The impulse response in the symbolic computing of modes for beams and plates Original Research Article

This work seeks to obtain in a systematic manner the symbolic normal modes of beams and plates in terms of the impulse response of an associated fourth-order ordinary differential equation and its derivatives. The problem of finding the modes of a beam subject to general boundary conditions amounts to considering a singular homogeneous matrix system involving the boundary conditions as well as the dynamical basis generated by the impulse response. For a plate, Levyʹs method, that assumes supported conditions on two parallel sides, is modified with the inclusion of the dynamical basis. For several boundary conditions, the initial conditions of the impulse response allows us to reduce computations.