Influence of active constrained layer damping on the coupled vibration response of functionally graded magneto-electro-elastic plates with skewed edges

This article makes the first attempt in assessing the influence of active constrained layer damping(ACLD)treatment towards precise control of frequency responses of functionally graded skew-magneto-electroelastic(FGSMEE)plates by employing finite element methods.The materials are functionally graded across the thickness of the plate in terms of modest power-law distributions.The principal equations of motion of FGSMEE are derived via Hamilton’s principle and solved using condensation technique.The effect of ACLD patches are modelled by following the complex modulus approach(CMA).Additionally,distinctive emphasis is laid to evaluate the influence of geometrical skewness on the attenuation capabilities of the plate.The accuracy of the current analysis is corroborated with comparison of previous researches of similar kind.Additionally,a complete parametric study is directed to understand the combined impacts of various factors like coupling fields,patch location,fiber orientation of piezoelectric patch in association with skew angle and power-law index.

Effect on Landau damping rates for a non-Maxwellian distribution function consisting of two electron populations

In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.

Effect of porosity on active damping of geometrically nonlinear vibrations of a functionally graded magneto-electro-elastic plate

This paper investigates the effect of porosity on active damping of geometrically nonlinear vibrations(GNLV)of the magneto-electro-elastic(MEE)functionally graded(FG)plates incorporated with active treatment constricted layer damping(ATCLD)patches.The perpendicularly/slanted reinforced 1-3 piezoelectric composite(1-3 PZC)constricting layer.The constricted viscoelastic layer of the ATCLD is modeled in the time-domain using Golla-Hughes-Mc Tavish(GHM)technique.Different types of porosity distribution in the porous magneto-electro-elastic functionally graded PMEE-FG plate graded in the thickness direction.Considering the coupling effects among elasticity,electrical,and magnetic fields,a three-dimensional finite element(FE)model for the smart PMEE-FG plate is obtained by incorporating the theory of layer-wise shear deformation.The geometric nonlinearity adopts the von K arm an principle.The study presents the effects of a variant of a power-law index,porosity index,the material gradation,three types of porosity distribution,boundary conditions,and the piezoelectric fiber’s orientation angle on the control of GNLV of the PMEE-FG plates.The results reveal that the FG substrate layers’porosity significantly impacts the nonlinear behavior and damping performance of the PMEE-FG plates.

GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

Some Remarks on Euler Equations with Damping in Multi-Dimensions

We consider the Cauchy problem of Euler equations with damping. Based on the Green function and energy estimates of solutions, we improve the pointwise estimates and obtainL 1 estimate of solutions.

Numerical analysis of added mass and damping of floating production,storage and offloading system

An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.

The separability of two-mode Gaussian state under amplification and symmetric damping

The performances of a two-mode Gaussian state under paxametric amplification, symmetric amplitude damping and thermal noise axe studied. The time-dependent complex correlation matrix of the state in evolution is given. The sepaxability of the final two-mode Gaussian state is examined under symmetric amplification and asymmetric amplification separately.

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping（i.e., ACLD）, combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.

Nonlinear Landau damping of high frequency waves in non-Maxwellian plasmas

Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized （r, q） distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k ＋1, it reduces to the kappa distribution function.

Rudder Roll Damping Autopilot Using Dual Extended Kalman Filter–Trained Neural Networks for Ships in Waves

The roll motions of ships advancing in heavy seas have severe impacts on the safety of crews,vessels,and cargoes;thus,it must be damped.This study presents the design of a rudder roll damping autopilot by utilizing the dual extended Kalman filter(DEKF)trained radial basis function neural networks(RBFNN)for the surface vessels.The autopilot system constitutes the roll reduction controller and the yaw motion controller implemented in parallel.After analyzing the advantages of the DEKF-trained RBFNN control method theoretically,the ship’s nonlinear model with environmental disturbances was employed to verify the performance of the proposed stabilization system.Different sailing scenarios were conducted to investigate the motion responses of the ship in waves.The results demonstrate that the DEKF RBFNN based control system is efficient and practical in reducing roll motions and following the path for the ship sailing in waves only through rudder actions.

Generalized Wigner Functions for Damped Systems in Deformation Quantization

Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function （WF） does not work for these systems. In this paper we show that in order to let WF satisfy a ,-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a ＊-Exponential expansion in deformation quantization.

Bessel Function and Damped Simple Harmonic Motion

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

Landau damping of twisted waves in Cairns distribution with anisotropic temperature

The consideration of orbital angular momentum of an electric field(twisted mode)is applied to the kinetic theory of plasma.The linearized Vlasov–Poisson equation is solved for the anisotropic thermal distributed bi-Maxwellian and Cairns distributions of electrons to obtain the damping rates of twisted waves.The dispersion relation and Landau damping of Langmuir twisted modes are obtained.The presence of twisted modes opens up two more possibilities in Landau damping and dispersion relations.This may generate a mixture with ion sound waves.It seems to play the role of a control parameter of Landau damping.

Effects of Landau damping and collision on stimulated Raman scattering with various phase-space distributions

Stimulated Raman scattering(SRS)is one of the main instabilities affecting success of fusion ignition.Here,we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations.The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated,which is consistent with our theoretical analysis quantitatively.Maxwellian distribution,flattened distribution,and bi-Maxwellian distribution are studied in detail,which represent three typical stages of SRS.We also demonstrate the effects of plateau width,hot-electron fraction,hot-to-cold electron temperature ratio,and collisional damping on the Landau damping and growth rate.They gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.

The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs.

Oscillation Criteria for Even Order Functional Differential Equations with Damped Term

This paper investigates a class of even order functional differential equations with damped term,and derives two new oscillatory criteria of solution.

Influence of Generalized （r, q） Distribution Function on Electrostatic Waves

Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma （Langmuir） waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized （r, q） distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.

GLOBAL EXISTENCE AND L^p ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL SPACE

In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p （2 ≤ p ≤ ∞） decay estimates of the solution.

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integrationoperator in coherent state representation and then perform this integral by virtue of the technique of integration withinan ordered product of operators.The normally ordered time evolution operator is thus obtained.We then derive theWigner function of u(t)|n>,where |n> is a Fock state,which exhibits a generalized squeezing,the squeezing effect isrelated to the varying mass with time.

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.