In mechanics a two body system problem is very easy to
solve while a problem of three or more bodies in the system is very difficult.
That’s why we have to use approximate methods. From mathematical point of view
differential equation of motion that describe a vibrating system cannot be
integrated in the closed form that’s why we have to use a numerical approach.
There are several numerical methods available for
solving vibration problems such as:
- Finite difference Method,
- Central difference Method
- Runge-Kutta Method
- Houbolt Method
- Wilson Method
- Newmark Method
Numerical integration methods have following
fundamental characteristics:
- They are not intended to satisfy the governing differential equation(s) at all-time t but only at discrete time intervals Δt apart
- Suitable type of variation of displacement x, velocity dx/dt and acceleration d^2x/dt^2 is assumed within each time interval Δt.
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