Logarithmic Decay Rate Research Articles

Rail pad damping characteristics in track vibration reduction evaluated through hammer tests and theoretical analysis

Although the majority of existing research addresses the stiffness characteristics of rail pads, the considerable impact of damping on vibration reduction underscores its significant research importance. In this study, the hammer test and theoretical calculation are both employed to assess the damping capacity across three rail pad types: prismatic (PRP), grooved (GRP), and mesh-type high-damping (MTHDRP). Through the hammer test, the MTHDRP notably surpassed GRP and PRP, achieving higher damping ratios by 51.40 % and 49.71 %, respectively, leading to significant vibration reductions in the track bed and rail. Comparison tests between three types of rail pads highlighted the enhanced performance of the MTHDRP, as it not only reduced vibration amplitudes and enhanced decay rates but also decreased vibration levels by 2−5 dB. Moreover, we established a refined finite element model of the fastener system and integrated it with the Logarithmic Decay Rate (LDR) method. Our findings demonstrate that this combination facilitates the calculation of the damping ratio of the rail pad. Furthermore, we conducted a comparative analysis between the LDR method and the envelope method, confirming its superior efficiency and reliability. Finally, the LDR method is used to predict the damping ratio of the rail pad with varying stiffness, showing that the softer the rail pad, the higher the corresponding damping ratio. Overall, our insights bridge the gap in theoretical calculations and experimental studies on rail pad damping characteristics, offering crucial guidance for rail pad selection in track vibration mitigation.

Research on the Dynamic Characteristics of Cantilever Rotor System With ISFD

Aiming at the common vibration problem of the cantilever rotor system and the nonlinear problem of traditional squeeze film damper (SFD), an integral squeeze film damper (ISFD) for the cantilever rotor system was proposed based on the traditional SFD. In order to investigate the effect of the ISFD on the dynamic characteristics of the cantilever rotor system, the vibration reduction experiment of the rotor system was carried out. The mechanical model and finite element model of the cantilever rotor system were established. The first‐order critical speed, strain energy, stability, and steady‐state response of the cantilever rotor system were numerically analyzed. Experimental research on the vibration reduction of the cantilever rotor system by the ISFD under different unbalance conditions and different rotational speed conditions was carried out on the test rig of the cantilever rotor system. The results showed that the ISFD has remarkable performance, which can reduce the bending deformation and strain energy of the rotating shaft, increase the logarithmic decay rate, and improve the overall stability of the system. Under various working conditions, the ISFD can effectively suppress the unbalanced vibration of the rotor and the shaft center displacement of the rotor, and the amplitude of the rotor system at the working frequency (1X) is greatly reduced.

Logarithmic Stabilization of an Acoustic System with a Damping Term of Brinkman Type

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term, we identify logarithmic decay of solutions with growing time. Logarithmic decay rate is shown through a new Carleman estimate which allows us to carry out a special analysis for the resolvent.

Numerical and experimental study on dynamic characteristics of tilting-pad journal bearings considering pivot stiffness in a vertical rotor system

Purpose The purpose of this paper is to study the influence of pivot stiffness on the dynamic characteristics of tilting-pad journal bearings (TPJBs) and the stability of the bearing-rotor system. Design/methodology/approach A theoretical numerical model is established, and the influences of pivot stiffness on TPJBs and a bearing-rotor system are analyzed. Then, two kinds of pivot structures with different stiffness are designed and the vibration characteristics are tested on the vertical rotor bearing test bench. Findings The pivot stiffness has an obvious effect on the dynamic characteristics of the TPJBs and the stability of the bearing-rotor system. As a result of appropriate pivot stiffness, the critical speed and the vibration amplification factor can be reduced, the logarithmic decay rate and the stability of the rotor system can be effectively increased. While the journal whirl orbit is smoother and the rubbing is obviously reduced when the bearings have flexible pivots. Originality/value The influence of pivot stiffness on TPJBs and a vertical rotor-bearing system is studied by theoretical and experimental methods.

