The level sets of scalar functions may imply the geometries of ropes and membranes [1]. Then, a set of isosurfaces over some three-dimensional bulk domain defines infinitely many geometries at once. Herein, following [2, 3], we propose a mechanical model which enables the simultaneous, dynamic analysis of all such geometries. For the solution of the governing equations, a tailored numerical method coined Bulk Trace FEM [3] is employed, using a three-dimensional background mesh in the bulk domain. One dimension lower, the situation is similar for a set of curved ropes implied by the set of isolines of a level-set function over a two-dimensional, planar bulk domain. Herein, we extend the preliminary model and numerical method for the stationary case from [3] by adding inertia terms. Different time stepping schemes are considered in the Bulk Trace FEM for the first time. Special emphasis is on the induced vibrations and resonance phenomena in the ropes and membranes. The simultaneous analysis allows to identify geometries with user-defined properties from one simulation only. Numerical results confirm the success of the new dynamic model and numerical treatment, even enabling higher-order accurate results provided that the solutions are sufficiently smooth. REFERENCES [1] Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge, 2nd edition, 1999. [2] T.P. Fries, D. Schöllhammer: A unified finite strain theory for membranes and ropes, Comp. Methods in Appl. Mech. Engrg., 365, 2020. [3] T.P. Fries, M.W. Kaiser: On the Simultaneous Solution of Structural Membranes on all Level Sets within a Bulk Domain, Comp. Methods in Appl. Mech. Engrg., 415, 116223, 2023.