Newmark Method Research Articles

THE TRANSLATION OF SALADIN AL AYYUBI: A STUDY OF METHODS, CLARITY, AND AUDIENCE RESPONSE

The purpose of this research is to reveal the clarity of the translation in the movie Saladin Al-Ayyubi. This research uses a qualitative approach with document analysis method. The data used in this study came from the dialog sentences of the two characters' speech in the subtitle of Saladin Al-Ayyubi episode 4 on the Arabic Cartoon YouTube channel and the results of a survey conducted on respondents totaling 21 participants. To collect data, the researcher watched and observed the movie Saladin Al-Ayyubi repeatedly to transcribe the movie. After that, the researcher distributed questionnaires to classify and analyze the types of methods, clarity, and audience responses to the Arabic - Indonesian translation in the Salahuddin Al-Ayyubi film. The findings of this study are the types of methods used in the Arabic - Indonesian translation of Saladin Al-Ayyubi movie and the level of clarity of the methods used according to the audience. The researcher found five out of eight Newmark methods used in the translation, namely (1) word-by-word method; (2) semantic method; (3 free method; (4) literal method; and (5) communicative method. The level of intelligibility in the Arabic - Indonesian subtitles of Saladin Al-Ayyubi movie shows that 19% of the text is at a low level of legibility, 59% of the text is at a medium level of legibility, and 22% of the text is at a high level of legibility.

A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge

Vortex-induced vibration (VIV) of long-span bridges can be of large amplitude, which can influence serviceability. Therefore, it is important to predict the response of vortex-induced vibration to aid the management of long-span bridges. A novel data-driven model is proposed to predict the time history of the dynamic response of VIV events. Specifically, the proposed model consists of gated recurrent unit (GRU) neural networks and the Newmark-beta method. GRU neural networks can perform accurate sequential prediction, and the Newmark-beta method can complement the physical meaning of the middle output of the proposed model. To aid the accurate prediction of the amplitude of VIV events, the proposed model employs weighted mean square error as the loss function, which can put more emphasis on the amplitude. The proposed model is validated on measured VIV events of a long-span suspension bridge. The weighted mean absolute percentage error and Pearson correlation coefficient of the trained model indicate the effectiveness of the proposed model.

Assessment of Axisymmetric Dynamic Snap-Through and Thermally Induced Vibrations in FGM Cylindrical Shells Under Instantaneous Heating

This paper addresses the investigation of axisymmetric thermally induced vibrations in Functionally Graded Material (FGM) cylindrical shells. It considers temperature-dependent (TD) properties and geometric non-linearity (the von Karman effect). The study systematically solves a transient heat conduction equation using finite differences method and the Crank–Nicolson method. During the heating stages, the evaluation of thermal forces and moments takes place. Equations of motion are derived through the application of Hamilton’s principle. Spatial dependencies are discretized using the generalized Ritz method, while temporal dependencies are approximated using the [Formula: see text]-Newmark method with Newton–Raphson linearization. A comparative analysis validates the procedure’s efficiency and precision. Parametric studies explore the influence of parameters, including the temperature-dependency material properties, geometric nonlinearity, and shell’s power-law index, providing valuable insights into FGM shell behavior under thermal shock.

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

AbstractThis article presents unified and efficient stochastic modal decomposition methods to solve stochastic structural static and dynamic problems. We extend the idea of deterministic modal decomposition method for structural dynamic analysis to stochastic cases. Standard/generalized stochastic eigenvalue equations are adopted to calculate the stochastic subspaces for stochastic static/dynamic problems and they are solved by an efficient reduced‐order method. The stochastic solutions of both static and dynamic equations are approximated by stochastic bases of the stochastic subspaces. Original stochastic static/dynamic equations are then transformed into a set of single‐degree‐of‐freedom (SDoF) stochastic static/dynamic equations, which are efficiently solved by the proposed non‐intrusive methods. Specifically, a non‐intrusive stochastic Newmark method is developed for the solution of SDoF stochastic dynamic equations, and the element‐wise division of sample vectors is used to solve the SDoF stochastic static equations. All of these methods have low computational effort and are weakly sensitive to the stochastic dimension, thus the proposed methods avoid the curse of dimensionality successfully. Two numerical examples, including two‐ and three‐dimensional spatial problems with low and high stochastic dimensions, are given to show the efficiency and accuracy of the proposed methods.

