Numerical integration Methods in Vibration Analysis

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:
  1. They are not intended to satisfy the governing differential equation(s) at all-time t but only at discrete time intervals Δt apart
  2. 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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