1,107 Results Found

This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping...

The present paper develops a new Bernoulli–Euler theory of microbeams for the consideration of small-scale effects and nonlinear terms, which are induced by the axial elongation of the beam and Kelvin–Voigt damping. The non-resonance and...

An exact solution of the collisionless time-dependent Vlasov equation is found. For the first time in a century, an analytical solution to the one-dimensional time-dependent Vlasov–Boltzmann equation has been found. It has been found that inste...

Nonlinear acoustic damping is a key nonlinearity in miniature loudspeakers when the air velocity is at a high amplitude. Measurement of nonlinear acoustic damping is beneficial for predicting and analyzing the performance of miniature loudspeakers. H...

A smooth and discontinuous (SD) oscillator is a typical multi-stable state system with strong nonlinear properties and has been widely used in many fields. The nonlinear dynamic characteristics of the system have not been thoroughly investigated beca...

This paper presents the derivation of an exact solution for a damped nonlinear oscillator of arbitrary order (both integer and non-integer). A coefficient relationship was defined under which such a solution exists. The analytical procedure was devel...

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general de...

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...

We consider the Cauchy problem for the stochastic nonlinear Schrödinger equation augmented by nonlinear energy-critical damping term arising in nonlinear optics and quantum field theory. Through examining the behavior of the momentum and energy...

In recent decades, nonlinear damping identification (NDI) in structural dynamics has attracted wide research interests and intensive studies. Different NDI strategies, from conventional to more advanced, have been developed for a variety of structura...

In this paper, we study the Cauchy problem for the p-system with nonlinear and space-dependent damping. We focus on analyzing the asymptotic behavior and decay rates of solutions when the state constants for the specific volume are the same and the t...

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...

This paper is concerned with the asymptotic behavior of the solution of a Timoshenko system with two nonlinear variable exponent damping terms. We prove that the system is stable under some specific conditions on the variable exponent and the equal w...

We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative ($0<\alpha <1$) with mi...

A reliable determination of the damping characteristics of railway bridges is essential for realistic dynamic assessments, as damping strongly influences predicted vibration responses and resonance effects caused by train traffic. Conventional analys...

This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies $g^{\prime }(t$...

In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governi...

DC-DC converters with constant power loads are mostly used in DC microgrids. Negative impedance and large disturbances of constant power loads may lead to the instability of DC-DC converters. To address this issue, a nonlinear control strategy consis...

The shear response of steel-reinforced elastomeric bearings (SREBs) governs their performance in bridges and base-isolated buildings, yet the material and geometric nonlinearities involved are not captured by the simplified design rules of current st...

Output-only methods for modal identification are only strictly valid if a set of requirements are fulfilled regarding both structural and environmental conditions. A particularly challenging effect in wind turbine dynamics is the significant presence...

In this paper, a mathematical model for the rolling motion of ships in random beam seas has been investigated. The ships’ steady-state rolling motion with a nonlinear restoring moment and damping effect is modeled by the nonlinear second-order...

This paper gives the continuous dependence of solutions for the damped nonlinear hyperbolic equation.

We study the focusing nonlinear Schrödinger equation with time-dependent linear damping in the mass-supercritical and energy-subcritical regime. After a gauge renormalization, the problem becomes a focusing Schrödinger equation with a time-...

Although the small-scale effect and nonlinear damping on the nonlinear vibration of microbeam electrostatic resonators are important, they have been overlooked by researchers. We use the slender beam model including the small-scale effect and nonline...

As a composite material, the damping energy consumption mechanism of fiber reinforced polymer-confined reinforced concrete (FRP-C RC) structure is very complex. In previous dynamic calculation models, the bond-slip effect for steel bars was often ign...

In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations,...

We establish global decay and scattering in the energy space $H^2\left({\mathbb{R}}^d\right)$, for $d\ge 5$, of radial solutions to the damped nonlinear biharmonic Schrödinger equation with general complex-valued, time-dependent damping coefficients. Assuming radial data e...

This article investigates the efficiency of hybridizing composites with thin layers of martensitic shape memory alloys for improvement of damping. The non-linear damping behaviour of martensitic shape memory alloys is simulated using a modified versi...

