AN UNSPLIT-FIELD PERFECTLY MATCHED LAYER FOR TRANSIENT SIMULATION OF FLEXURAL WAVES IN HETEROGENEOUS EULER-BERNOULLI BEAMS

초록

This paper presents a time-domain formulation and numerical implementation of an unsplit-field perfectly matched layer (PML) for flexural waves in unbounded Euler-Bernoulli beams. Accurately modelling wave propagation in unbounded domains requires truncating the computational domain while preventing artificial reflections at the boundaries. To achieve this, we develop an Euler-Bernoulli PML (EB-PML), which reformulates the flexural wave equations in the frequency domain by introducing a complex coordinate stretching. The stretched equations are then transformed back to the time domain via the inverse Fourier transform. The resulting EB-PML equations adopt a mixed-like formulation, treating deflection, slope, moment, and shear as independent variables. For implicit time integration, a third-order Newmark-ss method is employed to solve the semi-discrete equations of motion constructed using the finite element method. A series of numerical experiments is conducted to evaluate the performance of EB-PML under various loading conditions. Error analyses in both time and frequency domains confirm the effectiveness of the EB-PML in absorbing outgoing flexural waves, with reflections from truncated boundaries remaining minimal. The numerical error is shown to be less than 0.02%. The developed EB-PML framework has potential applications in the structural health monitoring of lifeline infrastructures, such as water and gas pipelines, using measured flexural wave data.

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