Conditioning and spectral properties of isogeometric collocation matrices for acoustic wave problems

The conditioning and spectral properties of the mass and stiffness matrices for acoustic wave problems are here investigated when isogeometric analysis (IGA) collocation methods in space and Newmark methods in time are employed. Theoretical estimates and extensive numerical results are reported for the eigenvalues and condition numbers of the acoustic mass and stiffness matrices in the reference square domain with Dirichlet, Neumann, and absorbing boundary conditions. This study focuses in particular on the spectral dependence on the polynomial degree p, mesh size h, regularity k, of the IGA discretization and on the time step size Δt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta t$$\\end{document} and parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} of the Newmark method. Results on the sparsity of the matrices and the eigenvalue distribution with respect to the number of degrees of freedom d.o.f. and the number of nonzero entries nz are also reported. The results show that the spectral properties of the IGA collocation matrices are comparable with the available spectral estimates for IGA Galerkin matrices associated with the Poisson problem with Dirichlet boundary conditions, and in some cases, the IGA collocation results are better than the corresponding IGA Galerkin estimates, in particular for increasing p and maximal regularity k=p-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=p-1$$\\end{document}.

Modal and response characteristics of rotor with angle misalignment fault based on cross-coordinate system substructure modeling method

Finite element models are widely used in dynamic analysis of misalignment rotor, but present finite element rotor models cannot simulate the axis characteristics of angle misalignment rotor, which consistent with the one with no misalignment. For achieving the precisely modeling of angle misalignment rotor, a novel modeling method called cross-coordinate substructure modeling method is introduced to establish the model of misalignment rotor, in which different parts of rotor rotate around different axis. Based on this modeling method, the 3D solid models of angle misalignment rotor are established with the help of ANSYS, and the modal characteristics and critical speeds of the misalignment rotor are achieved through modal analysis and harmonic response analysis. The numerical simulation based on Newmark method and experiment tests is carried out to obtain the response characteristics of the rotor model under the combined action of unbalanced force and misalignment load. The results show that the modal “rotation of rotor” appears, and the more amounts of response peaks can be aroused in harmonic response analysis when the rotor occurs angle misalignment. The typical fault characteristics of angle misalignment rotor in the spectrums and orbit diagrams are generally consistent both in the numerical simulation and experiment test. The research results can provide a theoretical basis for simulation and identification of the misalignment fault in rotating machinery system.

Three-dimensional active-control hygrothermal dynamic behavior of PFMLs structure subjected to laser heat treatment with dual-ellipse distribution form

Based on three-dimensional transient thermal conduction theory, the refined plate theory and Hamilton variational principle, the constitutive equations, geometrical equations, and governing equations for fiber metal laminates with piezoelectric layer (PFMLs) under hygrothermal environment is presented. Subsequently, the Newmark method and Galerkin method are used to solve the governing equations which in terms of displacement functions. The results show that electric potential function, fiber orientation, external load as well as thickness ratio have great influence on the deflection as well as normal stress. The selection of (45°/0°) fiber orientation is more resistance to deformation and normal stress.

Research on the Time-Domain Explicit and Implicit Solution Methods of the Shallow Water Seismic Wavefield Equations

The current time-domain solution methods for the wavefield equations of a single medium do not apply to the wavefield equations of shallow water seismic with a fluid–elastomer coupling. To solve this problem, based on the explicit central difference method and implicit Newmark method, the explicit–explicit method, implicit–implicit method, and explicit–implicit method time-domain expressions for the local solution are derived, and the time-domain expressions for the explicit and implicit methods in the global solution are derived.The stability and computational efficiency of different time-domain solving methods for the shallow water seismic wavefield equations are theoretically analyzed. The numerical results are compared with the simulation data from the multiphysics field simulation software COMSOL 6.0, and the numerical stability, computational efficiency and accuracy of the different solving methods are also analyzed theoretically. The results show that the implicit method in the global solution is relatively optimal among the methods proposed in this paper, which ensures numerical stability at the larger step size for improving the computational efficiency and considers the higher computational efficiency and accuracy.

