Introduction to Aircraft Aeroelasticity and Loads

G

MTLAB/SIMULINK Programs for Vibration

It is beyond the scope of this book to present a detailed treatment of the use of MATLAB and SIMULINK, but instead a few key programs are presented which the reader can use as a template for trying other related calculations. It is assumed that a basic knowledge of the packages will be obtained from other sources.

G.1 FORCED RESPONSE OF AN SDoF SYSTEM

In Chapter 1, the example of an SDoF system excited by a single cycle of a square wave was considered. The response was obtained in three ways, namely using superposition (essentially simple convolution), numerical integration and via the frequency domain (using the Fourier Transform).

G.1.1 Superposition (Essentially Convolution)

The superposition approach treats the double pulse excitation as the combination of three steps. The response to a single step is used as a constituent building block in generating the overall response. Clearly, different inputs such as square waves of different numbers of cycles and periods may be explored by simple modifications of the code.

The program is shown below. The theory in Chapter 1 will be required to follow the program.

% Response of SDoF system to single cycle of a square wave clear all; close all; % System parameters f_nat = 2; period = 1 / f_nat; w_nat = 2 * pi * f_nat; zeta = 0.05; mass = 1000; stiff = w_nat^2 * mass; force = 1000; w_dpd = w_nat* sqrt(1-zeta^2); psi = atan2(sqrt(1 - zeta^2), zeta); % Data parameters T = 8; dt = 0.01; t = [0:dt:T]; ...