Some Useful Approximations for Determining the Vibration of Structures Excited by Random Pressures

Abstract

even and odd functions g(z) = •(z) sin(w•z)dz, 0(z)= •(z) cos(w•z)&, finding in due course that j•= {O(x)-O(x) cos2w•x-g(x) sin2w•x}dx.1 -•. (10) Integration by parts leads to the simple and well-behaved result j,,•= •(x)•_ (l-x) cosw•x-w• -1 sinw•x•dx'l -•. (11) Presumably, there are corresponding expressions for oth r mode shapes.When • falls to a small enough value in a distance small as compared to the structural wavelength 2•-/w,•, •-----fo C(x)ax'•-•=«L/•' 02)where L is the correlation length in the appropriate direction. a.4 Here, j,•m•=•LiL2/lll2, in which L1L2 can be likened to the correlation arm [and equals it for the correlation of Eq. (9)•.This gives by far the quickest method of evaluating the joint acceptance for cases not already determined for the mode shape concerned. The alternative methods are to (a) use the Fourier transform of the correlation function and of the mode shape, which