An Approximation to the Influence Function for Plate‐like Wings: A General Solution for Small Deflexions

A general solution for the small deflexions of thin plates of slowly varying thickness under lateral loading in the form of an influence function is briefly presented. It is known that the influence function may be represented as an infinite series in terms of the eigenfunctions and eigenvalues associated with a homogeneous form of the plate differential equation. It is suggested that the series may give an acceptable approximation to the influence function when summed over a small number of terms when also the eigenfunctions and eigenvalues involved are deduced by an approximate procedure of the Rayleigh‐Ritz type. In order to test this assertion a numerical example is given for a uniform canti‐lever plate and the results are compared with experiment and with similar results deduced by an alternative theoretical procedure. Thus the calculation of a sufficient number of approximate normal vibration modes and frequencies for the plate as normally required for aeroelastic investigations may in this way be made to serve as the basis for a complete analysis of the plate. A simple approximate allowance for shear deflexion of the plate is presented and illustrated.