Various graphite targets with a tantalum core were exposed to 440 GeV pulsed proton beams at the HiRadMat facility at CERN. The dynamic response was investigated by monitoring the surface velocity of the samples by laser Doppler vibrometry. The study comprises different graphite grades, such as polycrystalline, expanded and carbon-fiber reinforced graphite, and low-density graphitic foams, all candidates for beam-intercepting devices in high-power accelerators. The purpose of the tantalum core is to concentrate the large energy deposition in this high-density material that withstands the localized beam-induced temperature spike. The generated pressure waves are estimated to result in stresses of several hundred MPa which subsequently couple with the surrounding graphite materials where they are damped. Spatial energy deposition profiles were obtained by the Monte Carlo code FLUKA and the dynamic response was modelled using the implicit code ANSYS. Using advanced post-processing techniques, such as fast Fourier transformation and continuous wavelet transformation, different pressure wave components are identified and their contribution to the overall dynamic response of a two-body target and their failure mode are discussed. We show that selected low-intensity beam impacts can be simulated using straight-forward transient coupled thermal/structural implicit simulations. Carbon-fiber reinforced graphites exhibit large (macroscopic) mechanical strength, while their low-strength graphite matrix is identified as a potential source of failure. The dynamic response of low-density graphitic foams is surprisingly favourable, indicating promising properties for the application as high-power beam dump material.