Two-dimensional in-plane free vibrations of functionally graded circular arches with temperature-dependent properties

Abstract In this paper, the in-plane free vibration analysis of functionally graded (FG) thick circular arches subjected to initial stresses due to thermal environment is studied. The formulations are based on the two-dimensional elasticity theory. The material properties are assumed to be temperature-dependent and graded in the thickness direction. Considering the thermal environment effects, the equations of motion are derived using the Hamilton’s principle. The initial thermal stresses are obtained by solving the two-dimensional thermoelastic equilibrium equations. Two types of temperature rise, uniform and variable through the thickness, is considered. Differential quadrature method (DQM) is adopted to solve the equilibrium equations and the equations of motion. The formulations are validated by comparing the results in the limit cases with those available in the literature for isotropic arches. The effects of temperature rise, material and geometrical parameters on the natural frequencies are investigated. The new results can be used as benchmark solutions for future researches.

[1]  M. S. Qatu,et al.  Vibration of laminated composite arches with deep curvature and arbitrary boundaries , 1993 .

[2]  P.A.A. Laura,et al.  Literature Review : Recent Research On Vibrations of Arch-Type Structures , 1987 .

[3]  M. Ganapathi,et al.  Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method , 2006 .

[4]  Y. P. Tseng,et al.  In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis , 2000 .

[5]  Ghodrat Karami,et al.  In-plane free vibration analysis of circular arches with varying cross-sections using differential quadrature method , 2004 .

[6]  Vebil Yıldırım,et al.  ROTARY INERTIA, AXIAL AND SHEAR DEFORMATION EFFECTS ON THE IN-PLANE NATURAL FREQUENCIES OF SYMMETRIC CROSS-PLY LAMINATED CIRCULAR ARCHES , 1999 .

[7]  A. Leissa,et al.  Vibrations of Planar Curved Beams, Rings, and Arches , 1993 .

[8]  B. P. Patel,et al.  Shear flexible field‐consistent curved spline beam element for vibration analysis , 1999 .

[9]  Y. S. Touloukian.  THERMOPHYSICAL PROPERTIES OF HIGH TEMPERATURE SOLID MATERIALS. , 1967 .

[10]  C. Lü,et al.  Exact two-dimensional solutions for in-plane natural frequencies of laminated circular arches , 2008 .

[11]  Athol J. Carr,et al.  Generalized finite element analysis of laminated curved beams with constant curvature , 1989 .

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

[13]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[14]  Mohamad S. Qatu,et al.  In-plane vibration of slightly curved laminated composite beams , 1992 .

[15]  H. Matsunaga.  Free vibration and stability of laminated composite circular arches subjected to initial axial stress , 2004 .

[16]  A. R. Setoodeh,et al.  A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches , 2008 .

[17]  P. Malekzadeh.  THREE-DIMENSIONAL FREE VIBRATION ANALYSIS OF THICK FUNCTIONALLY GRADED PLATES ON ELASTIC FOUNDATIONS , 2009 .

[18]  C. Lim,et al.  Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches , 2009 .

[19]  Chi-Hung Huang,et al.  In-plane free vibration and stability of loaded and shear-deformable circular arches , 2003 .

[20]  Mohamad S. Qatu,et al.  Theories and analyses of thin and moderately thick laminated composite curved beams , 1993 .