At 1415 central time, a North American T-28A was damaged while landing at West Houston Airport. The pilot was not injured. The flight had left Tulsa, Okla., about two hours earlier. At Tulsa the aircrafts nose gear shimmy damper was serviced prior to departure. Upon landing, the shimmy was so bad that, even at 20 knots, the airplane was vibrating so badly the pilot said he couldnt see. Examination of the airplane revealed damage to the nose gear box, lower engine cowlings and nose gear doors. In addition, the forward firewall was bent.