A vibration-damping sub is provided to mitigate shock and other sources of vibration in a tool string. In examples, a tubular damping body is rigidly coupled between a vibration-sensitive tool and a vibration source. The tubular damping body includes a tubular wall defining a plurality of shaped holes configured to dampen the mechanical vibration to below the design threshold for the vibration-sensitive tool. The tubular damping body may also include different portions having different materials and impedances to further disrupt the propagation of mechanical waveforms.