Energy Decay Rate Research Articles

Decay for thermoelastic laminated beam with nonlinear delay and nonlinear structural damping

<abstract><p>This paper discussed the decay of a thermoelastic laminated beam subjected to nonlinear delay and nonlinear structural damping. We provided explicit and general energy decay rates of the solution by imposing suitable conditions on both weight delay and wave speeds. To achieve this, we leveraged the properties of convex functions and employed the multiplier technique as a specific approach to demonstrate our stability results.</p></abstract>

Stability analysis for a Rao-Nakra sandwich beam equation with time-varying weights and frictional dampings

<abstract><p>In this paper, we studied the asymptotic behavior of solutions for a Rao-Nakra sandwich beam equation with time-varying weights and frictional damping terms acting complementarily in the domain. We studied the effect of the three damping on the asymptotic behavior of the energy function. Under nonrestrictive on the growth assumption on the frictional damping terms, we established exponential and general energy decay rates for this system by using the multiplier approach. The results generalized some earlier decay results on the Rao-Nakra sandwich beam equation.</p></abstract>

Additive manufacture of ultrasoft bioinspired metamaterials

The dynamic loading behavior of materials plays a vital role in various engineering applications, such as aerospace protective components, armor, marine infrastructures, and automotive crash safety. The advent of additive manufacturing technologies has enabled the design of metamaterials that exhibit exceptional mechanical performance and artificially engineered properties not found in nature. However, fabricating ideal materials that resist dynamic loading is challenging because of the complexity of dynamic mechanical processes and varying requirements across different applications. In this study, a novel hierarchical design is proposed that combines natural fiber-inspired frameworks with graphene-inspired parent structures. This design aims to produce metamaterials, with characteristics such as reduced dynamic compressive strength, high energy absorption, and programmable dynamic loading, via advanced manufacturing technologies. An additive-manufacturing-oriented digital design approach and machine learning techniques were employed to engineer the dynamic loading performance of graphene-inspired metamaterials using the bonding principles inspired by natural fibers, to facilitate the design of next-generation metamaterial for advanced manufacturing. Experimental results illustrate the significant improvements achieved with our metamaterials compared to their existing counterparts. These improvements include a decrease in dynamic compressive strength of up to 86 %, while maintaining a remarkable 682 % enhancement in energy absorption during dynamic compressions, with a 42 % reduction in the energy decay rate. A compositional design strategy and programmable dynamic compression curve methodology is proposed that enable the tailored optimization of dynamic loading behaviors without modifying the base topology of metamaterials. This research offers a promising pathway for the development of next-generation materials, engineered to withstand dynamic loadings with intelligent and programmable performances suitable for aerospace, defense, and other high-value applications. By leveraging the advantages of natural fiber-inspired structures and graphene-inspired metamaterials, this work contributes to the advancement of materials with tailored resistance to dynamic loading and opens new possibilities for intelligent dynamic loading performance.

General Stability for the Viscoelastic Wave Equation with Nonlinear Time-Varying Delay, Nonlinear Damping and Acoustic Boundary Conditions

This paper is focused on energy decay rates for the viscoelastic wave equation that includes nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. We derive general decay rate results without requiring the condition a2>0 and without imposing any restrictive growth assumption on the damping term f1, using the multiplier method and some properties of the convex functions. Here we investigate the relaxation function ψ, namely ψ′(t)≤−μ(t)G(ψ(t)), where G is a convex and increasing function near the origin, and μ is a positive nonincreasing function. Moreover, the energy decay rates depend on the functions μ and G, as well as the function F defined by f0, which characterizes the growth behavior of f1 at the origin.

Longtime behavior of the weakly coupled Euler-Bernoulli plate system with structural damping

In this paper, we study the longtime behavior of the weakly coupled Euler-Bernoulli plate system with one structural damping. The system consists of two plate equations coupled by zero order terms. First, we show that when the coupling coefficient function is a nonzero constant and the damping coefficient function is a positive constant, the optimal energy decay rate of the system is t−23. Then we consider the case that the coupling and damping coefficient functions have compact supports. By Carleman estimate and the frequency domain method, we show that the energy of the system decays logarithmically when the supports of the coupling and damping coefficient functions satisfy suitable assumptions.

