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In this study, a novel theoretical approach based on high-order shear deformation theory is proposed to investigate the damping properties of honeycomb panels partially filled with foam. The assessment of damping properties in composite materials is accomplished through finite element theory, which elucidates the theoretical underpinnings for determining damping parameters specific to these materials. Subsequently, the damping parameters of the partially foam-filled honeycomb panel are determined based on the ratio of dissipated energy to strain energy. Ultimately, a comprehensive theoretical testing methodology is established, with tests conducted concurrently on composite materials to benchmark against data obtained via theoretical approaches. The findings underscore the capability of the proposed approach to assess the damping characteristics of diverse materials and extract their corresponding damping parameters. This method provides an effective theoretical model for investigating the damping characteristics in partially foam-filled fully composite honeycomb core sandwich structures. The model can also be applied to assess the damping properties of similar structures, offering practical guidance.

Previously, classical boundary conditions (i.e. simple, fixed and cantilevered) have been adopted for the beams under the moving loads in deriving the dynamic response. In reality, most beams cannot be simply classified as the ones with classical supports, but are elastically restrained. For theoretical completeness, a general theory will be developed in this note for the damped beams with elastic restraints modeled by vertical and rotational springs subjected to a moving damped sprung mass. Essential to the present theory is the solution of the transcendental equation for the frequency by the bi-section method. The solution obtained can also be applied to the classical boundary conditions (i.e. simple, fixed and cantilevered) under a moving sprung mass. The reliability of the present theory, along with the bi-section method for solving the frequency and mode shape, is validated by comparison with the solution obtained by the finite element method (FEM) for various damping ratios, mass ratios and running speeds of the sprung mass.

The periodic characteristics of the track structure have filtering characteristics for the propagation of vibration waves within it, and the dispersion analysis is of great significance to understand the vibration transmission characteristics of the track structure. The accuracy of the traditional virtual spring method depends on the value of spring stiffness, which leads to poor stability. Therefore, this paper adopts a null space method with both stability, accuracy and efficiency, and takes the CRTSIII ballastless track structure as the research object. Based on the null space method and energy functional variational principle, the damping factor and the material frequency variation effect are considered in detail, and the complex frequency dispersion of the CRTSIII ballastless track structure is analyzed. The accuracy of the proposed method is verified by comparing it with the results of the existing literature, and the influence of fastener stiffness frequency variation, fastener damping and concrete support layer damping on the complex dispersion characteristics of vibration waves of track structures is analyzed by using this method. The results show that the stiffness frequency effect, fastener damping and concrete support layer damping have a great influence on the attenuation domain and attenuation rate of vibration, which must be considered in the vibration transmission analysis of track structures.

Particle damping technology is a widely used passive vibration control method known for its simplicity and efficiency in engineering applications. This study applies a Particle Damper (PD) to reduce low-frequency vibrations in a manipulator. A novel coupled dynamic model of the PD and manipulator is developed, considering the impact of low-frequency vibrations. To address the challenges posed by the nonlinear behavior of particles, Discrete Element Method (DEM) simulations using EDEM software are performed to investigate the effects of key factors, such as particle packing density, diameter, and material composition, on energy dissipation. The simulation results are validated through experiments, with the manipulator serving as the controlled object to assess the PD’s control performance. The PD design is further refined by incorporating multi-layer baffles, which enhance energy dissipation and improve the suppression of vibrations. The results demonstrate that the optimized PD system effectively reduces the manipulator’s low-frequency vibration response. By integrating simulations, experimental validation, and structural optimization, this study provides deeper insights into particle damping mechanisms and offers innovative solutions for vibration control in manipulators and similar engineering systems.

Structural damping, which has been widely used to quantify the energy dissipation of engineering structures, plays an important role in dynamic analysis during the design phase and the assessment of existing structures. However, the development of an accurate damping model remains an open question due to the unclear mechanism. In this study, structural damping was identified based on loss factors for beam structures, which were used for presenting the damping behavior during vibrations. The equation of motion for the bending deformation of a Timoshenko beam was derived, accounting for the material damping. To identify the loss factor of the beam from the response signals at a limited number of measurement points, an inverse algorithm based on wave coefficient estimation was developed, considering the numerical stability for data interpretation. Based on the proposed loss factor identification method, several beam models with different shapes of cross-sections were investigated, focusing on the feasibility of the method of varying cross-section cases. Comparing the spectral element model with the loss factor and the finite element model with Rayleigh damping, it was confirmed that the loss factor can better describe the actual energy dissipation behavior of the structure. It provides a more accurate theoretical model for estimating structural damping in practical engineering.

