Vibrations
 

Preface Introduction
Mass, Acceleration and Force
Gravitational Forces
Continua
Mechanical Vibrations & their Characteristic Modes
Friction
Vibration of Drill Rigs
Vortex-Induced Vibrations
Feedback
Stable & Unstable Motion induced by Forced Vibrations
Aerodynamics
Human-induced Vibrations
Electromagnetism
Probability Waves & Quantum Mechanics 

 

Continua

  Let us explore some of the ways material vibrations have an immediate impact on the world around us. Most tangible substances appear continuous to the eye. On close examination (with X rays) we now know that solid matter is composed of myriads of molecules arranged in different ways under the influence of intermolecular forces. The molecules themselves are built from a relatively small number of distinct atomic constituents. Many substances at room temperatures exhibit molecular patterns with long range regularities composed of repeating structural units. The nature of the constituents of a substance and the way in which the intermolecular forces are distributed govern its physical properties. They are ultimately responsible for the distinction between a lump of steel and a cotton thread. The ability of the intermolecular forces to resist bulk deformation of a solid is called elasticity and the forces that the body exerts across any plane in resisting such deformations are known as elastic stresses.
Most fluids (liquids and gases) have different characteristics from solids since the molecular constituents are freer to move in space being constrained only by any boundaries of containing vessels. Elastic stresses cannot be resisted by static deformations of a fluid and inevitable cause it to move. The laws of Newton are unable to predict the detailed properties of molecules in solids, liquids or gases. However since a single gramme of most substances at room temperature and pressure contains so many trillions of molecules it is found that they can be described in terms of relatively few average macroscopic parameters such as density, pressure, temperature, rigidity, elasticity and viscosity. Such quantities are adequate for a description of materials according to the laws of Newton.