A new model for quantifying wave damping by vegetation in combined wave–current flow

The propagation of waves in nearshore areas is often accompanied by the presence of tidal currents, which have an impact on the dissipation of wave energy in coastal vegetation regions. However, the existing models generally do not consider the in-canopy velocity, resulting incomplete energy dissipation terms and thus inaccurate estimation of drag coefficients. In this study, we developed a new analytical model to incorporate vertical velocity distribution and full energy dissipation terms in energy flux balance equation. This model is applied to interpret the data from a new flume experiment of vegetation in combined wave-current flows. New CD-Re relationships were derived by applying the new model. Additionally, we extracted the wave energy passage time and decay rate from both the experimental data and the model results, which shows that the wave energy passage time of opposing currents is up to 75% longer than that of following currents. This disparity in passage time is the primary factor contributing to the greater wave dissipation observed in the cases of opposing currents. This study offers novel insights into the process of wave dissipation, and can potentially improve our capability in predicting wave dissipation.

Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents

In this article, we consider a coupled system of two hyperbolic equations with variable exponents in the damping and source terms, where the dampings are modilated with time-dependent coefficients \(\alpha(t), \beta(t)\). First, we state and prove an existence result of a global weak solution, using Galerkin's method with compactness arguments. Then, by a Lemma due to Martinez, we establish the decay rates of the solution energy, under suitable assumptions on the variable exponents \(m\) and \(r\) and the coefficients \( \alpha\) and \(\beta\). To illustrate our theoretical results, we give some numerical examples.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/73/abstr.html

Feedback stabilization of non-homogeneous distributed bilinear systems with varying time delay

This paper deals with the feedback stabilization for a class of non-homogeneous distributed bilinear systems, with periodically varying time delay, evolving in Hilbert state space. Sufficient conditions for polynomial and exponential stabilization are given. Explicit energy decay rates are provided in both cases. Illustrative examples are displayed.

Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement

In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional.

Decay of a Thermoelastic Laminated Beam with Microtemperature Effects, Nonlinear Delay, and Nonlinear Structural Damping

This article deals with a non-classical model, namely a thermoelastic laminated beam along with microtemperature effects, nonlinear delay, and nonlinear structural damping, where the last two terms both affect the equation which depicts the dynamics of slip. With the help of convenient conditions in both weight delay and wave speeds, we demonstrate explicit and general energy decay rates of the solution. To attain our interests, we highlight useful properties regarding convex functions and apply a specific approach known as the multiplier technique, which enables us to prove the stability results. Our results here aim to show the impact of different types of damping by taking into account the interaction between them, which extends recent publications in the literature.

Well-posedness and polynomial energy decay rate of a transmission problem for Rayleigh beam model with heat conduction

In this paper, we investigate the stability of the transmission problem for Rayleigh beam model with heat conduction. First, we reformulate our system into an evolution equation and prove our problem’s well-posedness. Next, we demonstrate the resolvent of the operator is compact in the energy space, then by using the general criteria of Arendt–Batty, we prove that the thermal dissipation is enough to stabilize our model. Finally, a polynomial energy decay rate has been obtained which depends on the mass densities and the moments of inertia of the Rayleigh beams.

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

In this paper, we consider a piezoelectric beam model with nonlinear source terms and investigate the interaction between a viscoelastic damping and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we establish explicit formulae for the energy decay rates of this system and prove that the energy decays at a rate dictated by the weaker damping. Our results substantially improve some earlier related results in the literature.

Optimal energy decay rate for a kinetic equation coupled with the Stokes equations

In this paper, we study energy decay rate for a kinetic equation coupled with the Stokes equations. Using the Fourier splitting method, we obtain the optimal energy decay rate, in the sense that the energy of the system decays at a rate coinciding with the one corresponding to the underlying linear parabolic equations.

The acoustical characterization of clay pots in Ottoman architecture through experimental and numerical analysis.

In medieval age, clay pots are utilized as multi-functional building elements serving not only for structural and ventilative purposes but also for the improvement of the acoustic qualities of the space. Although the medieval usage of acoustic pots is vaguely connected with the acoustic vessels of Vitruvius, their employment is also interpreted as cavity resonators as in the case of Süleymaniye Mosque. The 16th century edifice designed by Sinan the Architect Laureate is a significant example among its European counterparts with 224 clay pots embedded into its central dome. The present work aims to discuss the contribution of clay pots in acoustics of historical edifices focusing on Süleymaniye Mosque. In this study, a clay pot sample employed in the mosque is reproduced and impedance tube measurements are held. The results are then compared with finite element model simulations carried out to examine the effective frequency range of the clay pots. Finally, the data acquired from numerical simulations and the experimental measurements are applied in ray tracing simulations. The final results reinforce the contribution of clay pots on the improvement of sound energy decay rate measured after the final restorations within the mosque with repaired pots.

