Experimental Structural Dynamics

1.1 Introduction

This text is about vibrating structures. The structures considered could be any of a broad range of engineered products, from TV sets, computers and other electronics products to cars, trucks, trains, aircraft, rockets and other vehicles. We could be talking about bridges or buildings. All of these products have the potential to fail in their product performance without proper engineering to avoid damage that could be caused by mechanical vibration. Aircraft are analyzed and tested to arrive at structural design characteristics that are successful in handling the aerodynamic loads encountered during flight. Vehicles are subject to vibration and noise originating from the engine, tires rolling over an irregular surface at high speed and turbulent air flow over the body. Vibration design characteristics are designed into the vehicle to avoid wear and fatigue failure of certain components and to provide a comfortable and quiet ride for the passenger.

For general arbitrary structures, the vibration process is very complicated, so complicated that one might expect the process impossible to comprehend. Impossible, except for the ability to analyze the most complex vibration motion as a superposition of relatively simple processes. It turns out that no matter how complicated the structure and no matter how complicated the vibratory motion of the many parts of the vibrating structure, it is usually possible to separate the process into easily understood fundamental vibratory processes.

It is the goal of this text to first present the theory underlying the simple vibratory process, then develop the concepts allowing application of this understanding to the analysis of any complicated vibratory process for the most complex structure. There is one limitation in the level of structural complexity to be considered, however: The text will be concerned with linear structures. Vibration displacements will be small and stiffness characteristics will be fixed, independent of the amount of structural deformation.

1.2 Simple Harmonic Motion

A natural starting point is to study the motion of the simplest of structures in a natural state of vibration. Figure 1-1 depicts such a structure and the simple vibratory motion that results when a lumped mass sitting on a spring is made to vibrate freely. The mass is initially displaced upward from its equilibrium position on the spring.

From this position it is released, accelerating downward under the pull of the stretched spring. The continuous motion of the mass is graphed with the solid curve in the figure. Instantaneous positions of the mass at key points in time are sketched. The mass is seen to oscillate, moving down until the upward force of the compressed spring brings the downward motion to a stop. Then the upward push of the compressed spring propels the mass upward until the cycle of oscillation is complete when the upward motion is stopped under the downward pull of the stretched spring. The cycle of motion is completed in one second in our example. From this point in time the mass will continue to oscillate in this fashion forever in the absence of any other influences, i.e, friction, human intervention, etc.