This paper presents an investigation of anharmonic effects in the IR spectra of [SiPAH](+) complexes by using Born-Oppenheimer molecular dynamics for a variety of PAHs ranging from naphthalene (C10H8) to ovalene (C32H14). The potential energy surfaces are calculated with the self-consistent charge density functional-based tight binding approach (DFTB). The DFTB parameters are modified to reproduce potential energy surfaces and the harmonic infrared spectra of the studied complexes with respect to DFT calculations. For bare PAHs, we find that the evolution of the vibrational frequencies of the C-H out-of-plane bending and C-C stretching modes as a function of temperature follows a linear law in quantitative agreement with experimental data. For cationic PAHs, the anharmonicity of the bands in terms of position shifts is found to be enhanced with respect to that of neutrals. As compared with bare cationic PAHs, the coordination of Si induces (i) larger broadenings, (ii) a slightly larger shift of the C-C stretching mode, and (iii) a smaller shift of the C-H out-of-plane bending modes. We discuss the implications of the work and the spectroscopic constraints for the detection of [SiPAH](+) in the interstellar medium.