Natural Frequency Analysis of Rotating Thin-Walled Beams with Embedded Shape Memory Alloy Wires Subjected to Uniform Temperature Field

Document Type : Research Article

Authors

1 Mechanic, Faculty of Mechanics, Sirjan University of technology, Sirjan, Iran

2 Mechanic, Faculty of Engineering Mechanics, Sirjan University of technology, Sirjan, Iran

Abstract

In this paper, ‌free vibration analysis of the rotating thin-walled composite beams with embedded shape memory alloy wires is represented. Pre-strained shape memory alloy wires are embedded in the middle of the cross section of thin-wall composite beam, symmetrically. The onedimensional thermo-mechanical constitutive law suggested by Liang-Rogers is applied to model the thermomechanical behavior of shape memory alloy wires. The differential governing equations are extracted by using the extended Hamilton’s principle based on first-order shear deformation theory. By heating the thin-walled beam, strain recovery operation will produce a tensile force along the longitudinal thin-walled beam. In order to solve the governing equations, the extended Galerkin method is used. The effect of rotational speed, recoverable strain limit, pre-twist angle, number of shape memory alloy wire and temperature difference on the natural frequency in temperature above the austenite finish are illustrated. It is found that the natural frequencies of rotating thin-walled beam increase as the number of shape memory alloy wires and compressive pre-strained shape memory alloy wires increases. In addition, results are in good agreement with those obtained in the literature.

Keywords

Main Subjects

References

[1] J.M. Jani, M. Leary, A. Subic, M.A. Gibson, A review of shape memory alloy research, applications and opportunities, Materials & Design, 56 (2014) 1078-1113.
[2] A. Damanpack, M. Bodaghi, M. Aghdam, M. Shakeri, On the vibration control capability of shape memory alloy composite beams, Composite Structures, 110 (2014) 325-334.
[3] C.A. Rogers, Active vibration and structural acoustic control of shape memory alloy hybrid composites: experimental results, The Journal of the Acoustical Society of America, 88(6) (1990) 2803-2811.
[4] A. Baz, K. Imam, J. McCoy, Active vibration control of flexible beams using shape memory actuators, Journal of Sound and Vibration, 140(3) (1990) 437-456.
[5] S. Seelecke, I. Muller, Shape memory alloy actuators in smart structures: Modeling and simulation, Applied Mechanics Reviews, 57(1) (2004) 23-46.
[6] W.J. Buehler, J. Gilfrich, R. Wiley, Effect of low‐temperature phase changes on the mechanical properties of alloys near composition TiNi, Journal of applied physics, 34(5) (1963) 1475-1477.
[7] G.B. Kauffman, I. Mayo, The story of nitinol: the serendipitous discovery of the memory metal and its applications, The chemical educator, 2(2) (1997) 1-21.
[8] K. Tanaka, A thermomechanical sketch of shape memory effect: one-dimensional tensile behavior,  (1986).
[9] C. Liang, C.A. Rogers, One-dimensional thermomechanical constitutive relations for shape memory materials, Journal of intelligent material systems and structures, 8(4) (1997) 285-302.
[10] L.C. Brinson, One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable, Journal of intelligent material systems and structures, 4(2) (1993) 229-242.
[11] K.-t. Lau, Vibration characteristics of SMA composite beams with different boundary conditions, Materials & design, 23(8) (2002) 741-749.
[12] K.-t. Lau, L.-m. Zhou, X.-m. Tao, Control of natural frequencies of a clamped–clamped composite beam with embedded shape memory alloy wires, Composite Structures, 58(1) (2002) 39-47.
[13] M.M. Barzegari, M. Dardel, A. Fathi, Vibration analysis of a beam with embedded shape memory alloy wires, Acta Mechanica Solida Sinica, 26(5) (2013) 536-550.
[14] S.-Y. Oh, L. Librescu, O. Song, Thermoelastic modeling and vibration of functionally graded thin-walled rotating blades, AIAA journal, 41(10) (2003) 2051-2061.
[15] L. Librescu, S.-Y. Oh, O. Song, Thin-walled beams made of functionally graded materials and operating in a high temperature environment: vibration and stability, Journal of Thermal Stresses, 28(6-7) (2005) 649-712.
[16] S.A. Fazelzadeh, M. Hosseini, Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials, Journal of fluids and structures, 23(8) (2007) 1251-1264.
[17] M. Naghmehsanj, B. Rahmani, Optimal control of supersonic pre‐twisted rotating functionally graded thin‐walled blades, Structural Control and Health Monitoring, 24(8) (2017).
[18] V. Birman, D.A. Saravanos, D.A. Hopkins, Micromechanics of composites with shape memory alloy fibers in uniform thermal fields, AIAA journal, 34(9) (1996) 1905-1912.
[19] N.K. Chandiramani, C.D. Shete, L.I. Librescu, Vibration of higher-order-shearable pretwisted rotating composite blades, International Journal of Mechanical Sciences, 45(12) (2003) 2017-2041.
[20] S. Fazelzadeh, P. Malekzadeh, P. Zahedinejad, M. Hosseini, Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method, Journal of sound and vibration, 306(1) (2007) 333-348.
[21] M. Crespo-Ballesteros, M. Antoniou, M. Cherniakov, Wind Turbine Blade Radar Signatures in the Near Field: Modeling and Experimental Confirmation, IEEE Transactions on Aerospace and Electronic Systems, 53(4) (2017) 1916-1931.
 
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 1
April 2020
Pages 127-140

Files

Share

How to cite

Statistics