Forced guided waves in linearly elastic plates (I) - An examination of the normal-mode expansion method

Guided waves in a plate can be generated by external loads such as body forces and surface tractions. The region of the plate where the external loads are applied is called the loading zone. Guided waves inside the loading zone are called forced guided waves. The classical normal-mode expansion method developed by Auld and Kino in 1973 has been used widely by numerous researchers and practitioners to study forced guided wave problems in plates, including both elastic and electromagnetic waves. As Part I of this investigation, the current paper shows that the classical normal-mode expansion method of Auld and Kino does not yield the exact elastodynamic solution when applied to forced Lamb waves, because its solution does not satisfy the Hooke's law inside the loading zone. The classical normal-mode expansion method, however, does yield the exact elastodynamic solution when applied to forced horizontally polarized shear waves in that its solution satisfies all the governing equations including the equation of motion, the Hooke's law and the prescribed traction boundary conditions. In Part II, a modified normal mode expansion method will be developed to mitigate the above limitations of the classical normal mode expansion method.