The present invention discloses a method for solving the
dispersion curve of ultrasonic guided
waves of a multilayer
helical structure, comprising establishing a 3D model of a multilayer
helical structure in which each
helical line has a single
pitch length; meshing the cross section; calculating the mesh size in the mesh sweep direction; mesh sweeping each
helical line; solving the unit
stiffness matrix and
unit mass matrix of each node, using a rectangular coordinate
system for straight lines and a spiral coordinate
system for spiral lines; assembling the cross-sectional overall
stiffness matrix and cross-sectional overall
mass matrix of each line, and assembling the
pitch overall
stiffness matrix and
pitch overall
mass matrix; periodically replicating and expanding the pitch overall stiffness matrix and pitch overall
mass matrix of each line to assemble the overall stiffness matrix and overall
mass matrix of the multilayer helical structure; solving the wave number,
group velocity, and
phase velocity; and matching the guided wave eigenvectors based on orthogonality. The present invention can achieve a fast and accurate solution to the
dispersion curve of a multilayer helical structure composed of different pitches, handedness, sizes, or materials.