Asymptotic stability for a laminated beam with structural damping and infinite memory
Wenjun Liu, Xiangyu Kong, Gang Li
Abstract
In this paper, we consider a one-dimensional laminated beam with structural damping and an infinite memory acting on the effective rotation angle. Under appropriate assumptions imposed on the relaxation function, we show that the system is well-posed by using the Hille–Yosida theorem, and then we establish general decay results, from which exponential and polynomial decays are only special cases, in the case of equal speeds of wave propagation as well as that of nonequal speeds. In the particular case when the wave propagation speeds are different and the relaxation function decays exponentially, we show the lack of exponential stability.
Topics & Concepts
Exponential stabilityRelaxation (psychology)Beam (structure)Exponential functionExponential growthMathematical analysisPolynomialFunction (biology)Stability (learning theory)Exponential decayPhysicsMathematicsRotation (mathematics)Timoshenko beam theoryClassical mechanicsGeometryQuantum mechanicsOpticsComputer sciencePsychologyBiologyNonlinear systemMachine learningEvolutionary biologySocial psychologyAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential EquationsNumerical methods in inverse problems