International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-8 Issue-4, November 2019 5926 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: D8974118419/2019©BEIESP DOI:10.35940/ijrte.D8974.118419 Characterization of Functionally Graded Timoshenko Beams with Variable Rotational Speed S.N.Padhi, K. S. Raghu Ram, Jasti Kasi Babu, T.Rout Abstract: This paper investigates the free vibration characteristics and stability of a functionally graded Timoshenko beam spinning with variable angular speed. Material properties of the beam are assumed to be varied continuously along the thickness of the beam according to a power law and exponential law. The results show that increasing beam rotational speed increases fundamental mode frequency and the beam becomes more and more stable at higher speeds. This paper reports the dynamic behaviour of a rotating FGM beam subjected to axial periodic forces using the finite element method. The numerical results show good agreement with the reported beams models. Effects of static and time dependent components of axial loads on the stability of the FGM beam have been studied. Index Terms: Exponential distribution, Timoshenko beam, load factor, Power law, Rotational speed, Stability. I. INTRODUCTION The modern engineering application demands the design and analysis of rotating shafts, beams, and gears. The whirling of beams has also been increasingly used in the exploration of space. The vibration analysis and hence the stability of a rotating cantilever beam is performed in this paper because it may represent many of these structures. Composite materials have been used for several years for their advantage of achieving desired properties. The Metal Matrix Composite includes two metals which includes aluminum, and chromium. Aluminum is chosen because of its superior strength to weight ratio. Chromium is chosen because of its strength-weight ratio. The fabrication of composite material is done through stir casting method. Deformation of composite done using manual rolling after the casting of composite. Further analysis of composite includes microstructural study, hardness values and machinability results. The specimens are collected for every work to analyses the composite[1,2]. The determination of designing MMC is to enhance the required characteristic of metals and porcelains to the base metals. Aluminium Metal Matrix Composites (AMMCs) are significantly important in the structural, aerospace, medicine, marine and automobile applications. [3]. The fiber orientation in composites has a significant effect on the properties of natural fiber-reinforced polymer composites.Longitudinally aligned fiber composites show maximum strength along the direction of the fiber reinforcement and they are orthotropic in nature. In the Revised Manuscript Received on November 15, 2019 Surya Narayan Padhi, Department of Mechanical Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram (A.P.) India. K.S.Raghu Ram, Jasti Kasi Babu, Dept. of Mechanical Engg.,Vignan’s Institute of Information Technology, Visakhapatnam, India. Trilochan Rout, Dept.of Mechanical Engg., Parala Maharaja Engineering College, Berhampur,India. transverse direction, composite properties are lower than those in unidirectional, which may also be less than that of a neat polymer matrix sample[4]. Friction Stir Processing (FSP) is a new method by which the surface modification can be done for alloys and composites. Friction Stir Processing can enhance the mechanical properties of the composite[5]. Vibrating structures under rotation such as compressors, motors, pumps and micro-electro-mechanical systems is a naturally occurring phenomenon and results severe vibration in a structural resonant mode with an excitation by harmonic loading because of imbalanced rotor or variable fluid dynamic force, which causes heavy mechanical damage. Thus, the understanding of stability and dynamic response of rotating structures inservice is highly important to avoid the risk of such resonance problems. In real life, the above mentioned rotating structures are normally pretwisted and the cross-section is asymmetric in nature. However, Prismatic beams under rotation may be used as a sample model and compared at par with the actual rotating structures for investigation of stability and dynamic response. The research on functionally graded materials (FGMs) is rapidly growing because of its ability to meet desired material properties in contrast to the conventional homogeneous and layered composite materials which suffer from debonding, huge residual stress, locally large plastic deformations etc. An FGM can be a good replacement for the material of rotating beams. Timoshenko beam theory and classical Ritz method is employed to derive the governing equations. In order to solve the nonlinear governing equations, direct substitution iterative technique is used. Effects of various parameters such as rotating speeds, radius of hub, depth of crack, location of crack, and different functionally graded material properties on linear and nonlinear vibration characteristics are studied [6-8]. From a mechanics viewpoint, the main advantages of material property grading appear to be improving bonding strength, toughness, wear and corrosion resistance, and reduced residual and thermal stresses. Therefore, now-a-days, an FGM has been a promising candidate for many engineering applications where a high temperature gradient field is the main concern [9-11]. Effects of rotary inertia and shear deformation are not negligible for thick beams or even thin beams that are vibrating at high frequencies. Due to their dimensions, resonance frequencies of micro- and nano-scale resonators are extremely high, namely in the range of kHz to GHz [12]. The high resistance of the ceramic at various temperature gradients, thermal stress, abrasion and oxidation and the toughness and strength of metal can be taken advantage of at the same time[13].