Forced vibrations of plates and cylindrical shells with regular orthogonal system of stiffeners

A wide range of engineering structures, such as aircraft fuselages or ship hulls have as the foundation a shell orthogonally strengthened by two sets of stiffeners. Solution of the task related to determining the vibrations of such complicated structures requires an application of special methods which permit accounting for the interaction between the shell and the two sets of discrete stiffeners correctly. The present work proposes an effective method of predicting the vibrations of a finite orthogonally stiffened structure as a part of an infinite one when the edge conditions permit. The prediction method proposed is based on the method of space-harmonic expansions when the shell displacements and forces are presented in the form of special double trigonometric series. The method allows the interconnection of all three components of displacement and rotation of the shell and the stiffeners to be taken into account. The vibration velocity of the construction is determined directly without a need for solving the task of eigen-values first. The vibration shapes are broken into a large number of non-interacting groups of shapes. The solution reduces to a system of equations relating to the generalized reactions at supports. All this allows predictions to be made for large parts of the investigated construction over practically the whole frequency range of sound.