Optimal energy decay rates for viscoelastic wave equations with nonlinearity of variable exponent

In this article, we consider the viscoelastic wave equation $$ u_{tt}-\Delta u+\int_0^{t}g(t-s)\Delta u(s)ds+a| u_t| ^{m(\cdot )-2}u_t=0 $$ with a nonlinear feedback having a variable exponent \(m(x)\). We investigate the interaction between the two types of damping and establish an optimal decay result under very general assumptions on the relaxation function \(g\). We construct explicit formulae which provide faster energy decay rates than the ones already existing in the literature.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/53/abstr.html

Variable-coefficient viscoelastic wave equation with acoustic boundary conditions: global existence, blowup and energy decay rates

Variable-coefficient viscoelastic wave equation with acoustic boundary conditions: global existence, blowup and energy decay rates

Research on the detection of the hole in wood based on acoustic emission frequency sweeping

In order to detect the hole defect in the wood, the intrinsic frequency of wood is investigated by frequency sweeping and combining with pencil-lead break (PLB) tests to examine the influence of the hole defect on the intrinsic frequency to obtain the significant change index for non-destructive detection of the holes. Initially, the sweeping frequency test is conducted in the range of 10–180 kHz on two different sizes of Zelkova schneideriana and Pinus sylvestris var. mongholica specimens, followed by the signal's frequency domain analysis to determine the natural frequency and its range. Then, holes with diameters of 5, 10, and 20 mm are drilled on the Zelkova schneideriana specimens to explore the impact of hole diameter on the natural frequency using PLB and frequency sweeping. Finally, 1, 3, and 5 holes of 8 mm are drilled to investigate the influence of hole number on natural frequency. The results showed that the natural frequency of wood falls within two frequency ranges of 30–50 kHz and 150–180 kHz. In addition, the hole hinders the AE signal's propagation. The energy decay rate in the two natural frequency ranges increases as the diameter and number of holes rise. In addition to the traditional method for calculating signal propagation speeds, this study proposes effective measures for detecting holes in wood.

In Situ Optical Microspectroscopy Study of Isothermal Bleaching of γ-Irradiated International Simple Glass.

The isothermal bleaching of γ-irradiated glass was studied at elevated temperatures (280-340 °C) by real-time in situ optical microspectroscopy for the first time. The study was performed on γ-irradiated (0.83 and 1.99 MGy) International Simple Glass (ISG) borosilicate nuclear waste simulant made by Mo-SCI Corporation (Rolla, MO, USA). The current investigation proposes real-time optical transmission methodology for the activation energy assessment of isothermal bleaching of γ-irradiated glass. The method is based on robust quantification of the Urbach energy decay rates and yields similar activation energies for both doses within ∼0.24-0.26 eV.

On the asymptotic behavior of solutions to a structural acoustics model

This article is concerned with the long term behavior of solutions to a structural acoustics model consisting of a semilinear wave equation defined on a bounded domain Ω⊂R3 which is coupled with a Berger plate equation acting on a flat portion of the boundary of Ω. The system is influenced by several competing forces, in particular a source term acting on the wave equation which is allowed to have a supercritical exponent.Our results build upon those obtained by Becklin and Rammaha [8]. With some restrictions on the parameters in the system and with careful analysis involving the Nehari manifold we obtain global existence of potential well solutions and establish either exponential or algebraic decay rates of energy, dependent upon the behavior of the damping terms. The main novelty in this work lies in our stabilization estimate, which notably does not generate lower-order terms. Consequently, the proof of the main result is shorter and more concise.

Optimal energy decay for a viscoelastic Kirchhoff equation with distributed delay acting on nonlinear frictional damping

In this paper, we have analysed the influence of viscoelastic and frictional damping on the decay rate of solutions for a Kirchhoff-type viscoelastic wave equation with a distributed delay acting on nonlinear internal damping. Taking the relaxation function of a fairly large class and using the method of energy in which we introduce an adapted Lyapunov functional and by exploiting certain properties of convex functions, under certain assumptions on the constants of system, we obtain the optimal decay rate of energy in the sense that it is compatible with the decay rate of the relaxation function.