Decay conditions for 1D quasicrystal beams

For 1D quasicrystal (QC) beams, the reciprocal theorem and the general solution of plane elasticity of QCs are applied to obtain the appropriate decay conditions accurate to all order. A decay analysis technique is used to establish necessary conditions that the prescribed data on the edge of the beams must satisfy in order that it should generate a decaying state within the beams. For the case of bending and stretching deformations, these decaying state conditions are obtained explicitly for the first time when the mixed conditions are imposed on the beam edge.