In a general case (arbitrary piezoelectric material, orientation, mode etc…), both closed (resonance) and open (antiresonance) circuit boundary conditions will affect the response of the piezoelectric structure, since both impose electrical boundary conditions. There are many practically important special cases (e.g. thickness excitation of thickness vibrations in some popular crystal cuts) where the antiresonance frequency is not affected by the piezoelectric effect, i.e. the effective elastic constant that governs this vibration is not “stiffened” by the piezoelectric coefficients. In this sense, you can say that the open circuit boundary condition produced a purely structural response. In other cases, such as lateral excitation of thickness vibrations or thickness excitation of longitudinal vibrations in piezoelectric rods, the closed circuit solution (resonance) produces a purely structural frequency for some crystal orientations, while the open circuit solution becomes a function of the piezoelectric coupling. You need to examine several factors—material properties (stiffness,piezoelectric,dielectric matrices), orientation, electrode location, type of vibration—before you can say whether the open circuit piezoelectric structure response will be identical to the purely structural one. Sometimes, it is easier to do it numerically: perform a piezoelectric modal analysis (closed and open circuit), a structural modal analysis (piezoelectric coeff. set to zero or structural keyoption) and compare the results. Note that there is a mistake in the VM175 problem (corrected in MAPDL 6.0) in which the open circuit boundary condition was imposed without coupling the nodes on one of the electrodes, causing the open circuit response to be identical to a purely structural one. It may have given the impression that the open-circuit does not affect the response.