Plate vibrations – from Chladni to the present day

The paper provides a historical sketch of the development of theoretical mechanics from antiquity to modern times. The achievements of Polish authors in mechanics during the pre-war period are discussed. Against the background of the historical development of mechanics, the origins of the plate dynamics problem are presented. Chladni’s research on the eigenvalue problem of plates is discussed. A simple computer program leading to the so-called Chladni figures is provided. The equations of motion for Kirchhoff thin plates and Mindlin medium-thickness plates are analyzed. Several applications of plate theory are presented in computational examples, including FEM computer simulations.Three sciences are considered the oldest in the world: mathematics, astronomy, and mechanics, which until the time of Newton was essentially a philosophical system. The beginnings of the development of mechanics reach back to the deep antiquity of Babylon, Egypt, Mesopotamia, and Rome.
The name mechanics originates from ancient Greece, more precisely from the ancient Greek theater, and is associated with the name of Aristotle (384-322 BC). The Greek word
“µεχανε” [read] “mechane” has many meanings. It means, among other things, a theatrical machine that lifted up and lowered down an actor with a laurel wreath on a chest, symbolizing a god. Hence the later well-known saying in ancient Rome “deus ex machina”, or god from the machine. As Newton writes in the Principia (1687), the second meaning of the word “mechane” in ancient times also means: mechanism, invention, way, ruse, trick, method. (…)

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