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Effect of Taper on Free Vibration of Functionally Graded Rotating Beam by Mori-Tanaka Method

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Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

Rotating beams are the practical application for aircraft propellers, helicopter blades, wind mill propeller, turbine blades and spinning space structures. In these structures, taper beams are preferred due to optimum weight distribution with uniform strength. Vibration behavior of tapered variable section beams subjected to centrifugal forces is important in analysis of structures. The research work deals with flapwise vibration of functionally graded (FG) rotating taper beam. The material properties of the beam change symmetrically in the direction of thickness from middle surface to the outer surfaces. Mori-Tanaka method estimates these properties of FG beam. The flapwise frequencies are obtained using Differential Transform Method (DTM). The effect of different parameters such as rotating speed, taper ratio, hub radius ratio and gradient index on flapwise frequency is discussed.

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Abbreviations

A(x):

Area of the beam at a distance x

E(z):

Equivalent young’s_modulus

Iy(x):

Moment of inertia

M:

Mass of the beam per unit length

n:

Gradient index

r:

Hub root radius

Vc :

Ceramic volume fraction

Vm :

Metal volume fraction

w:

Flapwise displacement

x:

Longitudinal coordinate of the beam

z:

Lateral coordinate of the beam

γ:

Non dimensional rotating speed

δ:

Hub radius ratio

ζ:

Non dimensional beam length

ρ(z):

Equivalent density

ω:

Flapwise frequency

Ω:

Rotating speed

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Authors and Affiliations

  1. Mechanical Engineering Department, Prasad V. Potluri, Siddhartha Institute of Technology, Vijayawada, 520007, India

    Pacharu Ravi Kumar

  2. Mechanical Engineering Department, Velagapudi Ramakrishna Siddhartha Engineering College, Vijayawada, 520007, India

    Koganti Mohana Rao

  3. Mechanical Engineering Department, University College of Engineering, Jawaharlal Nehru Technological University Kakinada, Kakinada, 533003, India

    Nalluri Mohan Rao

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  1. Pacharu Ravi Kumar
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  2. Koganti Mohana Rao
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Correspondence to Pacharu Ravi Kumar.

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Kumar, P.R., Rao, K.M. & Rao, N.M. Effect of Taper on Free Vibration of Functionally Graded Rotating Beam by Mori-Tanaka Method. J. Inst. Eng. India Ser. C 100, 729–736 (2019). https://doi.org/10.1007/s40032-018-0477-z

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  • DOI: https://doi.org/10.1007/s40032-018-0477-z

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