Bending vibration of axially loaded Timoshenko beams with locally distributed Kelvin–Voigt damping

Abstract Utilizing the Timoshenko beam theory and applying Hamilton's principle, the bending vibration equations of an axially loaded beam with locally distributed internal damping of the Kelvin–Voigt type are established. The partial differential equations of motion are then discretized into linear second-order ordinary differential equations based on a finite element method. A quadratic eigenvalue problem of a damped system is formed to determine the eigenfrequencies of the damped beams. The effects of the internal damping, sizes and locations of damped segment, axial load and restraint types on the damping and oscillating parts of the damped natural frequency are investigated. It is believed that the present study is valuable for better understanding the influence of various parameters of the damped beam on its vibration characteristics.

[1]  T. Kocatürk,et al.  Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load , 2006 .

[2]  Stefano Marchesiello,et al.  A new analytical technique for vibration analysis of non-proportionally damped beams , 2003 .

[3]  Kangsheng Liu,et al.  Stability for the Timoshenko Beam System with Local Kelvin–Voigt Damping , 2005 .

[4]  Thomas J. R. Hughes,et al.  A simple and efficient finite element for plate bending , 1977 .

[5]  M. Friswell,et al.  THE MODES OF NON-HOMOGENEOUS DAMPED BEAMS , 2001 .

[6]  Chun-Sheng Chen,et al.  Vibration analysis of a beam with partially distributed internal viscous damping , 2009 .

[7]  Jack Dongarra,et al.  Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[8]  S. Nima Mahmoodi,et al.  Non-linear free vibrations of Kelvin-Voigt visco-elastic beams , 2007 .

[9]  M. Gurgoze,et al.  On the eigencharacteristics of multi-step rods carrying a tip mass subjected to non-homogeneous external viscous damping , 2003 .

[10]  J. Reddy.  ON LOCKING-FREE SHEAR DEFORMABLE BEAM FINITE ELEMENTS , 1997 .

[11]  J. Bruch,et al.  Integral equation approach for piezo patch vibration control of beams with various types of damping , 2008 .

[12]  Sondipon Adhikari,et al.  Non-local finite element analysis of damped beams , 2007 .

[13]  M. Gurgoze,et al.  ON THE EIGENVALUES OF A VISCOUSLY DAMPED CANTILEVER CARRYING A TIP MASS , 1998 .

[14]  K. Bathe.  Finite Element Procedures , 1995 .

[15]  Clarence W. de Silva,et al.  Vibration damping, control, and design , 2007 .

[16]  Nader Jalili,et al.  An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams , 2008 .

[17]  M. G. Shebl,et al.  Exact frequency and mode shape formulae for studying vibration and stability of Timoshenko beam system , 1995 .

[18]  Ed Anderson,et al.  LAPACK Users' Guide , 1995 .

[19]  Analysis of non-homogeneous Timoshenko beams with generalized damping distributions , 2007 .

[20]  J. N. Reddy,et al.  Convergence properties and derivative extraction of the superconvergent Timoshenko beam finite element , 2001 .

[21]  M. Gurgoze,et al.  On the eigencharacteristics of a cantilevered visco-elastic beam carrying a tip mass and its representation by a spring-damper-mass system , 2007 .

[22]  J. Z. Zhu,et al.  The finite element method , 1977 .