  The vibrational response of structural components carries valuable
information about their underlying mechanical properties, health status and
operational conditions. This underscores the need for the development of
efficient physics-based inversion algorithms which, given a limited set of
sensing data points and in the presence of measurement noise, can reconstruct
the response at locations where measurement data is not available and/or
identify the unknown mechanical properties. Addressing this challenge,
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach.
PINNs seamlessly integrate governing equations into their architecture and have
gained significant interest in solving inversion problems. In the context of
learning and inversion of multimodal, multiscale vibrational responses, this
paper introduces a novel spectral extension of PINNs, utilizing Fourier basis
functions in the wavenumber domain, commonly known as k-space. The proposed
k-space PINN (k-PINN), offers a robust framework for adjusting complexity and
wavenumber composition of the response. Notably, the spectral formulation of
k-PINN, coupled with the generally sparse representation of vibrations in
k-space, facilitate efficient reconstruction and learning of broadband
vibrations and alleviate the spectral bias associated with standard PINN.
Additionally, the spectral solution space introduced by k-PINN substantially
reduces the computational cost associated with computing physics-informed loss
terms. We evaluate the effectiveness of the proposed methodology on
reconstructing the bending vibrational mode shapes of a thin composite laminate
and identifying its effective bending stiffness coefficients. It is shown that
the proposed k-PINN methodology outperforms the standard PINN in terms of both
learning and computational efficiency.