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.

The dynamics analysis of a magnetic fluid shock absorber with different inner surface materials

Suffering low frequency and small amplitude shaking, energy dissipation of long overhanding structures on the spacecraft under weightless environment is a key research topic for the safety of such spacecraft. The paper presented a novel magnetic fluid shock absorber to reduce the vibration of low frequency and small amplitude. The proposed shock absorber had the composite magnet structure including three magnets in the working element and it was attached with different inner surface materials. To the best of our knowledge, this was the first time to consider the relationship between inner surface materials and damping performance of the shock absorber. First, the damping performance of the shock absorber with various magnetic fluid volume percentage and gap size was investigated by reducing the free oscillations of the brass plate. Meanwhile, the magnetic restoring force between the working element and the repulsion magnet was measured. The experimental results showed that the magnetic restoring force versus the distance was almost linear, under small amplitude. When the distance was greater than 20 mm, the approximate calculation formula of the equivalent stiffness could be obtained. We analyzed the influence of the different internal surface materials of the shock absorber on the damping performance by calculating the fluid resistance which was determined by both the viscous shear force and the capillary force. Experimental results verified that the capillary force had a significant influence on fluid resistance and couldn’t be ignored. In terms of the vibration decay time, the damping efficiency of chemigum was 61.39% and 57.87% better than that of fluororubber for the gap of 2 mm and 3 mm respectively. According to the logarithmic decay rate, the damping efficiency of chemigum was 2.965 times that of fluororubber under the gap of 2 mm and was 2.515 times under the gap of 3 mm. For the reason that the shock absorber was used in aerospace, weight was an important factor. Our experiments proved that we must take into account both the densities of materials and the damping performance when selecting inner surface materials.

Stabilization of transmission system of Kirchhoff plate and wave equations with a localized Kelvin–Voigt damping

In this paper, we consider the stabilization for the Kirchhoff plate and equations connected by transmission conditions. We show that the energy of the transmission system is stable with logarithmic decay rate when feedback control acts on the small part of the plate as a viscoelastic material with Kelvin–Voigt constitutive relation. The proof is based on a new resolvent estimate by using some careful analysis for Kirchhoff plate-wave transmission system.

Athermal sediment creep triggered by porous flow

Quasi-2D experiments of a submerged sediment layer creeping downward were performed, varying the channel tilt and a porous flow under the respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^*$, accounting for both mean porous flow and gravity force effects on particle motion, allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified, and correspond to a systematic change of the void size distribution as $P^*$ increases.

On the boundedness of Toeplitz operators with radial symbols over weighted sup-norm spaces of holomorphic functions

We prove sufficient conditions for the boundedness and compactness of Toeplitz operators Ta in weighted sup-normed Banach spaces Hv∞ of holomorphic functions defined on the open unit disc D of the complex plane; both the weights v and symbols a are assumed to be radial functions on D. In an earlier work by the authors it was shown that there exists a bounded, harmonic (thus non-radial) symbol a such that Ta is not bounded in any space Hv∞ with an admissible weight v. Here, we show that a mild additional assumption on the logarithmic decay rate of a radial symbol a at the boundary of D guarantees the boundedness of Ta. The sufficient conditions for the boundedness and compactness of Ta, in a number of variations, are derived from the general, abstract necessary and sufficient condition recently found by the authors. The results apply for a large class of weights satisfying the so called condition (B), which includes in addition to standard weight classes also many rapidly decreasing weights.

Development of a Machine Learning-Based Damage Identification Method Using Multi-Point Simultaneous Acceleration Measurement Results.

