Natural frequency split estimation for inextensional vibration of imperfect hemispherical shell

In this study, mathematical model of hemispherical shell is introduced using inextensional vibration mode shapes. Adopting energy equations, the natural frequency of the shell is determined by applying Rayleigh's energy method. Further, the vibration for imperfect shell is investigated with point mass elements representing imperfections on the structures. Also, the effects are considered via energy relations, and the split amount of the natural frequencies can be determined. Finally, the influences of point mass are presented by explicit functions for the split of the natural frequency and shifting angle of mode orientation. Based on the proposed model of imperfect shell with multiple point masses, the structure can be expressed as an equivalent single mass model.

[1]  V. Ph. Zhuravlev,et al.  A CONTROLLED FOUCAULT PENDULUM AS A MODEL OF A CLASS OF FREE GYROS , 1997 .

[2]  Chan-Shin Chou,et al.  MODAL PRECESSION OF A ROTATING HEMISPHERICAL SHELL , 1996 .

[3]  Alavandi Bhimaraddi.  Nonlinear Dynamics of In-Plane Loaded Imperfect Rectangular Plates , 1992 .

[4]  V.C.M. de Souza,et al.  An energy analysis of the free vibrations of isotropic spherical shells , 1980 .

[5]  Herbert Saunders,et al.  Inextensional Vibrations of a Sphere-Cone Shell Combination , 1959 .

[6]  Stewart McWilliam,et al.  MULTI-MODE TRIMMING OF IMPERFECT RINGS , 2001 .

[7]  A Achong.  VIBRATIONAL ANALYSIS OF MASS LOADED PLATES AND SHALLOW SHELLS BY THE RECEPTANCE METHOD WITH APPLICATION TO THE STEELPAN , 1996 .

[8]  Chintsun Hwang.  Some Experiments on the Vibration of a Hemispherical Shell , 1966 .

[9]  Santosha K. Dwivedy,et al.  DYNAMICS OF A SLENDER BEAM WITH AN ATTACHED MASS UNDER COMBINATION PARAMETRIC AND INTERNAL RESONANCES PART I: STEADY STATE RESPONSE , 1999 .

[10]  W. Soedel.  Vibrations of shells and plates , 1981 .

[11]  Yu. N. Chelnokov.  QUATERNIONS AND RELATED TRANSFORMATIONS IN DYNAMICS OF A SYMMETRIC RIGID BODY. I. I , 1997 .

[12]  G. Venkateswara Rao,et al.  Fundamental frequency for large amplitude vibrations of uniform Timoshenko beams with central point concentrated mass using coupled displacement field method , 2006 .

[13]  Stewart McWilliam,et al.  On the statistics of natural frequency splitting for rings with random mass imperfections , 2005 .

[14]  Paolo Bisegna,et al.  Frequency split and vibration localization in imperfect rings , 2007 .

[15]  Myung-Seog Yang,et al.  A study on the free vibration of the joined cylindrical–spherical shell structures , 2000 .

[16]  Jintai Chung,et al.  VIBRATION ANALYSIS OF A NEARLY AXISYMMETRIC SHELL STRUCTURE USING A NEW FINITE RING ELEMENT , 1999 .

[17]  R. Blevins,et al.  Formulas for natural frequency and mode shape , 1984 .

[18]  S.-J. Yoon,et al.  A CONCENTRATED MASS ON THE SPINNING UNCONSTRAINED BEAM SUBJECTED TO A THRUST , 2002 .

[19]  C.H.J. Fox,et al.  A simple theory for the analysis and correction of frequency splitting in slightly imperfect rings , 1990 .