In this paper, we present the interaction between a five-level $\mathrm{\Lambda }$-configuration atom and a two-mode quantized field in the presence of the damping with the nonlinearity. According to the generalized nonlinear Jaynes–Cummings model (JCM) and the analytical solution of the Schrödinger equation, the general formula of the wave function for this system under special conditions, where the atom (the field) is initially prepared in the excited state (coherent state), has been found. Under some particular conditions, the five-level $\mathrm{\Lambda }$-type atom can be reduced to the three-level $\mathrm{\Xi }$-type atom. Some physical aspects of the atom-field entangled state showing the entanglement degree, such as the field entropy. Moreover, we evaluate some of their non-classical statistical aspects such as atomic inversion. The effects of the physical parameters such as a Kerr medium, detuning parameter and the intensity-dependent coupling on the temporal behavior of the latter mentioned non-classical statistical aspects have been explored. We show that by choosing the evolved parameters in the interaction process, each of the above non-classical statistical features can be treated. We found that the parameters have an important influence on the properties of these phenomena.

We approach the case of two coupled oscillators where the first one may correspond to a photonic field, while the second one is damped and driven. We model the oscillator's damping via a bath and consider the relevant master equation. We use perturbation theory to handle it. We then path integrate over the effective Hamiltonian of the two oscillators and derive the path integrated density matrix. We suppose that initially both of the oscillators are in coherent states and study the quadrature squeezing effect of the second oscillator.

In this paper we study the interaction between two two-level atoms with a two-mode quantized field in the presence of damping. Dipole–dipole interaction between the two atoms and the correlation between the two modes of field are also taken into account. To solve the model, using appropriate transformations, we reduce the considered model to a well-known Jaynes–Cummings model. After finding the analytical solution for the atom–field system, the effects of damping, field–field correlation and atomic dipole–dipole interaction on the entanglement between atoms and population inversion are investigated, numerically. It is observed that the dynamical behavior of the degree of entanglement for damped systems, in relatively large domains of time, takes a low but constant value adequately far from the beginning of the interaction. In addition, it is found that the value of population inversion after the initial oscillations takes negative values for damped systems and eventually vanishes by increasing time. Also, it is seen that simultaneous presence of both dipole–dipole interaction and field–field correlation provides typical collapse–revival phenomenon in the time-behavior of atomic inversion.

We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.

We studied numerically the influences of damping and temperature of medium on the properties of the soliton transported bio-energy in the α-helix protein molecules with three channels by using the dynamic equations in the improved Davydov theory and fourth-order Runge–Kutta method. From the simulation experiments, we see that the new solitons can move along the molecular chains without dispersion at a constant speed, in which the shape and energy of the soliton can remain in the cases of motion, whether short-time at T=0 or long time at T=300 K. In these motions, the soliton can travel over about 700 amino acid residues, thus its lifetime is, at least, 120 ps at 300 K. When the two solitons undergo a collision, they can also retain themselves forms to transport towards. These results are consistent with the analytic result obtained by quantum perturbed theory in this model. However, the amplitudes of the solitons depress along with increase of temperature of the medium, and it begins to disperse at 320 K. In the meanwhile, the damping of the medium can influence the states and properties of the soliton excited in α-helix protein molecules. The investigation indicates that the amplitude and propagated velocity of the soliton decrease, when the damping of medium increases. The soliton is dispersed at the large damping coefficient Γ=4 Γ₀ at 300 K. The results show that the soliton excited in the α-helix protein molecules with three channels is very robust against the damping and thermal perturbation of medium at biological temperature of 300 K. Thus we can conclude that the soliton can play important part in the bio-energy transport and the improved model is possibly a candidate for the mechanism of the energy transport in the α-helix proteins.

Smart Grid is expected to provide a reliable power supply with fewer and briefer outages, cleaner power, and self-healing power systems through advanced Power Quality (PQ) monitoring, analysis and diagnosis of the PQ measurements and identification of the root cause, and timely automated controls. It is important to understand that signal processing has been an integral part of advancing and expanding the horizons of this PQ research significantly and the capabilities and applications of signal processing for PQ are continually evolving. This paper thus presents a survey on the proven and emerging signal applications for enhancing PQ, focusing on algorithms for estimating system modal parameters because resonant frequencies and their damping information are critical signatures in evaluating the PQ. In particular, we discuss the need for investigating time-varying and nonlinear characteristics of the modal parameters due to dynamic changes in system operating conditions and introduce promising signal processing techniques for this purpose.

Departing from the OGY method reported in 1990, many methodologies for chaos control have been proposed. A major criticism is that most of them are merely straightforward applications of methodologies borrowed from feedback control theory. In fact, an authentic chaos control methodology should rely on the underlying structure (e.g. topology, dynamics, etc.) of chaotic behavior in order to provide simple and successful feedback control algorithms. This brief paper focuses on this objective; namely, to exploit chaos structure to design feedback controllers aimed to eliminate chaos. The well-known Duffing oscillator is used to show how the mechanisms leading to chaotic behavior can be destroyed by means of a simple feedback control. Specifically, it is shown that injected damping, via feedback control, is able to eliminate the transverse homoclinic orbit responsible for the chaotic behavior of the Duffing oscillator.

