belt driven pump vibration

hi
we have a belt driven pump mounted on a base supported by 4 bolts the pump has a Very high 12.6 Hz component on motor DE and NDE axial direction, this component is almost matching the pump running speed (12.4 Hz) as well as matching the skid natural frequency in axial direction (12.2 Hz) as per the bump test result, it is also very near the Belt Passing Frequency (16 Hz), this lead us to consider that the problem is structural resonance specially in axial direction due to bad design
we tried to increase the stiffness of the 4 bolts by bolting these rings shown in red in the attached drawing , but this modification altered the skid natural frequency from 12Hz (that was matching the pump running speed) to 16Hz (that is matching the belt passing frequency), i need to know if our understanding of the problem is right and if there is a standard or a text book for designing such kind of pump base to help me make a better modification of the base
thanks.

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