Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t), u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I under a certain local Lipschitzian condition on f, a global existence and uniqueness theorem is proved. The proof is based on the paper [10] associated to a contraction mapping theorem and standard arguments of density. In Part} 2, under more restrictive conditions it is proved that the solution u(t) and its derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page

The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.Comment: 18 page

Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical resultsComment: 2

Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil

This paper is concerned with the linear ODE in the form $y'(t)=\lambda\rho(t)y(t)+b(t)$, $\lambda <0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $\rho(t)$, a linear drift in the coefficient $b(t)$ involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given.Comment: 18 page

Study on the influence of bus suspension parameters on ride comfort

This study proposes a three-dimensional vibration model of bus with 10 DOF (degree of freedom) based on Dragan Sekulić model to analyze the suspension parameters directly influenced ride comfort. The suspension parameters which include the stiffness and damping parameters are analyzed based on the weighted r.m.s. (root-mean-square) acceleration responses of the space of a driver, passenger in the middle part of the bus and passenger in the rear overhang according to ISO 2631-1:1997. The results show that both stiffness and damping parameters of vehicle suspension have important influences on ride comfort. Especially, the stiffness and damping values of vehicle suspension are within the value ranges (0.5k0 ≤ k ≤ 0.75 k0) and (0.5c0 ≤ c ≤ 0.75c0) to improve the ride comfort of driver and passengers

Model Updating for Large-Scale Railway Bridge Using Grey Wolf Algorithm and Genetic Alghorithms

This paper proposes a novel hybrid algorithm to deal with an inverse problem of a large-scale truss bridge. Grey Wolf Optimization (GWO) Algorithm is a well-known and widely applied metaheuristic algorithm. Nevertheless, GWO has two major drawbacks. First, this algorithm depends crucially on the positions of the leading Wolf. If the position of the leaderis far from the best solution, the obtained results are poor. On the other hand, GWO does not own capacities to improve the quality of new generations if elements are trapped into local minima. To remedy the shortcomings of GWO, we propose a hybrid algorithm combining GWO with Genetic Algorithm (GA), termed HGWO-GA. This proposed method contains two key features (1) based on crossover and mutation capacities, GA is first utilized to generate the high-quality elements (2) after that, the optimization capacity of GWO is employed to seek the optimal solutions. To assess the effectiveness of the proposed approach, a large-scale truss bridge is employed for model updating. The obtained results show that HGWO-GA not only provides a good agreement between numerical and experimental results but also outperforms traditional GWO in terms of accuracy

Damage detection for a large-scale truss bridge using Tranmissibility and ANNAOA

In this paper, we propose an efficient approach to enhance the capacity of Artificial Neural Network (ANN) to deal with Structural Health Monitoring (SHM) problems.  Over the last decades, ANN has been extensively utilized for damage detection in structures. In order to identify damages, ANN frequently utilizes input information that is based on dynamic features such as mode shapes or natural frequencies. However, this type of data may not be able to detect minor damages if the structural defects are insignificant. To transcend these limitations, in this work, we propose utilizing transmissibility to create input data for the input layer of ANN. Moreover, to deal with local minimum problems of ANN, a combination between the Arithmetic Optimization Algorithm (AOA) and ANN is proposed. The global search capacity of AOA is employed to remedy the local minima of ANN. To evaluate the effectiveness of the proposed approach, a numerical model with different damage scenarios is considered. The suggested approach detects damage location precisely and with higher severity detection precision than the conventional ANN method

Damage detection for a large-scale truss bridge using Tranmissibility and ANNAOA

In this paper, we propose an efficient approach to enhance the capacity of Artificial Neural Network (ANN) to deal with Structural Health Monitoring (SHM) problems.  Over the last decades, ANN has been extensively utilized for damage detection in structures. In order to identify damages, ANN frequently utilizes input information that is based on dynamic features such as mode shapes or natural frequencies. However, this type of data may not be able to detect minor damages if the structural defects are insignificant. To transcend these limitations, in this work, we propose utilizing transmissibility to create input data for the input layer of ANN. Moreover, to deal with local minimum problems of ANN, a combination between the Arithmetic Optimization Algorithm (AOA) and ANN is proposed. The global search capacity of AOA is employed to remedy the local minima of ANN. To evaluate the effectiveness of the proposed approach, a numerical model with different damage scenarios is considered. The suggested approach detects damage location precisely and with higher severity detection precision than the conventional ANN method

Influence of damping coefficient into engine rubber mounting system on vehicle ride comfort

This study presents a method to improve vehicle ride comfort using additional damping coefficient values for an internal combustion engine (ICE) rubber mounting system. To analyze the effect of the adding damping coefficient values into the rubber mounting system on vehicle ride comfort, a full-vehicle vibration model with 10 degrees of freedom is established under the combination of road surface roughness and ICE excitations. The damping coefficient values are added into ICE rubber mounting system which are respectively analyzed and evaluated according to the international standard ISO 2631-1 (1997). The study results do not only evaluate the influence of the adding damping coefficients on vehicle ride comfort but also suggest the optimal design solution for ICE mounting system to improve vehicle ride comfort