We consider the 2D Boussinesq equations with a velocity damping term in a strip domain, with impermeable walls. In this physical scenario, where the Boussinesq approximation is accurate when density or temperature variations are small, our main result is the asymptotic stability for a specific type of perturbations of a stratified solution.

This paper studies a non-linear model for the damped oscillations of a pendulum.

This paper gives a short remark on variational principle for the fractal Telegraph equation [K. L. Wang, S. W. Yao, Y. P. Liu et al., Fractals28(4) (2020) 2050058], the emphasis is put on temporal and spatial fractal derivatives and the derivation process of the fractal variational principle.

Time dependent analysis of the dynamic damped behavior of continua are mathematically modelled by partial differential equations. One obtains uniqueness, existence and stability (well posed problems) by the implementation of the correct initial boundary conditions. However, by taking memory effects into consideration, any change in the past of the system changes the future dynamic behavior. Classical damping descriptions fail when describing the behavior of many materials, like teflon. This is because in classical theory the operators are local ones. The implementation of fractional time derivatives into the partial differential equations is an alternative technique to overcome these problems. Thereby the time derivative operator is a global one, memory effects in structure borne sound can be calculated. In this paper the theory of fractional time derivative operators and their application in continuum mechanics is presented. The main result when using this method for damping behavior is that a global operator is needed which takes the whole history into account. We call this theory the functional calculus method instead of the well-known fractional calculus with the use of initial conditions. In order to show the efficiency of this method the calculated impulse response of a viscoelastic rod is compared with measurements. It is shown that the damping behavior is described much better than by other models with comparably few parameters. Moreover, it is the only one that works in a wide frequency range and can describe the dispersion of the resonance frequencies. The implementation of this damping description in a Boundary Element Code is an application of dynamics of 3D continua in the frequency domain.

The two-sided second-order Arnoldi algorithm is used to generate a reduced order model of two test cases of fully coupled, acoustic interior cavities, backed by flexible structural systems with damping. The reduced order model is obtained by applying a Galerkin–Petrov projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving the low frequency moments of the coupled system. The basis vectors for projection are computed efficiently using a two-sided second-order Arnoldi algorithm, which generates an orthogonal basis for the second-order Krylov subspace containing moments of the original higher dimensional system. The first model is an ABAQUS benchmark problem: a 2D, point loaded, water filled cavity. The second model is a cylindrical air-filled cavity, with clamped ends and a load normal to its curved surface. The computational efficiency, error and convergence are analyzed, and the two-sided second-order Arnoldi method shows better efficiency and performance than the one-sided Arnoldi technique, whilst also preserving the second-order structure of the original problem.

We consider the Cauchy problem for the nonlinear self-focusing Schrödinger equation in ℝ^N with an inhomogeneous smooth damping coefficient and we prove, for suitable initial data, and in the spirit of the seminal work of R. Glassey, a blowup result for the corresponding local solutions. We also give some lower bound estimates for the blowing-up solutions.

We consider the nonlinear Schrödinger equation with L²-critical exponent and an inhomogeneous damping term. By using the tools developed by Merle and Raphael, we prove the existence of blowup phenomena in the energy space H¹(ℝ).

The lever-type multiple tuned mass dampers (LT-MTMD), consisting of several lever-type tuned mass dampers (LT-TMDs) with a uniform distribution of natural frequencies, are proposed for the vibration control of long-span bridges. Using the analytical expressions for the dynamic magnification factors (DMF) of the LT-MTMD structure system, an evaluation, with inclusion of the LT-MTMD stroke, is conducted on the performance of the LT-MTMD with identical stiffness and damping coefficients but unequal masses for mitigating harmonically forced vibrations. The LT-MTMD is found to possess the near-zero optimum average damping ratio regimen when the total number of dampers exceeds a certain value. In comparison, the LT-MTMD without the near-zero optimum average damping ratio and the traditional hanging-type multiple tuned mass dampers (HT-MTMD) without the near-zero optimum average damping ratio can achieve approximately the same optimum frequency spacing (an indicator for robustness), effectiveness, and stroke. Compared with the HT-MTMD, the LT-MTMD needs lesser optimum average damping ratio but significantly higher optimum tuning frequency ratio. Its main advantage is that the static stretching of the spring may be adjusted to meet the practical requirements through the support movement, while maintaining the same robustness, effectiveness, and stroke. Consequently, the LT-MTMD is a better choice for suppressing the vibration of long-span bridges as the static stretching of the spring required is not large.