions [1]. In a metal-ceramic FGM, the metal-rich side is placed in regions where mechanical properties, such as toughness need to be high whereas the ceramic-rich side which has low thermal conductivity and can withstand high temperatures is placed in regions of large temperature gradients. Due to these characteristics, FGM Neha Ahlawat (&) Roshan Lal Indian Institute of Technology Roorkee, Roorkee, India e-mail: [email protected] Roshan Lal e-mail: [email protected] © Springer Science+Business Media Singapore 2016 M. Pant et al. (eds.), Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing 436, DOI 10.1007/978-981-10-0448-3_21
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plate-type components of different geometries are extensively used as structural elements in various fields of modern science and technology. A lot of studies have been concerned dealing with the vibration characteristics of FGM plates and reported in Refs. [2–12], to mention a few. Out of these, Jha et al. [2] have presented a critical review of recent research on functionally graded plates till 2012. Ferreira et al. [3] used collocation method to analyse the free vibrations of functionally graded rectangular plates of various aspect ratios. Zhao et al. [4] used element-free kp-Ritz method for free vibration analysis of rectangular and skew plates with different boundary conditions taking four types of functionally graded materials on the basis of first-order shear deformation theory. Liu et al. [5] have analysed the free vibration of FGM rectangular plates with in-plane material inhomogeneity using Fourier series expansion and a particular integration technique on the basis of classical plate theory. Free vibration analysis of functionally graded thick an
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