... the boundary 11 1rCRC (2.27) However, recalling 11 1CrC from Eq. (2.24), it can be found that 11 1 (1) 0rrR C (2.28) For nontrivial solutions, 11 () 1 0rFs rR ... equation is due to the fact that R1r recursively expands to include all the effects of constraints in the remaining side of the string until its expansion terminates at the rightmost boundary ... of Euler-Bernoulli beams including waves of both propagating and near-field types. By the phase-closure principle, also referred to as the wave-train closure principle (Cremer et al., 19 73),...