Numerical Evaluation-Central Difference Method

Dynamic response of a structure can be solved numerically by using central difference method. This method is also known as an explicit method for dynamic analysis. First, we look into the expression of dynamic responses in terms of displacement response, which is a function of time.

Then, we substitute these variables into the equation of motion to further determine a general equation. This equation can help us predict the displacement response at the next instance, without using the parameters available at this and previous moments.

Following the derivation of analysis formulas, we look into an example of application for central difference method. To ease our analysis, it is advisable to construct a table to organize our calculation. We can calculate the displacement response until any time instance, even when there is no external force anymore. This helps us in inspecting the behaviour of structure under the effect of damping. From central difference method, we can obtain the curve of displacement response against time, and eventually plotting a hysteresis curve.

The following shows the derivation and application of central difference method. Watch the video above for full details.