This is the generating field for the phase-conjugate beam, ? 4.
2.
From the above comparisons, we can state two theorems related to the conjugate beam:
3.
Note that the constant of proportionality between the signal and conjugate beams can be greater than 1.
4.
Here the conjugate beam has a free end, since at this end there is zero shear and zero moment.
5.
Although this occurs, the M / EI loading will provide the necessary " equilibrium " to hold the conjugate beam stable.
6.
Theorem 2 : The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.
7.
Note that, as a rule, neglecting axial forces, statically determinate real beams have statically determinate conjugate beams; and statically indeterminate real beams have unstable conjugate beams.
8.
Note that, as a rule, neglecting axial forces, statically determinate real beams have statically determinate conjugate beams; and statically indeterminate real beams have unstable conjugate beams.
9.
Consequently, from Theorems 1 and 2, the conjugate beam must be supported by a pin or a roller, since this support has zero moment but has a shear or end reaction.
10.
When drawing the conjugate beam it is important that the shear and moment developed at the supports of the conjugate beam account for the corresponding slope and displacement of the real beam at its supports, a consequence of Theorems 1 and 2.
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