The vibration of a non-prismatic beam on an inertial elastic half-plane

The problem of vibration of a non-prismatic beam resting on an inertial elastic half-plane described by classical elastokinetics equations is solved using Chebyshev series approximation. As a result, closed analytical formulae for the sought solutionʹs coefficients—the passive foundation pressure function and the system displacement function—were obtained. The method was applied to solve the problem of harmonically excited vibration.