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The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements.

Introduction The impact of vibrations excited by incident sound fields has become a major concern today, due to its influence on the performance of systems and installations. Vibrations have the potential to cause considerable dynamic disturbances and instabilities, which can lead to significant structural and functional damage. Consequently, it is crucial to control vibration phenomena right from the system design phase. To solve the problem of vibration, it is sometimes possible to increase the damping level of the structure by incorporating a damping treatment. Objective The aim of this paper is to present a simplified numerical approach to study the vibro-acoustic responses of structures with PCLD “Passive Constrained Layer Damping” treatment in the thermal environment, taking into account the frequency and temperature dependence of the different viscoelastic behavior laws. Material and Methods The modal stability procedure MSP is based on the finite element method in order to discretize and formulate the equation of motion. The asymptotic numerical method “ANM” is applied to approximate the solution of complex eigenvalue problems and construct the modal basis. The variability of the frequency responses is evaluated by a Monte Carlo simulation (MCS) combined with MSP and ANM to evaluate the stochastic behavior of a sandwich beam with random properties. Results The comparison with the direct frequency responses (DFR) demonstrates that the results are highly satisfactory in terms of the validity of the present MSP approach. A comparative study of viscoelastic behavior models was carried out to evaluate their damping properties provided to the structure. The viscoelastic materials provide significant damping particularly for amplitudes corresponding to the high frequencies. This is in contrast to the responses obtained without the viscoelastic layer. Conclusion The obtained results show the importance of viscoelastic damping, which has a significant effect on the vibro-acoustic behavior, implying the improvement of the damping of the structure, especially for large frequencies and high temperatures.

A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton’s principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.

The aim of this work was to assess the numerous approaches to structural and material modeling of brain tissue under dynamic loading conditions. The current technological improvements in material modeling have led to various approaches described in the literature. However, the methods used for the determination of the brain’s characteristics have not always been stated or clearly defined and material data are even more scattered. Thus, the research described in this paper explicitly underlines directions for the development of numerical brain models. An important element of this research is the development of a numerical model of the brain based on medical imaging methods. This approach allowed the authors to assess the changes in the mechanical and geometrical parameters of brain tissue caused by the impact of mechanical loads. The developed model was verified through comparison with experimental studies on post-mortem human subjects described in the literature, as well as through numerical tests. Based on the current research, the authors identified important aspects of the modeling of brain tissue that influence the assessment of the actual biomechanical response of the brain for dynamic analyses.

This paper discusses the different methods used for calculating first- and second-order sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.

An enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained layer damping (ACLD) thin plate structure is taken as the research object to study vibration control. Based on the FEM method, energy method, and Hamilton principle, the dynamic model of an ACLD thin plate structure is derived, in which the Golla–Hughes–McTavish (GHM) model is used to characterize the damping characteristics of the viscoelastic layer, and the equivalent Rayleigh damping is used to characterize the damping characteristics of the base layer. The order of the model is reduced based on the high-precision physical condensation method and balance reduction method, and the model has good controllability and observability. An LQR controller is designed to actively control the ACLD sheet, and the controller parameters and piezoelectric sheet parameters are optimized. The results show that the finite element model established in this paper is accurate under different boundary conditions, and the model can still accurately and reliably describe the dynamic characteristics of the original system in the time and frequency domain after using the joint reduction method. Under different excitation and boundary conditions, LQR control can effectively suppress structural vibration. Considering the performance and cost balance, the most suitable control parameter for the system is: Q-matrix coefficient is between 1 × 104 and 1 × 105, the R-matrix coefficient is between 1 and 10, and the thickness of the piezoelectric plate is 0.5 mm.

The mechanisms driving the uplift and outward expansion of the Tibetan Plateau remain debated. The Qinghai Lake region at the plateau front, characterized by pronounced basin–range differential uplift, provides a key natural laboratory. Here, we first predict vertical deformation induced by the horizontal GPS velocity field and then construct a three-dimensional (3D) viscoelastic finite-element model to evaluate how lithospheric rheology shapes present-day 3D deformation. Horizontal GPS velocities predict higher uplift in the Songpan–Ganzi Terrane and the Qilian Orogen and lower values in the intervening basins, capturing the first-order basin–range pattern; the predicted uplift in the Qilian Orogen is ~1.0 mm/yr and agrees with observations, indicating that its dominant mechanism is crustal shortening and thickening. However, horizontal constraints alone leave vertical-velocity residuals of ~0.8–1.5 mm/yr in several localized areas, including the West Qinling Orogen, the southern Elashan region, the Qinghai–Nanshan region, and areas south of the Lenglongling Fault. Lateral rheological heterogeneity in the mid–lower crust, acting under mantle-flow drag, can better account for these residuals and more accurately reproduce the present 3D velocity field in the basin–range system. We further propose northeastward mid–lower crustal flow along a weak channel; when the flow is impeded by rigid domains (e.g., the Gonghe Basin and the Qinghai Lake Basin), it promotes material accumulation and localized deformation. These results support a hybrid mechanism that combines crustal shortening and mid–lower crustal flow for the Qinghai Lake basin–range system.

