ANALYTICAL DETERMINATION OF THE NATURAL COUPLED FREQUENCIES AND MODE SHAPES AND THE RESPONSE TO OSCILLATING FORCING FUNCTIONS OF TANDEM HELICOPTERS

摘要

A method is presented for the analytical determination of the natural coupled frequencies and mode shapes of vibrations in the vertical plane of tandem helicopters. The coupled mode shapes and frequencies are then used to calculate the response of the helicopter to applied oscillating forces. Degrees of freedom included in the analysis are translation, pitching, and bending of the fuselage;translation, flapping, and bending of the blades;and translation of the engine. The method employs the Lagrange dynamical equations for free vibrations in conjunction with the kinetic and potential energies of the system in order to obtain the differential equations of motion for the coupled system which are then written in matrix form. The elements of the determinant of the matrix equation include the natural frequencies, mode shapes, and mass distributions of the uncoupled compo¬nents of the helicopter (such as fuselage, blades, and engine) and permit the inclusion of experimental data of the uncoupled components in the evaluation of the coupled frequencies of the coupled system.