**5. Conclusions**

This article was aimed at 4D printing adaptive metastructures with locally resonated and Bragg-type stop-bands. The FDM 4D printing technology was implemented to program shape-memory elements during the layer-by-layer deposition process in a functionally graded manner. Experiments

were conducted to explore 1D-to-2D self-bending features characterized in terms of 4D printer head speed. Boundary value problems were solved to explain thermomechanical mechanisms behind inducing prestrain during 4D printing and shape recovery after thermal activation. In this respect, a straightforward approach was introduced and implemented into the commercial FE software package of COMSOL Multiphysics, which is much simpler than writing a user-defined material model (UMAT) subroutine or an in-house FE code. The 4D-printed elements were simulated as functionally graded materials whose thermal expansion changed through the thickness direction. The excellent accuracy of the proposed technique was checked via a comparative study with experiments and computational results from the developed in-house FE MATLAB-based solution. Two periodic architected temperature-sensitive metastructures with adaptive dynamical characteristics were conceptually proposed. The COMSOL-based computational tool was then applied to dynamically analyze periodic metastructures with self-bending active elements 4D-printed at di fferent printing speeds. It was found that the metastructures have the capability of controlling elastic wave propagation by forming bandgaps or frequency ranges where the wave cannot propagate. It was observed that the bandgap size and frequency range could be controlled and broadened through local resonances by changing 4D printing speed and thermal excitation. Due to the absence of a similar concept and results in the specialized literature, this article is likely to advance the state-of-the-art tunable metastructures for vibration mitigation and sound attenuation.

**Author Contributions:** Conceptualization, M.B.; methodology, R.N., M.B. and H.J.; software, R.N. and H.J.; validation, R.N., M.B. and H.J.; investigation, R.N., M.B., H.J., A.Z. and M.F.; formal analysis, R.N., M.B., H.J., A.Z. and M.F.; resources, M.B.; writing—original draft preparation, R.N., M.B. and H.J.; writing—review and editing, R.N., M.B., H.J., A.Z. and M.F.; supervision, M.B.; project administration, M.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
