论文信息 - Finite element displacement method for large amplitude free flexural vibrations of beams and plates

Finite element displacement method for large amplitude free flexural vibrations of beams and plates

Abstract A finite element method to determine the nonlinear frequency of beams and plates for large amplitude free vibrations is presented. The equation of motion is characterized by the basic stiffness, mass, geometrical stiffness and the associated inplane force matrices. The procedures for solving the system equations of motion are discussed, and the explicit formulations of the geometrical stiffness and inplane force matrices of a rectangular plate element are given. Examples of large amplitude free oscillations for rectangular plates and beams with various boundary conditions are given. Characteristics of convergence are investigated. In all the cases where comparisons with previous investigations are made, good agreement has been obtained. It indicates that the present method will give results entirely adequate for engineering purposes.

Chuh Mei | C. Mei

[1] Arthur W. Leissa,et al. Vibration of Plates , 2021, Solid Acoustic Waves and Vibration.

[2] H. Berger. A new approach to the analysis of large deflections of plates , 1954 .

[3] Noboru Yamaki,et al. Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates , 1961 .

[4] George Herrmann,et al. Influence of large amplitudes on flexural motions of elastic plates , 1956 .

[5] Thein Wah. The Normal Modes of Vibration of Certain Nonlinear Continuous Systems , 1964 .

[6] A. V. Srinivasan,et al. Non-linear vibrations of beams and plates , 1966 .

[7] J. Eisley. Nonlinear vibration of beams and rectangular plates , 1964 .

[8] F. Bogner,et al. The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulae , 1965 .

[9] S. Timoshenko,et al. THEORY OF PLATES AND SHELLS , 1959 .

[10] Thein Wah,et al. Large amplitude flexural vibration of rectangular plates , 1963 .

[11] D. Evensen. Nonlinear vibrations of beams with various boundary conditions. , 1968 .

[12] Chuh Mei,et al. Nonlinear vibration of beams by matrix displacement method. , 1972 .