Stiffen at the antinode. Stiffening at the node will do you no good.
The word "node" is a corruption of "no displacement". So there is no movement at a node. Therefore there is not going to be a benefit to making a change (other than perhaps a mass change) to a node. Best regards, Tom Murphy
Changing stiffness, mass, or damping at a node point would not significantly affect natural frequencies or vibration levels at that point or other parts of the structure. Walt
You want to place a brace at an antinode. Determining which bending mode will come down to the frequency at which the component is vibrating. If you have determined there are 3 bending modes on a pump discharge pipe. Say the first is at 1700 CPM, the second occurs at 2250 CPM and the third at 3890 CPM. The motor driving the pump is on a VFD and has an operating range from 1500 to 1785 RPM. Measured vibration on the pipe is highest when the machine shaft speed approaches 1700 RPM. In this case, the 1st bending mode is becoming resonant. Place the brace at the point of peak displacement. Bracing the pipe will increase stiffness, which in turn may shift other natural frequencies higher in the spectra. Additional testing should be performed after bracing to ensure other natural frequencies have not aligned with different forcing frequencies.