An improved Wittrick-Williams algorithm for beam-type structures

With the help of the dynamic stiffness method, the problem of dynamic characteristics analysis of an engineering structure can be transformed into the problem of solving the transcendental frequency equation. The Wittrick-Williams algorithm can provide the upper and lower bounds of any given modal frequency, so that the numerical solution of the equation can be obtained. However, for a complex beam-like structure, the method is no longer suitable because it is difficult to determine the corresponding the clamped-clamped frequency. For this reason, this paper proposes an improved Wittrick-Williams algorithm-hypothetical structure method, which calculates the clamped-clamped frequency count of the original structure indirectly through the “hypothetical structure” so that the dynamic characteristics analysis problem of the complex beam-like structure can be solved. Two typical beam structure examples and a complex double beam-like structure example are used to verify the accuracy and effectiveness of the proposed method.