The bending behavior of woven fabrics under low curva-ture conditions has been analyzed by linear viscoelastictheory.The fabric is assumed to behave viscoelasticallyand to be subjected to frictional restraints in bend...The bending behavior of woven fabrics under low curva-ture conditions has been analyzed by linear viscoelastictheory.The fabric is assumed to behave viscoelasticallyand to be subjected to frictional restraints in bending de-formation.The frictional restraint is considered to beproportional to the curvature and can be described by africtional moment.A model has been constructed by astandard three-element solid model and a paralleledfrictional sliding element.The equations of the model fora cyclic curvature variation are derived.A set of param-eters of the equations for each fabric has been obtainedexperimentally.Predictions of the bending rigidity andhysteresis for wool,cashmere,wool/polyester blended,polyester and cotton fabrics are made,displaying verygood agreement with the experimental observations.展开更多
Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the ker...Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions： What if the kernel is tested against a different function （say Gamma） other than the exponential function？ Would there still be stability？ In the affirmative, what kind of decay rate we get？ It is proved that for a non- decreasing function ＂Gamma＂ whose ＂logarithmic derivative＂ is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential.展开更多
文摘The bending behavior of woven fabrics under low curva-ture conditions has been analyzed by linear viscoelastictheory.The fabric is assumed to behave viscoelasticallyand to be subjected to frictional restraints in bending de-formation.The frictional restraint is considered to beproportional to the curvature and can be described by africtional moment.A model has been constructed by astandard three-element solid model and a paralleledfrictional sliding element.The equations of the model fora cyclic curvature variation are derived.A set of param-eters of the equations for each fabric has been obtainedexperimentally.Predictions of the bending rigidity andhysteresis for wool,cashmere,wool/polyester blended,polyester and cotton fabrics are made,displaying verygood agreement with the experimental observations.
基金the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through project No. IN111034
文摘Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn that the system is exponentially stable if the kernel in the memory term is sub- exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions： What if the kernel is tested against a different function （say Gamma） other than the exponential function？ Would there still be stability？ In the affirmative, what kind of decay rate we get？ It is proved that for a non- decreasing function ＂Gamma＂ whose ＂logarithmic derivative＂ is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential.
