Vibration and damping analysis of orthotropic sandwich shaft-disc system using finite element method
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Vibration and damping analysis of orthotropic sandwich shaft-disc system using finite element method R. Venkatachalam • S. Balasivanandha Prabu
Received: 12 November 2011 / Accepted: 2 May 2012 / Published online: 22 May 2012 Springer Science+Business Media, B.V. 2012
Abstract This paper focuses on investigating the effect of various constrained layers [electro rheological fluid (ERF), magneto rheological fluid (MRF) and viscoelastic layer (VEL)] over natural frequency and damping loss factor with five different fiber orientations (0, 30, 45, 60 and 90) for a boron/epoxy (B/E), carbon/epoxy (C/E) and kevlar/epoxy (K/E) shaft disc system. Finite element technique is employed to evaluate the natural frequency and damping loss factor for various combinations. Also the vibrational characteristics of composite sandwich shaft disc system are compared for better damping capabilities. From the study VEL core shows excellent frequency and loss factor performances and the 90 fiber oriented composites is dominant in vibration damping. Also, it is evident that the damping performance of ERF and MRF core depends on applied electric and magnetic field. Keywords Finite element analysis Electro rheological Magneto rheological Shaft disc structure Vibration R. Venkatachalam (&) Department of Automobile Engineering, K.S.R. College of Engineering, Tiruchengode 637 215, India e-mail: [email protected] S. Balasivanandha Prabu Department of Mechanical Engineering, College of Engineering, Guindy, Anna University, Chennai 600 025, India
List of symbols [K] Assembled stiffness matrix [Ds] Elasticity matrix [Ki] Imaginary part of [K] gi Modal loss factor for ith circumferential mode of vibration [Kr] Real part of K [B] Strain matrix k The complex eigenvalue {Ui} Undamped mode shapes of corresponding mode of vibration {r} Mechanical stress {D} Electric displacement vector {Q} Applied charge density T {S } Mechanical strains = {Sss, Shh, Shz, Szs, Ssh}T a Outer radius of circular plate b Inner radius of circular plate hc Thickness of viscoelastic material hp Thickness of circular plate l Length of the shaft m Circumferential mode me Element mass matrix n Radial mode N Shape function Ni Shape function corresponding mode Ra Outer radius of shaft R Radius of the middle surface of shell Ri Inner radius of shaft S, h, Z Coordinate directions T Kinetic energy
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tc tf u, v, w u o, v o, w o ue EL ET G GR GI m x E* B e i j m i, o, c
R. Venkatachalam, S. Balasivanandha Prabu
Thickness of core Thickness of facing Displacements in the S, h, Z Midsurface displacements Element displacement vector Young’s modulus in longitudinal direction Young’s modulus in transverse direction Shear modulus Storage modulus Loss modulus Poisson’s ratio Natural frequency Electric Field in kV/mm Magnetic Induction in Oersted Elemental ith node jth layer mth circumferential mode Inner and outer facing and core
1 Introduction Shaft disc system is an important machine component used in industries. Most often the shaft disc systems are subjected to
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