It is necessary to assess damage properly for the safe use of a structure and for the development of an appropriate maintenance strategy. Although many efforts have been made to measure the vibration of a structure to determine the degree of damage, the accuracy of evaluation is not high enough, so it is difficult to say that a damage evaluation based on vibrations in a structure has not been put to practical use. In this study, we propose a method to evaluate damage by measuring the acceleration of a structure at multiple points and interpreting the results with a Random Forest, which is a kind of supervised machine learning. The proposed method uses the maximum response acceleration, standard deviation, logarithmic decay rate, and natural frequency to improve the accuracy of damage assessment. We propose a three-step Random Forest method to evaluate various damage types based on the results of these many measurements. Then, the accuracy of the proposed method is verified based on the results of a cross-validation and a vibration test of an actual damaged specimen.

Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping

In this paper, we analyze the longtime behavior of the wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-diff-calculus, we obtain a Carleman estimate, and then establish an estimate on the corresponding resolvent operator. As a result, we show the logarithmic decay rate for energy of the system without any geometric assumption on the subdomain on which the damping is effective.

Effect of Interfacial Water on the Fatigue Performance of Composite Asphalt Mixture Beams

This study investigated the effect of interfacial water on the performance of asphalt pavement. Composite asphalt beams were used to carry out the four-point bending fatigue test and the direct shear test. Road construction was simulated, and the effects of interlayer water sprinkle amount and water immersion time on the shear strength and fatigue life of the composite beams were analyzed. The water damage mechanism of the composite beams under different water sources was determined by laser scanning with the longitudinal profile of the beams. Results show that the effect of immersion time on the shear strength of the composite beams is greater than that of interlayer water sprinkle amount. Under the same test conditions, the logarithmic decay rate of fatigue life increases with increasing interlayer water sprinkle amount or prolonged water immersion. However, the increase trend changes depending on immersion time, that is, it obviously slows down with time. With the increase in interlayer water sprinkle amount, the bending stiffness modulus loss of the composite beams increases nonlinearly to an amount less than 10%. Moreover, the bending stiffness modulus loss increases gradually with prolonged water immersion. It reaches 31% and then stabilizes after 5 days. Laser scanning shows that interlayer sprinkling creates a small gap in the interstitial interface of the composite beams, whereas water immersion forms a large area of peeled aggregate inside the upper interface mix. These results indicate that water immersion causes serious damage to the composite beams.

Local energy decay for Lipschitz wavespeeds

We prove a logarithmic local energy decay rate for the wave equation with a wavespeed that is a compactly supported Lipschitz perturbation of unity. The key is to establish suitable resolvent estimates at high and low energy for the meromorphic continuation of the cutoff resolvent. The decay rate is the same as that proved by Burq for a smooth perturbation of the Laplacian outside an obstacle.

Vibration damping of naval ships based on ship shock trials

Presently, the vibration damping mechanism of naval craft subjected to underwater shock is not well understood, and ship shock trials remain the most effective means of researching ship vibration damping problems. A damping modeling strategy for naval ship systems is presented for ship shock transient time-domain analysis. The total vibration damping ratios of a naval vessel under different shock conditions are calculated using the logarithmic decay rate based on measured shock trial data. The least-squares complex exponential method is used for the extraction of modal parameters in the time domain. The obtained modal parameters were employed to construct synthesized time histories, which compared favorably to the original time histories, verifying the proposed method. The structural damping is quantified and evaluated based on the extracted modal frequency and modal damping ratio, and Rayleigh damping coefficients and are experimentally obtained. The values of and presented in this work are respectively less and greater than those proposed for the U.S. Navy ship DDG-53.

Stabilization of the wave equation with Ventcel boundary condition

We consider a damped wave equation on a open subset of Rn or a smooth Riemannian manifold with boundary, with Ventcel boundary conditions, with a linear damping, acting either in the interior or at the boundary. This equation is a model for a vibrating structure with a layer with higher rigidity of thickness δ>0. By means of a proper Carleman estimate for second-order elliptic operators near the boundary, we derive a resolvent estimate for the wave semigroup generator along the imaginary axis, which in turn yields the logarithmic decay rate of the energy. This stabilization result is obtained uniformly in δ.

