An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams

Abstract The nonlinear vibration analysis of a directly excited cantilever beam modeled as an inextensible viscoelastic Euler–Bernoulli beam has been studied by the authors and is reported in the literature. The viscoelastic damping was modeled as Kelvin–Voigt damping, and the nonlinearities arisen from the inextensibility assumption. This paper extends our theoretical developments presented in the previous papers and utilizes the method of multiple scales in order to arrive at the modulation equations and the closed-form frequency response function. The analytically derived frequency response is experimentally verified through harmonic force excitation of samples of carbon nanotube-reinforced beams. The beam used in experiment consists of two elastic layers of high-carbon steel sandwiched together through a viscoelastic layer of carbon nanotube–epoxy mixture. The results demonstrate that increasing the excitation amplitude or decreasing damping ratio can cause a minor decrease in the nonlinear resonance frequency despite the significant increase in the amplitude of vibration due to reduced damping.

[1]  M M Kamel,et al.  Response of parametrically excited one degree of freedom system with non-linear damping and stiffness , 2002 .

[2]  Ali H. Nayfeh,et al.  Nonlinear Nonplanar Dynamics of Parametrically Excited Cantilever Beams , 1998 .

[3]  Nader Jalili,et al.  A nonlinear double-winged adaptive neutralizer for optimum structural vibration suppression , 2003 .

[4]  M. R. Silva Non-linear flexural-flexural-torsional-extensional dynamics of beams—I. Formulation , 1988 .

[5]  Ali H. Nayfeh,et al.  Nonlinear Normal Modes of a Cantilever Beam , 1995 .

[6]  M. A. Jalali,et al.  Nonlinear Oscillations of Viscoelastic Rectangular Plates , 1999 .

[7]  S. E. Khadem,et al.  Passive Nonlinear Vibrations of a Directly Excited Nanotube-Reinforced Composite Cantilevered Beam , 2005 .

[8]  Hong Hee Yoo,et al.  DYNAMIC ANALYSIS OF A ROTATING CANTILEVER BEAM BY USING THE FINITE ELEMENT METHOD , 2002 .

[9]  M. R. Silva,et al.  Equations for Nonlinear Analysis of 3D Motions of Beams , 1991 .

[10]  M. R. Silva,et al.  Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion , 1978 .

[11]  N. Jalili,et al.  Determination of Strength and Damping Characteristics of Carbon Nanotube-Epoxy Composites , 2004 .

[12]  N. Jalili,et al.  Passive vibration damping enhancement using carbon nanotube-epoxy reinforced composites , 2005 .

[13]  Christophe Pierre,et al.  Normal modes of vibration for non-linear continuous systems , 1994 .

[14]  Herbert Shea,et al.  Carbon nanotubes: nanomechanics, manipulation, and electronic devices , 1999 .

[15]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[16]  Nader Jalili,et al.  Theoretical development and closed-form solution of nonlinear vibrations of a directly excited nanotube-reinforced composite cantilevered beam , 2006 .

[17]  Ali H. Nayfeh,et al.  Investigation of subcombination internal resonances in cantilever beams , 1998 .

[18]  Vimal Singh,et al.  Perturbation methods , 1991 .

[19]  Y. A. Amer,et al.  Vibration control of a cantilever beam subject to both external and parametric excitation , 2004, Appl. Math. Comput..

[20]  Ali H. Nayfeh,et al.  On Nonlinear Modes of Continuous Systems , 1994 .

[21]  M. R. Silva,et al.  Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. II. Forced Motions , 1978 .

[22]  W. Schultz,et al.  Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method , 2004 .

[23]  Mousa Rezaee,et al.  Analysis of non-linear mode shapes and natural frequencies of continuous damped systems , 2004 .

[24]  Ser Tong Quek,et al.  Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator , 2000 .

[25]  Nader Jalili,et al.  Parametric response of cantilever Timoshenko beams with tip mass under harmonic support motion , 1998 .

[26]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[27]  M. R. Silva,et al.  Non-linear flexural-flexural-torsional-extensional dynamics of beams—II. Response analysis , 1988 .

[28]  Ali H. Nayfeh,et al.  Nonlinear Responses of Buckled Beams to Subharmonic-Resonance Excitations , 2004 .