Algorithm Improvement of Transfer Matrix Method for Vibration Propagation of Periodic Pipeline Structure

Abstract

This paper proposes an improved transfer matrix method (TMM) algorithm to calculate frequency response function (FRF) for finite periods of periodic composite pipelines structures. Traditional TMM usually generate instable matrix and inaccurate calculation results for Phononic crystals (PCs) pipeline. Under the assumption that periodic distribution of pipeline structure with no intermediate excitation, the main idea of the improved algorithm is to reasonably divide finite periodic pipeline into several effective segments, then the transfer relationship of state vector for each connected pipe part could be expressed individually, thereby realizing the calculation order reduction by expanding the dimension of overall stiffness matrix. This improved algorithm could effectively avoid cumulative error caused by diagonal sparse matrix operations, thus getting true dynamic response to calculate exact FRF curves. Moreover, this algorithm could fundamentally improve the accuracy and stability of traditional TMM calculations. The transverse FRF for finite periods calculated by improved TMM shows excellent consistency with corresponding band gap structures (BGs), validate the correctness of derived theory and algorithm. This improved TMM algorithm supplies an effective method for FRF calculation of finite pipeline periods, and also provide effective verification of BGs for infinite structures, which could guide the vibration and noise reduction design of pipeline system.