Perfectly Matched Layers for the Simulation of Flexural Waves in Unbounded Euler–Bernoulli Beams

This paper presents the formulation and implementation of a perfectly matched layer (PML) wave-absorbing boundary for unbounded Euler–Bernoulli beams (EB-PML) in the time domain. To simulate flexural waves in an unbounded beam, the infinite domain is truncated and terminated with the EB-PML to suppress wave reflections. The PML is modeled by introducing a complex coordinate stretching into the frequency-domain governing equations of the Euler–Bernoulli beam, enforcing wave attenuation within the PML regions. These stretched equations are then transformed back to the time domain using the inverse Fourier transform, yielding a system of flexural wave equations expressed in terms of deflection and bending moment. The equations are numerically solved using a third-order Newmark- β time integration scheme. The wave-absorbing performance of the EB-PML is validated through error analyses, where the numerical results show close agreement with exact solutions for unbounded wave propagation in both the time and frequency domains. The results confirm that the EB-PML effectively minimizes reflections from truncated boundaries, with the L 2 -error of the numerical solution remaining below 0.02%. The proposed EB-PML has potential applications in damage assessment of deep foundations and lifeline structures that support flexural wave propagation under applied loads.