Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach

Abstract An analytical model is proposed for free vibration and geometrically linear thermal buckling phenomenon of a thin rectangular isotropic plate containing a continuous line surface or internal crack located at the centre of the plate using classical plate theory. The crack terms are formulated using Line Spring Model. The in-plane forces are due to the uniform heating of the cracked plate. Applying the Galerkin׳s method, the equation is transformed into Duffing equation which shows the effect of uniform rise in temperature on natural frequencies. A classical relation for buckling temperature for a cracked plate is also determined.

[1]  P. Jeyaraj,et al.  Vibration and acoustic response of a composite plate with inherent material damping in a thermal environment , 2009 .

[2]  Lawrence N. Virgin,et al.  The Effect of Thermal Prestress on the Free Vibration Characteristics of Clamped Rectangular Plates: Theory and Experiment , 1997 .

[3]  William L. Ko,et al.  Mechanical- and Thermal-Buckling Behavior of Rectangular Plates With Different Central Cutouts , 1998 .

[4]  P Kerfriden,et al.  Linear free flexural vibration of cracked functionally graded plates in thermal environment , 2011 .

[5]  Said Rechak,et al.  Vibration analysis of cracked plates using the extended finite element method , 2009 .

[6]  Y. Shih,et al.  Dynamic instability of rectangular plate with an edge crack , 2005 .

[7]  Danial Panahandeh-Shahraki,et al.  Buckling of cracked functionally graded plates under tension , 2014 .

[8]  Hui-Shen Shen,et al.  VIBRATION CHARACTERISTICS AND TRANSIENT RESPONSE OF SHEAR-DEFORMABLE FUNCTIONALLY GRADED PLATES IN THERMAL ENVIRONMENTS , 2002 .

[9]  Vai Pan Iu,et al.  Three-dimensional vibration analysis of functionally graded material plates in thermal environment , 2009 .

[10]  Robert M. Jones,et al.  Buckling of Bars, Plates and Shells , 2007 .

[11]  Jeng-Shian Chang,et al.  THERMAL BUCKLING ANALYSIS OF ISOTROPIC AND COMPOSITE PLATES WITH A HOLE , 1990 .

[12]  J. Rice,et al.  The Part-Through Surface Crack in an Elastic Plate , 1972 .

[13]  Ahmad Rahbar-Ranji,et al.  Ultimate strength of stiffened plates with a transverse crack under uniaxial compression , 2015 .

[14]  Chi-Hung Huang,et al.  VIBRATION ANALYSES OF CRACKED PLATES BY THE RITZ METHOD WITH MOVING LEAST-SQUARES INTERPOLATION FUNCTIONS , 2014 .

[15]  Chiara Bisagni,et al.  Semi-analytical buckling analysis of omega stiffened panels under multi-axial loads , 2015 .

[16]  M. Alinia,et al.  Influence of central cracks on buckling and post-buckling behaviour of shear panels , 2007 .

[18]  Rahman Seifi,et al.  Experimental and numerical studies on buckling of cracked thin-plates under full and partial compression edge loading , 2011 .

[19]  K. D. Murphy,et al.  Thermal buckling of rectangular plates , 2001 .

[20]  Nicholas Fantuzzi,et al.  Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape , 2013 .

[21]  S. E. Khadem,et al.  INTRODUCTION OF MODIFIED COMPARISON FUNCTIONS FOR VIBRATION ANALYSIS OF A RECTANGULAR CRACKED PLATE , 2000 .

[22]  Zeng Zhao-jing,et al.  Stress intensity factors for an inclined surface crack under biaxial stress state , 1994 .

[23]  Jeom Kee Paik,et al.  Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study , 2002 .

[24]  Young-Wann Kim,et al.  TEMPERATURE DEPENDENT VIBRATION ANALYSIS OF FUNCTIONALLY GRADED RECTANGULAR PLATES , 2005 .

[25]  S Natarajan,et al.  A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method , 2013, 1305.4486.

[26]  R. Szilard.  Theories and Applications of Plate Analysis , 2004 .

[27]  Jiang Jie-sheng,et al.  A finite element model of cracked plates and application to vibration problems , 1991 .

[28]  N. Ganesan,et al.  Vibration and Acoustic Response of an Isotropic Plate in a Thermal Environment , 2008 .

[29]  Marek Krawczuk,et al.  Finite element model of plate with elasto-plastic through crack , 2001 .

[30]  N. K. Jain,et al.  Analytical modeling and vibration analysis of internally cracked rectangular plates , 2014 .

[31]  Matthew P. Cartmell,et al.  Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading , 2009 .

[32]  Roberto Brighenti,et al.  Buckling sensitivity analysis of cracked thin plates under membrane tension or compression loading , 2009 .

[33]  F. Erdogan,et al.  Interaction of part-through cracks in a flat plate , 1985 .

[34]  M. Cartmell,et al.  An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation , 2012 .

[35]  A. Mohanty,et al.  Vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position , 2013 .

[36]  Philippe Rigo,et al.  Residual Ultimate Strength of Cracked Steel Unstiffened and Stiffened Plates under Longitudinal Compression , 2014 .

[37]  A. Saidi,et al.  Accurate Critical Buckling Load/Temperature of Thick Annular Sector Plates , 2012 .