Use of dynamic influence coefficients in forced vibration problems with the aid of fast fourier transform

Abstract The use and importance of dynamic stiffness influence coefficients in flexural forced vibrations of structures composed of beams are described. The dynamic forces can be either harmonic or general transient forces. The dynamic influence coefficients are defined in the Fourier transform plane, are computed there and are given in Table form for a uniform free-free beam. The dynamic problem formulated in terms of these coefficients is reduced to a static form. The dynamic response is obtained, in general, by a matrix inversion in the Fourier transform plane and a numerical inversion, based on the Cooley-Tukey algorithm, of the transformed solution. Structural examples of forced vibrations of a simple beam and a rigid frame illustrate the use of dynamic coefficients and demonstrate their advantages over other known methods in accuracy, simplicity of formulation and speed of computation.

[1]  K. W. Levien,et al.  Dynamic Flexibility Matrix Analysis of Frames , 1963 .

[2]  Daniel D.McCracken,et al.  Fortran with engineering applications , 1967 .

[3]  H. E. Salzer,et al.  Tables for the Numerical Calculation of Inverse Laplace Transforms , 1958 .

[4]  Maurice A. Biot,et al.  Mathematical methods in engineering , 1940 .

[5]  T. M. Wang,et al.  Vibrations of frame structures according to the Timoshenko theory , 1971 .

[6]  John M. Biggs,et al.  Introduction to Structural Dynamics , 1964 .

[7]  J. Cooley,et al.  Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals , 1967, IEEE Transactions on Audio and Electroacoustics.

[8]  N M Brenner,et al.  THREE FORTRAN PROGRAMS THAT PERFORM THE COOLEY-TUKEY FOURIER TRANSFORM , 1967 .

[9]  Francis C. Moon,et al.  One-Dimensional Transient Waves in Anisotropic Plates , 1973 .

[10]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[11]  W. G. BICKLEY.  Mechanical Admittances and their Applications to Oscillation Problems , 1948, Nature.

[12]  J. J. Fitzgerald,et al.  Application of the Fast Fourier Transform to linear systems in civil engineering , 1973 .

[13]  M. F. Rubinstein,et al.  Dynamics of structures , 1964 .

[14]  Shih-Chi Liu,et al.  EARTHQUAKE INTERACTION BY FAST FOURIER TRANSFORM , 1971 .

[16]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[17]  Bulent A. Ovunc,et al.  Dynamics of frameworks by continuous mass method , 1974 .

[18]  D. G. Stephenson,et al.  A Computer Oriented Adaption of Salzer's Method for Inverting Laplace Transforms , 1961 .

[19]  Harold Clifford Martin,et al.  Introduction to Matrix Methods of Structural Analysis , 1966 .