Determination of material properties of orthotropic plates with general boundary conditions using Inverse method and Fourier series

Abstract Determination of material properties of orthotropic plates with general elastic boundary supports using the Inverse method is presented in this paper. The material properties were identified through updating four parameters in the governing equation of a symmetrically laminated thin plate. The sum of the squared difference of the natural frequencies obtained from modal testing was minimized using the Forward method. The displacement function was expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. A classical solution was derived by letting the series exactly satisfy the governing differential equation and all the boundary conditions at every field and boundary point. In the Inverse method, the series expansions for all the relevant derivatives of the eigen frequencies were obtained through term-by-term differentiations of the displacements. Many simulations were done but one numerical example is presented to demonstrate the accuracy and convergence of the solutions.

[1]  Ronald F. Gibson,et al.  An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions , 2009 .

[2]  S. W. Gong,et al.  Spline-Discretization-Based Free Vibration Analysis for Orthotropic Plates , 2008 .

[3]  O. Z. Chao,et al.  Study of open crack in rotor shaft using changes in frequency response function phase , 2013 .

[4]  Paolo Vannucci,et al.  A special class of uncoupled and quasi-homogeneous laminates , 2001 .

[5]  Rachman Setiawan.  Composite plate mechanical characterisation through dynamic tests , 2004 .

[6]  Hamid Bahai,et al.  Optimization of the Dynamic Characteristics of Composite Plates Using an Inverse Approach , 2007 .

[7]  Zubaidah Ismail,et al.  Approach to Reduce the Limitations of Modal Identification in Damage Detection Using Limited Field Data for Nondestructive Structural Health Monitoring of a Cable-Stayed Concrete Bridge , 2012 .

[8]  M. Grédiac,et al.  On the Design of Some Particular Orthotropic Plates with Non-Standard Ply Orientations , 2000 .

[9]  Zubaidah Ismail.  Combined modal parameters-based algorithm for damage identification in a beamlike structure: theoretical development and verification , 2011 .

[10]  Zhou Ding,et al.  NATURAL FREQUENCIES OF RECTANGULAR PLATES USING A SET OF STATIC BEAM FUNCTIONS IN RAYLEIGH-RITZ METHOD , 1996 .

[11]  Hashim Abdul Razak,et al.  Combined modal parameters-based index for damage identification in a beamlike structure: theoretical development and verification , 2011 .

[12]  W. L. Li.  Vibration analysis of rectangular plates with general elastic boundary supports , 2004 .

[13]  W. L. Li,et al.  A FOURIER SERIES METHOD FOR THE VIBRATIONS OF ELASTICALLY RESTRAINED PLATES ARBITRARILY LOADED WITH SPRINGS AND MASSES , 2002 .

[14]  Zubaidah Ismail,et al.  Effectiveness of Impact-Synchronous Time Averaging in determination of dynamic characteristics of a rotor dynamic system , 2011 .

[15]  Michel Grédiac,et al.  On the stiffness design of thin woven composites , 2001 .

[16]  Jingtao Du,et al.  An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports , 2009 .

[17]  D. J. Gorman,et al.  Vibration Analysis of Plates by the Superposition Method , 1999 .

[18]  Zhi Chao Ong,et al.  Honeycomb damage detection in a reinforced concrete beam using frequency mode shape regression , 2012 .

[19]  Emmanuel Ayorinde,et al.  Elastic constants of orthotropic composite materials using plate resonance frequencies, classical lamination theory and an optimized three-mode rayleigh formulation , 1993 .

[20]  C. Bert,et al.  FREE VIBRATION ANALYSIS OF TAPERED RECTANGULAR PLATES BY DIFFERENTIAL QUADRATURE METHOD: A SEMI-ANALYTICAL APPROACH , 1996 .

[21]  Arthur W. Leissa,et al.  The free vibration of rectangular plates , 1973 .

[22]  M. Cengiz Dökmeci,et al.  Vibration Analysis of a Rectangular Plate , 1973 .

[23]  T. Rossing,et al.  Determination of modal coupling in vibrating rectangular plates , 1984 .

[24]  Ronald F. Gibson,et al.  Determination of elastic constants of orthotropic plates by a modal analysis/Rayleigh-Ritz technique , 1988 .

[25]  H. Abdul Razak,et al.  Determination of damage location in RC beams using mode shape derivatives , 2006 .

[26]  Zubaidah Ismail.  An approach to reduce the limitations of modal identification in damage detection using limited field data for non-destructive SHM of a cable- stayed concrete bridge , 2012 .

[27]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[28]  K. Bhaskar,et al.  Accurate and elegant free vibration and buckling studies of orthotropic rectangular plates using untruncated infinite series , 2008 .

[29]  J Eskandari Jam,et al.  IDENTIFICATION OF MECHANICAL PROPERTIES IN LAMINATED COMPOSITE PLATESUSING GENETIC ALGORITHM , 2005 .

[30]  R. Gibson.  Principles of Composite Material Mechanics , 1994 .

[31]  Paolo Vannucci,et al.  Stiffness design of laminates using the polar method , 2001 .

[32]  W. L. Li.  FREE VIBRATIONS OF BEAMS WITH GENERAL BOUNDARY CONDITIONS , 2000 .

[33]  Siamak Noroozi,et al.  The development of laminated composite plate theories: a review , 2012, Journal of Materials Science.

[34]  D. J. Gorman,et al.  The superposition-galerkin method for free vibration analysis of rectangular plates , 1996 .

[35]  Paolo Vannucci,et al.  Some exact solutions for fully orthotropic laminates , 2005 .

[36]  Zubaidah Ismail,et al.  Application of residuals from regression of experimental mode shapes to locate multiple crack damage in a simply supported reinforced concrete beam , 2012 .