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Coalescence of binary neutron stars (BNSs) is one of the sources ofgravitational waves (GWs) able to be detected by ground-based interferometricdetectors. The event GW170817 was the first observed in the gravitational andelectromagnetic spectra, showing through this joint analysis a certaincompatibility with the models of short gamma-ray bursts (sGRBs) to explain thesignature of this system. Due to the intense magnetic fields of the neutronstars, the plasma magnetosphere stays strongly magnetized and the propagationof the GW through plasma can excite magnetohydrodynamic (MHD) modes such asAlfv\'en and magnetosonic waves. The MHD modes carry energy and momentumthrough the plasma, suggesting a mechanism to accelerate the matter during thecoalescence of the binaries, explaining some characteristics of the fireballmodel of the sGRBs. We present a semianalytical formalism to determine theenergy transferred by the GW-MHD interaction during the inspiral phase of thestars. Using the inferred physical parameters for GW170817, we show that theenergy in the plasma can reach maximum value $\sim 10^{35}\,{\rm J}$ ($\sim10^{32}\,{\rm J}$) for the Alfv\'en mode (magnetosonic mode) if the angleformed between the background magnetic field and the GW propagation directionis $\theta = \pi / 4$. Particularly, for $\theta = \pi / 2$ only themagnetosonic mode is in coherence with the GWs. In this case, the excitedenergy in the plasma reaches maximum value $\sim 10^{36} {\rm J}$. If themagnetic field on the surface of the progenitors of the event GW170817 was$\sim 2\times 10^{9}\,{\rm T}$ then energies comparable to those inferred forthe GRB 170817A could be obtained. In particular, our semianalytical formalismshow consistence with the results obtained by other authors through fullgeneral relativistic magnetohydrodynamics (GRMHD) simulations. [ABRIDGED]

Magnetohydrodynamic waves excited by a coupling between gravitational waves and a strongly magnetized plasma in binaries of neutron stars