@article{(Open Science Index):https://publications.waset.org/pdf/17346,
	  title     = {Geometrically Non-Linear Axisymmetric Free Vibrations of Thin Isotropic Annular Plates},
	  author    = {Boutahar Lhoucine and  El Bikri Khalid and  Benamar Rhali},
	  country	= {},
	  institution	= {},
	  abstract     = {The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,
},
	    journal   = {International Journal of Mechanical and Mechatronics Engineering},
	  volume    = {7},
	  number    = {9},
	  year      = {2013},
	  pages     = {1887 - 1893},
	  ee        = {https://publications.waset.org/pdf/17346},
	  url   	= {https://publications.waset.org/vol/81},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 81, 2013},
	}