Under the shadow of the far-field effect of the India-Eurasia collision, the Tianshan orogenic belt underwent tectonic re-activation in the Cenozoic, accompanied by strong tectonic deformation and frequent large earthquakes. Bounded by two rigid cratonic blocks located in its north and south, a series of marginal foreland fold-and-thrust belts are developed within the Tianshan orogenic belt and continue to develop to the bilateral pull-apart basins. Meanwhile, the faults in the orogenic belt are reactivated. The deformation caused by thrust-related structure accounts for larger than 50% of the total convergence of the Tianshan Mountains, which results in the most active structure with large earthquakes in the Tianshan area. Therefore, it is of great significance to study the dynamic process of the newly generated and reactivated thrust-nappe structures in Tianshan orogen via numerical modeling. This paper selects a classical cross-section profile in the western segment of the Southwest Tianshan Mountains, which contains the Kalpin-Maidan-Nalati-Kemin fault system from the south to the north. We attempt to establish a two-dimensional plane strain, viscoelastic finite element model, by treating the regional faults as a whole fault system and considering the topography, fault geometry, and GPS data. The displacement and stress fields of the model are retrieved, the short-term cumulative deformation field of the overall fault system is analyzed, and the rate of Coulomb failure stress change of each fault is also considered. The results show that the deformation is concentrated in the middle and southern parts of the Southwest Tianshan Mountains. In contrast, the deformation of the Kemin fault in the north is relatively small. According to the Coulomb failure stress changes of these four faults and the historical earthquake catalog, the potential seismicity of each fault is qualitatively analyzed. Our preliminary results suggest that the possibility of large earthquake occurrence is higher in the Kalpin fault, Maidan fault, and Nalati fault but lower in the Kemin fault in the near future.

Introduction The complex dynamics of structures under external excitations, with emphasis on the design and analysis of Constrained Layer Damping (CLD) structures was studied using FEM and modified Ross-Kerwin-Ungar (RKU) model. Materials and method The 5-layer CLD structures consisting of mild steel substrate, NBR-PVC (5-5) 20HAF viscoelastic damping layers (2 no’s) paired with Aluminum (configuration-1) and GRP (configuration-2) as constraining layers (2 No’s) were fabricated. Series of vibration experiments were conducted on electrodynamic vibration shaker integrated with data acquisition system. Modal and harmonic analysis was also carried out using modified RKU, FEM to predict frequency response and system loss factor for two CLD configurations. Results It is observed that, two CLD configurations exhibited substantial variation in the system loss factor (0.012 to 0.19), compared to the substrate, which is well below 0.01. Further, the CLD with Aluminum as constraining layer indicated superior damping performance compared to its counterpart GRP. The comparison of results from FEM and modified RKU method with experimental data revealed, deviations of approximately 5–15% and 15–23% respectively indicating relative accuracy of FE simulation data, especially in complex structural scenarios. Conclusion The study offers valuable insights into the distinct performances of different constraining layers, improves our understanding of the dynamic behavior of multilayer CLD structures.

In recent years, hard-magnetic soft (HMS) structures have emerged with meritorious properties for potential applications in many fields, such as soft robotics, wearable devices, and stretchable electronics. Developments in reliable computationally efficient dynamic models of HMS structures, however, are vital not only to gain a better understanding of their magneto-mechanical behaviors but also to design effective control algorithms. This study proposes a time-dependent computationally efficient magneto-viscoelastic model of a cantilever HMS structure subject to an external magnetic field. The Kelvin–Voigt internal energy dissipation model is utilized to accurately capture the nonlinear time-dependent response behavior of the HMS beam subject to large magnitudes of the magnetic field at different frequencies. The Galerkin modal decomposition scheme and Bogacki–Shampine method are used to discretize and solve the proposed model. A 2D finite element (FE) model is further developed to assess the effectiveness of the proposed nonlinear model in terms of computational efficacy and accuracy. Moreover, A hardware-in-the-loop framework is developed to experimentally characterize the deflection responses of the HMS beam to steady as well as harmonically varying magnetic fields. The nonlinear deflection responses of the proposed magneto-viscoelastic model subject to magnetic flux density up to 30 mT showed very good agreements with the measured data and the FE model, while the response saturation occurred under a field exceeding 15 mT . The measured and model responses were further analyzed to obtain time-histories, phase-plane, and hysteretic response characteristics of the structure considering different magnitudes ( 5 - 30 mT ) and frequencies ( 0.25 - 1 Hz ) of harmonic as well complex harmonic variations in the magnetic field. The simulation results from the developed model aligned well with the experimental findings across all considered excitations. Moreover, the computation time varied from approximately 3.2 to 31 s, depending on the number of generalized coordinates used in the modal decomposition. The computation time of the FE model on the same computing platform was in excess of 4700s.