Transient Analysis of a Simply Supported Beam

Transient Analysis using ANSYS

2008-09-23T20:09:00.002-07:00

FEM analysis software ANSYS© provides many features related to the analysis of the vibrations in a structure. One such feature is transient analysis. Transient analysis in ANSYS© is carried out for any application to study the system properties with respect to time. Transient vibration analysis gives useful information about system damping and other effects of the controlling forces on vibration with a function of time. ANSYS© provides excellent coding features by which the controller logic can be built in itself and controller simulation can be carried out. This feature of ANSYS© is used for active vibration control in the present case.

Controlling analysis is carried out in this section by iterative selection of controller gain. Controller gain is not designed based on the earlier results obtained from MATLAB©. In this section an attempt is made to control the first and second mode of vibration.

Simulation Study to Control First Mode using ANSYS

2008-09-23T20:09:00.001-07:00

The closed loop controller is introduced in ANSYS© by means of a macro. The sensor output is taken by taking the difference between the X direction displacement (u1 and u2) of two nodes, in the same plane on either side of the centre line. This is divided by the distance between them to get strain. It is then appropriately amplified by multiplying it with sensor gain ks. The controller is then defined by the error function and the voltage va to be applied is calculated by multiplying the error function with appropriate actuator gain (ka).

The generic macro used to simulate the controller action is given below:

*set,dt,0.0088
*set,ts2
*set,nv,559
*set,nr1,1117
*set,nr2,455
*set,dx,18*(8.33e-3)
*set,ks,1000
*set,kv,1000
*set,kc,1
*set,va,0
*do,t,3*dt,ts,dt
*get,u1,node,nr1,u,x
*get,u2,node,nr2,u,x
err=0-ks*(u2-u1)/dx
va=kc*kv*err
d,nv,volt,va
time,t
solve
*enddo

Where,

dt : Time step for Transient Analysis in ANSYS©
ts : Time for which analysis is carried out
nv : Node at which voltage is applied
nr1 : Higher node considered for strain calculation
nr2 : Lower node considered for strain calculation
dx : Distance between nodes nr1 and nr2
ks : Sensor gain
kv : Actuator gain
kc : Proportional (controller) gain
va : Applied voltage
err : Error function

The value of kc is varied to obtain desired controller effect. But constraint is placed on the maximum value of kc due to voltage. The values of Rayleigh damping are taken as 0.002.

Displacement v/s Time Plot for different kc values

Voltage v/s Time Plot for different kc values

Though in above case, the vibration settling time is decreased. But the rate of decrease is quite low. A steeper decrease of vibration settling time can be obtained by increasing the patch size.

Simulation Study for Controlling Second Mode using ANSYS

2008-09-23T20:08:00.001-07:00

Second mode of vibration can be controlled by placing the patch at a distance of 0.25 times the length of the beam, from any one end of the simply supported beam. The force for the transient analysis is applied at the same point to excite the second mode of vibration.

Meshed Integrated Structure for Control of Second Mode

All parameters like ks, kv and damping values are kept constant. The value of kc is varied for finding the controller effectiveness. The graphs of displacement v/s time and voltage v/s time are plotted.

Displacement v/s Time Plot for different kc values

Voltage v/s Time Plot for different kc values

Though in above case, the vibration settling time is decreased. But the rate of decrease is very low. A steeper decrease of vibration settling time can be obtained by increasing the patch size or using more than one patch.