Structure preserving and energy dissipative contact approaches for implicit dynamics

AbstractIn this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long‐time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

The efficient data-driven solution to estimate the nonlinear bending of sandwich doubly curved panel subjected to transient loading

This paper investigates nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading which is extensively used in aerospace structures. Due to the lack of a dataset for the nonlinear transient bending of the sandwich doubly curved panel for the data-driven solution, mathematical modeling is used. The sandwich doubly curved panel is made of two graphene nanoplatelets (GPLs) reinforced face sheets, and a polymer core. In the mathematical modeling section, the effective Young's modulus is obtained via modified Halpin-Tsai methodology, and the role of the mixture is used to estimate other material properties of the composite face sheets. The presented structure is analyzed using Reddy's third-order shear deformation theory (RTSDT), which incorporates von Kármán nonlinear geometric assumptions and Hamilton's principle. The governing equations and associated boundary conditions are derived accurately by imposing shear stress-free conditions on the upper and lower surfaces of the panel. The meshfree radial point interpolation method (RPIM) with interpolation functions is utilized to determine the unknown degrees of freedom to numerically simulate the mid-plane of the sandwich doubly-curved panel. The Newton-Raphson approach is used to solve the nonlinear ordinary differential using the constant-average acceleration strategy from Newmark's time integration method. After obtaining the dataset, the data is collected, and using an efficient data-driven approach, the results are tested, validated, and trained. In future studies, the presented efficient data-driven approach can be used with low computational cost to simulate nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading for related aerospace industries.

Vibration of Non-Uniform Bernoulli-Euler Beam Under Moving Distributed Masses Resting on Pasternak Elastic Foundation Subjected to Variable Magnitude

This paper investigates the dynamic response of a clamped-clamped non-uniform Bernoulli-Euler beam resting on a Pasternak elastic foundation to variable magnitude moving distributed masses. The predicament is dictated by a partial differential equation of fourth order, which features coefficients that are both variable and singular. The primary aim is to derive an analytical solution for this category of a dynamic problem. To achieve this, we employ the method of Galerkin with a series representation of the Heaviside function to reduce the equation to second-order ordinary differential equations with variable coefficients. We simplify these transformed equations using (i) the Laplace transformation technique in conjunction with convolution theory for solving moving force problems, and (ii) finite element analysis in conjunction with the Newmark method for solving analytically unsolvable moving mass problems due to their harmonic nature. We first solve the moving force problem using the finite element method and compare it against analytical solutions as validation for its accuracy in solving analytically unsolvable moving mass problems. The numerical solution obtained from the finite element method is shown to be comparable favorably against analytical solutions of our moving force problem. Lastly, we calculate displacement response curves for both moving distributed force and mass models at various time t for our dynamical problem presentation purposes.

A parametric study of a bolted joint rotor-bearing system with an unbalanced offset disk

The turbine disk is the core component of an aero-engine whose position and unbalanced force seriously affect the vibration stability of the rotor system. Ignoring the influence of the offset disk may result in discrepancies between real-world scenarios and numerical simulation results. The present work aims to explore the nonlinear dynamic characteristics of rotor systems under the coupling of bolted joint and offset disk effect, as well as the influence of offset disk position and its unbalanced force on the system dynamic behavior and bending stiffness of bolted joint also investigated. The governing equations of a bolted joint rotor-bearing system with an offset disk were established based on the finite element method and derived as a dimensionless expression in the first. Then, the Newmark method was employed for the numerical solution of the motion equations, and then a bifurcation analysis of the rotor system and the evolution of bending stiffness for the bolted joint was studied. Next, by comparing the frequency-amplitude diagrams, bifurcation diagrams, time history, shaft obits, and bending stiffness diagrams of the bolted joint, the effect of the offset disk position and its unbalanced force on the nonlinear system dynamic was revealed. Finally, an experimental study was carried out to verify the numerical result using the bolted joint rotor test rig with an offset disk. The analysis result of the present work can provide theoretical guidance for structure design and stability analysis on the aero-engine.

