IMPACT OF A BODY ON A PLATE RESTING ON AN ELASTIC BASE

The plane problem of collision of a finitely-wide body with a thin plate resting on the surface of an elastic medium, of the compressible-fluid type is examined. The problem reduces to the solution of an integrodifferential equation with a complex kernel and a semi-infinite interval for variable variations. The exact solution of the equation is found with the help of integral conversions and the Fock method. Simple formulas, applicable for small time intervals are found for determining the shape of the deformed plate, when the body moves with a constant velocity after the impact. A law determining the motion of the body is found when the initial velocity of the body is known. In both cases, the force acting on the body from the liquid and the plate is determined. The solution found is compared with the solution of the problem dealing with impact of a body with the surface of a compressible liquid without a cover. As a result of the comparison effects of the cover on the impact of the body with the liquid are examined.
Edited trans. of mono. Vsesoyuznyi Simpozium po Rasprostraneniyu Uprugo-Plasticheskikh Voln v Sploshnykh Sredakh, Baku, 1964. Materialy, Baku, 1966 p149-158.