We will show, in any space dimension $d\ge 3$, the decay and scattering in the energy space for the solution to the damped nonlinear Schrödinger equation posed on ${\mathbb{R}}^d\times \mathbb{T}$ and initial data in $H^1({\mathbb{R}}^d\times \mathbb{T})$. We will also derive new bilinear Mora...

In this article, we consider the dynamics of a viscoelastic plate equation with internal fractional damping, a nonlinear logarithmic source, and infinite memory effects. The existence of a local weak solution is shown effectively through the framewor...

We will explore, in any space dimension $d\ge 4$, the decay in the energy space for the damped magnetic Schrödinger equation with non-local nonlinearity and radial initial data in $H^1\left({\mathbb{R}}^d\right)$. We will also display new Morawetz identities and correspond...

In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal cond...

We formulate a chain of damped harmonic oscillators as a mechanical analogy for a single-lane vehicle platoon and show that it reproduces, and yields analytical insight into, the congestion patterns of car-following traffic. Each follower is treated...

In order to apply the nonlinear energy sink (NES) to reduce the low-frequency noise inside a 3D acoustic cavity with an impedance boundary, a two degrees-of-freedom (DOF) dynamic model of the coupled system of one damped acoustic mode of a regular 3D...

Since the structural mechanics of the super magnetostrictive actuator (GMA) system involves problems related to viscoelastic damping materials, the fractional order is more accurate than the integer order calculus to characterize the viscoelastic fea...

In this paper, we investigate the partial approximate controllability of a class of fractional diffusion control systems with three-parameter damping and nonlinear perturbations. First, based on the theory of $(\mu ,\nu ,\xi ,e,k)$-resolvent families d...

The dynamic response of tall bridge piers with varying damping ratios under three-dimensional pulse ground motion remains insufficiently understood. To control the pulse characteristic parameters accurately and eliminate interference from actual seis...

We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ${\varphi }_{tt}(t,\omega )-\Delta \varphi (t,\omega )+{\varphi }_t(t,\omega )=\frac{1}{\Gamma (1-\rho )}{\int }_0^t{(t-\sigma )}^{-\rho }{\left|\varphi (\sigma ,\omega )\right|}^{q}d\sigma +\mathrm{\&m}$...

This work aims to address the P-bifurcation of a stochastic nonlinear system with fractional damping driven by Gaussian white noise. Based on a stochastic averaging method, a fractional damping stochastic nonlinear equation has been studied. Furtherm...

We used the classical Lie symmetry method to study the damped Klein–Gordon equation (Kge) with power law non-linearity $u_{tt}+\alpha \left(u\right)u_t={\left(u^{\beta }{u}_x\right)}_x+f\left(u\right)$. We carried out a complete Lie symmetry classification by finding forms for $\alpha \left(u\right)$ and...

Viscoelasticity and variable mass are common phenomena in Micro-Electro-Mechanical Systems (MEMS), and could be described by a fractional derivative damping and a stochastic process, respectively. To study the dynamic influence cased by the viscoelas...

In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system b...

In this paper, a novel nonlinear robust damping controller is proposed to suppress power oscillation in interconnected power systems. The proposed power oscillation damping controller exhibits good nonlinearity and robustness. It can consider the str...

This proposal suggests a novel nonlinear position-stabilizing controller for magnetic levitation (MAGLEV) applications. The proposed scheme is devised by combining the active damping injection technique and disturbance observers (DOBs), considering t...

This article investigates longitudinal deformation waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid between them. The presence of a viscous incompressible fluid between the shells, as well as the influenc...

In this work, the response of a ship rolling in regular beam waves is studied. The model is one degree of freedom model for nonlinear ship dynamics. The model consists of the terms containing inertia, damping, restoring forces, and external forces. T...

This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relat...

One of the current directions in the development of the modern theory of oscillations is the elaboration of effective methods for analyzing the stability of solutions of dynamical systems. The aim of the work is to develop a new asymptotic method for...

A novel coated damping structure for metal rubber (MR) of bellows is designed based on large-size metal rubber sheets. This structure is dynamically tested in the bending direction at normal temperature. According to the test results, a model of the...

In this study, we examine a q-Kirchhoff-type equation defined on a bounded domain, incorporating nonlinear boundary damping and source terms with variable exponents. Assuming appropriate conditions on the initial data and the variable exponent functi...