Unsteady hydroelastic waves generated by impulsively-starting surface and submerged concentrated loads in a fluid with an underlying uniform current are studied analytically. The fluid is assumed to be homogeneous, incompressible, inviscid, and of finite depth. For the case of irrotational motion with small-amplitude deflections, linear potential-flow theory is employed. The Laplace equation is the governing equation, with the dynamic condition representing a balance among the hydrodynamic, elastic, inertial forces and the downward applied load. It is shown that the analytical solution, obtained by the Laplace-Fourier integral transform, consists of steady-state and transient responses. For the steady response, an explicit expression is further derived by the residue theorem, while the transient response is obtained by the stationary-phase method. These expressions allow the effects of various physical parameters on the hydroelastic responses to be studied in detail. It is found that the flexural-gravity wave motion depends on the ratio of current speed to phase or group speeds.

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