An open-source application software for spatial prediction of permanent displacements in earthquake-induced landslides by the Newmark sliding block method: pyNewmarkDisp

This paper presents pyNewmarkDisp, an open-source application software developed in Python for calculating the spatial distribution of permanent displacements (up) in earthquake-triggered shallow landslides through the Newmark sliding block method. up are often estimated by simplified methods using empirical correlations instead of the direct Newmark method in which ground motion accelerations exceeding a critical value are integrated twice. These simplified procedures have traditionally been justified because of the time consumption, labor intensiveness, and impracticality of the direct Newmark method at large spatial scales. However, pyNewmarkDisp has a well-optimized code taking advantage of NumPy array operations and just-in-time Numba compilation that allows performing the direct Newmark method at large-scale spatial domains, even on general-purpose computers. pyNewmarkDisp is exemplified through a hypothetical study case, and its results are compared to three empirical correlations, showing significant differences and confirming that simplified methods can lead to inaccurate results.

A non-iterative partitioned computational method with the energy conservation property for time-variant dynamic systems

A non-iterative partitioned computational method with the energy conservation property is proposed in this study for calculating a large class of time-variant dynamic systems comprising multiple subsystems. The velocity continuity conditions are first assumed in all interfaces of the partitioned subsystems to resolve the interface link forces. The Newmark integration scheme is subsequently employed to independently calculate the responses of each system based on the obtained link forces. The proposed method is thus divided into two computational modules: multi-partitioned structural analyzers and an interface solver, providing a modular solution for time-variant systems. The proposed method resolves the long-standing problem of iterative computation required in partitioned time-variant systems. More specifically, the proposed method eliminates the need for time-variant matrix formation and the utilization of complex iterative procedures in partitioned computations, which significantly improves computational efficiency. The derivation process and theoretical demonstration of the proposed method are thoroughly presented through a representative example, i.e., a vehicle-rail-sleeper-ballast time-variant system. The proposed method’s accuracy, energy conservation property, and efficiency are systematically demonstrated in comparison with the results of the global model, highlighting its superior performance. A more general example provided in Appendix C demonstrates that the proposed method is not confined to the analysis of vehicle-rail-sleeper-ballast systems but applies to other structural dynamic systems.

Analiza izazvanog dinamičkog ponašanja funkcionalno stepenovanih greda pod harmoničnim pokretnim opterećenjem na elastičnoj osnovi pomoću metode konačnih elemenata

Introduction/purpose: This paper presents a numerical study of the forced dynamic behavior of a functionally graded beam subjected to a harmonically varying transversely concentrated moving force using a higher-order shear deformation theory. Methods: The governing equations are derived using Hamilton's principle. These equations are then transformed into the weak form using the Galerkin method. The problem is solved using the finite element method by developing a three-node finite element with four degrees of freedom per node. The Newmark beta method is chosen for the time integration and the Gauss method for the spatial integration. Results: The effects of several parameters were investigated, including the slenderness ratio, the material index, foundation stiffness, velocity and the frequency of the moving load. Good agreement was observed with the results obtained from the literature. Conclusion: This study illustrates the importance of using a higher order theory in the case of short beams and clearly shows the change in the behavior of the FGM beam as a function of different parameters.