The Magnetic Relaxation of MgB2Thin Films Grown by Hybrid Physical–Chemical Vapor Deposition

The magnetic relaxation of MgB 2 thin film deposited on Al 2 O 3 substrate by hybrid physical-chemical vapor deposition method was investigated. The rate of magnetic relaxation (the logarithmic decay rate) S, which was obtained by the time dependence of magnetic moment m(t) at fixed magnetic field H and temperature T, of the MgB 2 thin film was investigated. The decay of magnetic moment m(t) was carried out at temperatures between 5 and 37.5 K in the field ranges of 0.1-1.0 T, using PPMS-VSM (Quantum Design). The decrease of magnetic moment m(t) for 7200 s at T = 5 K was about 2%-3% and 0.2%-0.3% when the field was applied parallel to the c-axis and the ab-plane, respectively. The logarithmic decay rate S in the field parallel to the ab-plane was much smaller than that parallel to the c-axis over all temperature ranges. The time-independent behavior of logarithmic decay rate S at low temperatures below T = 10 K implies the presence of quantum creep effect.

Local well-posedness in the critical Besov space and persistence properties for a three-component Camassa-Holm system with N-peakon solutions

In this paper we mainly investigate the Cauchy problem of a three-component Camassa-Holm system. By using Littlewood-Paley theory and transport equations theory, we establish the local well-posedness of the system in the critical Besov space. Moreover, we obtain some weighted $L^p$ estimates of strong solutions to the system. By taking suitable weighted functions, we can get the persistence properties of strong solutions on exponential, algebraic and logarithmic decay rates, respectively.

Logarithmic Local Energy Decay for Scalar Waves on a General Class of Asymptotically Flat Spacetimes

This paper establishes that on the domain of outer communications of a general class of stationary and asymptotically flat Lorentzian manifolds of dimension $$d+1$$ , $$d\ge 3$$ , the local energy of solutions to the scalar wave equation $$\square _{g}{\uppsi }=0$$ decays at least with an inverse logarithmic rate. This class of Lorentzian manifolds includes (non-extremal) black hole spacetimes with no restriction on the nature of the trapped set. Spacetimes in this class are moreover allowed to have a small ergoregion, but are required to satisfy an energy boundedness statement. Without making further assumptions, this logarithmic decay rate is shown to be sharp. Our results can be viewed as a generalisation of a result of Burq, dealing with the case of the wave equation on flat space outside compact obstacles, and results of Rodnianski–Tao for asymptotically conic product Lorentzian manifolds. The proof will bridge ideas from Rodnianski and Tao (see [58]) with techniques developed in the black hole setting by Dafermos and Rodnianski (see [21, 22]). As a soft corollary of our results, we will infer an asymptotic completeness statement for the wave equation on the spacetimes considered in the case where no ergoregion is present.

Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes

We construct quasimodes for the Klein-Gordon equation on the black hole exterior of Kerr-Anti-de Sitter (Kerr-AdS) spacetimes. Such quasi-modes are associated with time-periodic approximate solutions of the Klein Gordon equation and provide natural candidates to probe the decay of solutions on these backgrounds. They are constructed as the solutions of a semi-classical non-linear eigenvalue problem arising after separation of variables, with the (inverse of the) angular momentum playing the role of the semi-classical parameter. Our construction results in exponentially small errors in the semi-classical parameter. This implies that general solutions to the Klein Gordon equation on Kerr-AdS cannot decay faster than logarithmically. The latter result completes previous work by the authors, where a logarithmic decay rate was established as an upper bound.

Carleman estimates for elliptic boundary value problems with applications to the stablization of hyperbolic systems

A Carleman estimate for some first-order elliptic systems is established. This estimate is extended to elliptic boundary value problems provided the boundary condition satisfies a Lopatinskii-type requirement. Based on these estimates conservative hyperbolic systems of first order can be stabilized with a logarithmic decay rate by introducing a localized interior dissipation. The support of the dissipative term does not need to satisfy a geometric condition.