{"title":"Equilibrium Violation from the Complex Stiffness","authors":"N. Makris","doi":"10.1115/1.4062263","DOIUrl":null,"url":null,"abstract":"\n Evidence from cyclic tests on metals, elastomers and sandy soils reveals that damping forces are nearly rate-independent and structural (hysteretic or rate-independent) damping was widely adopted since the 1940s. While there is no time-domain constitutive equation for a linear spring connected in parallel with a rate-independent dashpot, the dynamic stiffness (transfer function) of this mechanical network can be constructed in the frequency-domain; and it was known since the early 1960s that this mechanical network exhibits a non-causal response. In view of its simplicity in association with the wide practical need to model rate-independent dissipation, this mechanical network was also implemented in time-domain formulations with the label complex stiffness where the force output, P(t) is related in the time-domain to the displacement input, u(t), with P(t) = k(1 + i η)u(t). This paper shows that the complex stiffness, as expressed in the time-domain by various scholars, is a fundamentally flawed construct since in addition to causality it violates equilibrium.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4062263","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Evidence from cyclic tests on metals, elastomers and sandy soils reveals that damping forces are nearly rate-independent and structural (hysteretic or rate-independent) damping was widely adopted since the 1940s. While there is no time-domain constitutive equation for a linear spring connected in parallel with a rate-independent dashpot, the dynamic stiffness (transfer function) of this mechanical network can be constructed in the frequency-domain; and it was known since the early 1960s that this mechanical network exhibits a non-causal response. In view of its simplicity in association with the wide practical need to model rate-independent dissipation, this mechanical network was also implemented in time-domain formulations with the label complex stiffness where the force output, P(t) is related in the time-domain to the displacement input, u(t), with P(t) = k(1 + i η)u(t). This paper shows that the complex stiffness, as expressed in the time-domain by various scholars, is a fundamentally flawed construct since in addition to causality it violates equilibrium.
期刊介绍:
All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation