ESDU 87002:2011

ESDU 87002 introduces computer programs and a graphical method
for estimating the lower natural frequencies of initially
unstressed isotropic plates with either all edges simply-supported
or all edges fixed in both rotation and translation. The ratio of
length (and width) to thickness should exceed 20, the ratio of
width to radius should be less than 1.5, and the graphical method
is for aspect ratios of 0.1 to 10. For fixed edge conditions,
typical mode shapes are illustrated for a range of aspect ratios
and curvatures, and some experimental results for the first modes
of one geometry plate are compared with predictions. The two
programs, ESDUpacs A8702 and B8702, use energy methods of analysis.
ESDUpac A8702 is for edges simply-supported and gives an exact
solution to the equations of motion and boundary conditions.
ESDUpac B8702 is for fixed edges and uses a Rayleigh-Ritz analysis
in which the number of terms in the assumed displacement function
can be varied to provide the required accuracy. Worked examples
illustrate the use of both graphical and program methods, and
application to stiffened structural panels is discussed.