Local modeling method for multi-field coupling of electric-magnetic-thermal-structure of pulsed high current linear driving device

The pulsed high current linear driving device operates under extreme conditions, and various forms of metal damages will reduce the service life of the device. At present, the multi-physics coupling mechanism of pulsed high current linear driving device is still unclear, and the multi-parameter diagnosis method in the laboratory environment is limited. Therefore, it is urgent to clarify the evolution process of multiple physical parameters through numerical modeling methods, in order to guide the optimization of the overall performance and improve the service life of the device. In this work, mathematical and physical models of electromagnetic field, temperature field and structural field under dynamic conditions are established. The local solution is carried out by using the characteristics of rail reverse motion and the invariant physical quantities at the distal end of the contact. The constraint equations of the non-equipotential surface of the rail entrance and the armature-rail interface conditions under the technical framework are derived. The constraint equations are applied by the penalty function method. The model also takes into account the practical factors such as the temperature dependence of the material properties, thermal stresses, and the frictional heat of the contact surface. The finite element discrete format of the electromagnetic field and the temperature field is solved in the form of Euler’s backward differentiation, and the structural field is solved by the Newmark method. The reliability of the model is verified by comparing the calculation results with the numerical tools EMAP3D and Comsol under the same configuration and input conditions, as well as related experiments. Through the numerical simulation of the C-type armature, the typical evolution process of the corresponding multi-parameter is obtained. During sliding electrical contact, the velocity skin effect becomes more pronounced with velocity increasing. The current is gradually concentrated on the surface of the rail, and the highest current density is found at the rear edge of the contact surface and at the edge of the outer arm of the armature. Moreover, the magnetic induction intensity at the tail of the contact surface continues to shrink over time. The heat-concentrated region appears at the top edge of the contact surface, and with time going by, it extends along the sliding direction and bottom direction of the armature. In addition, there is peak stress in the front of the rail contact and significant stress at the armature throat. When the local stress at the throat of the armature exceeds the corresponding yield strength, it can cause serious deformation or even fracture of the armature.

Research of rigid-flexible coupling dynamics model for riser-LMRP/BOPs-wellhead system

The deepwater drilling riser system is the most vulnerable part of the offshore drilling operation. Understanding its dynamic response under complex marine environment is crucial for ensuring drilling safety. However, the coupling mechanism between the riser and LMRP/BOPs is not well understood in existing analysis models of riser system dynamic response. In this paper, a theoretical model for the rigid-flexible coupling dynamics of multi-scale riser-LMRP/BOPs-wellhead system is proposed to reveal the coupling mechanism between the riser and LMRP/BOPs. Considering the characteristics of flexible riser and rigid LMRP/BOPs as well as the nonlinear coupling effect between conductors and soil, a rigid-flexible coupling dynamics model of the riser-LMRP/BOPs-wellhead system is established based on the theory of rigid-flexible coupling dynamics and Lagrange equation, which is numerically solved by the Newmark method. To verify the correctness of the proposed model, a simulation model of the riser-LMRP/BOPs-wellhead system is applied, which is modelled by the combination of pipe and mass elements. The research results demonstrate that the numerical results of the proposed theoretical model agree with the simulation results of the coupling system, thus verifying the correctness of the proposed model and revealing the rigid-flexible coupling mechanism between the riser and LMRP/BOPs.

Nonlinear dynamic analysis of a geometrically imperfect sandwich beam with functionally graded material facets and auxetic honeycomb core in thermal environment

In this study, a model for the nonlinear dynamic analysis of the geometrically imperfect sandwich beam with functionally graded material (FGM) facets and auxetic honeycomb core is proposed. The auxetic feature of the honeycomb material is realized by a homogenization method, which gives the expressions of the effective material coefficients in terms of material property and cellular geometric parameters. The nonlinear motion equation of the geometrically imperfect beam is derived based on the Reddy's higher shear deformation theory, von Kármán nonlinear theory, as well as general geometric imperfection function. The thermal effect on the material properties and structural rigidity is also taken into account in this model. The Newmark method and Newton–Raphson iterative method are employed to solve the nonlinear motion equation of the sandwich beam. In numerical examples, the dynamic response of the sandwich beam under two types of load, i.e. moving load and impulse load, are discussed in details. The influences of various factors (such as material parameter, geometric imperfection, and thermal condition) on the nonlinear dynamic behaviors of the sandwich beam are elaborately investigated. The numerical results show those factors can play significant roles in the bearing ability, structural stiffness, or nonlinear dynamic behaviors of the sandwich beam in certain conditions. Some key conclusions on the influences are drawn from the numerical results, which can be a useful reference for future investigations.

