Beam Vibration Equation Of The Characteristic Value Of The Solution,

Generally, the mathematical expression of physical vibration is a linear partial differential equation. The beam's vibration can be described by the equation (?)=-(?)((t,x)∈[0,+∞]×[0,τ]). In order to solve this equation, we must set the appropriate initial and boundary conditions, thus we solve four problems in detail and explain the rationality of initial and boundary conditions. In this article, we prove that the solution of the above equation is existent and unique. And the eigenvalue method plays a key role in the proof.