Application Of Partial Differential Equation In String Vibration

The Partial differentia equation is a type of equation which reflects relatively unknown variate about restricting relation between time variate derivative and space variate derivative and accordingly, is widely used in physics, etc. String vibration a kind of mechanical movement, but string isn't particle and the particle mechanics laws aren't suitable for string vibration. Therefore string vibration can only be expressed by string vibration equation. Actually, string vibration equation is a typical model of partial differentia equation and its deduced process is fairly complicated, thus the dominant factors must be considered and the secondary factors may be ignored. The boundary conditions must be known, namely considering its physical conditions of the research object to obtain the unique solution of string vibration.Several actual applications of string vibration for boundary value problem were studied in this paper. At first, string vibration equation without outside force and string transverse vibration equation with outside force were respectively deduced, based on suitable assumption of string vibration. Method of separation of variables was used to study the existence of the problem of fixing solution of string vibration equation under different conditions. Afterward significance of the corresponding problem of fixing solution was studied and its application equations in rod vibration, etc were deduced. Secondly, cable tension of cable-stayed bridge was studied at the point of basic theory of string vibration and the equation between natural frequency of cable vibration and cable tension was obtained through calculating the string vibration equation. Understanding and controlling its tension has important engineering significance to insure run-time safety of cable-stayed bridge (estimation of loading charge and running condition) and cable car (tension controlling), etc. Finally, problem of cop application was also analyzed and discussed.