A time harmonic line force or moment is applied at the junction of two plates in welded contact, with or without unilateral fluid loading. The objective is the 2Γ2 matrix of admittances relating the applied force and moment to the deflection and rotation at the load. The structural asymmetry leads to coupling between force and rotation, and between moment and deflection, even in the absence of fluid loading. The impedance matrix is derived for sources with linear phase variation of the form e ik y y for real ky . The dry plate problem is addressed first, and displays the possibility of a resonance when the drive is in phase with a flexural Stoneley wave, which is defined here. The fluid-loaded problem is attacked by expressing the vibration of either plate and the acoustic response in the fluid as transforms, the integrands of which are derived using the Wiener-Hopf technique. It is found that the wet response shows the same general behaviour as for the dry plates, but without the possibility of a structural resonance. Numerical examples are presented showing the frequency dependence of the admittance matrix for joined steel plates in water. The general theory for distinct plates under fluid loading also provides a new formula for the line admittance of a uniform plate in a fluid.