The Influence of Vertical Seismic Acceleration on the Triggering of Landslides Constrained by Bedding Faults under an Inertial Frame Reference: The Case of the Daguangbao (DGB) Landslide

The Daguangbao (DGB) landslide was the largest landslide that was triggered by the 2008 Wenchuan earthquake with a magnitude of Ms8.0. The sliding surface of this landslide was constrained on a bedding fault 400 m below the ground surface. Seismic records show that the landslide suffered not only from strong horizontal but also vertical ground shaking that was almost equal to the horizontal component. In this study, to reveal the landslide triggering mechanism of the DGB landslide, this study ignores the steep dipping tension fracture section and the leading edge-locking section of the trailing edge of the DGB landslide, and the geological model of the large optical package landslide is generalized into a block model with the bottom controlled slip soft zone as the interface. Based on the improved Newmark method that considers vertical ground motion, the three-way seismic acceleration data and the shear strength parameter of the sliding surface being taken as a variable are used to calculate the cumulative permanent displacement of the slider. Then, by considering the cumulative permanent displacement ratio of vertical seismic acceleration or not and the cumulative permanent displacement ratio value considering the inertial force as the index, the response characteristics of the cumulative permanent displacement of the block-to-vertical ground motion and inertial forces were analyzed. The results show that both the horizontal inertial force and the vertical acceleration significantly increased the permanent displacement. The permanent displacement is 4.9 cm when considering the vertical acceleration, whereas it is only 2.0 cm without taking this into account. The contribution of vertical acceleration is significantly enlarged (87.8–90.7%) by the decreasing of the internal friction angle of the slide surface, while it is less influenced (5–27.4%) by the cohesion. Compared with the lower shear strength parameter of the sliding surface, the contributions of vertical acceleration and inertial force to the permanent displacement are more obvious when the shear strength parameter of the sliding surface is higher. When ϕ > 18°, the D/D* is greater than 1, and the maximum D/D* reaches 7. The fast accumulation event of permanent displacement is triggered in the concentration stage of the seismic energy release. In the DGB landslide area, 50% of the energy is released within 30–50 s, as indicated by the acceleration peaks recorded at the nearest seismic station, Qingping station. It is assumed that the DGB landslide may be triggered at 30–50 s due to half of the seismic energy being released during that time span.

Vibrational analysis of a coupled damaged Timoshenko beam-arch mechanical system with von Kármán nonlinearities and layer discontinuity

The present study investigates vibrations in the nonlinear regime of a partially elastically connected beam with damage and either a curved or straight beam, focusing on the time domain. The mechanical system under consideration consists of two beams with varying discontinuities: one in an elastic layer and the other in a narrow cross-section area of the beam. To analyze the vibrations in this coupled system, a p-version finite element method is employed. This method allows for the examination of shear deformable beam-beam or beam-arch systems with small or large discontinuities in the elastic layer and cross-section area of the beam. The main contribution of this work lies in the dynamic analysis of a novel coupled geometrically nonlinear mechanical system. It has been discovered that in specific cases of combinations of discontinuities in the upper beam and elastic layer, a different energy transmission occurs, caused by geometrically nonlinear couplings of the nonlinearity of the elastic layer, to the lower arch, resulting in multiple cycles of oscillations executed by the system in the steady-state regime of vibrations. The analysis considers various scenarios, including the effects of the discontinuity in the viscoelastic connection layer, beam damage, and the varying curvature of the lower arch. General mode shapes are determined, and forced damped vibrations in the time domain are analyzed using the Newmark method. The findings from this dynamic analysis have broad applications in engineering and technical practice.