We consider a simple reaction–diffusion system that models propagating fronts occurring in autocatalytic reactions of order m≥ 1. We obtain results concerning the evolution of reaction–diffusion wavefronts and accelerating wavefronts, which extend to systems those results which have been previously established for an analogous scalar problem. We provide an alternative approach to studying this system (via comparison theorems) to that given by Malham & Oliver in 2000 (using weighted L2 estimates), which enables a considerable extension of the results therein.
{"title":"Acceleration and reaction–diffusion wavefronts in a simple model for mth-order autocatalysis","authors":"D. Needham","doi":"10.1098/rspa.2003.1252","DOIUrl":"https://doi.org/10.1098/rspa.2003.1252","url":null,"abstract":"We consider a simple reaction–diffusion system that models propagating fronts occurring in autocatalytic reactions of order m≥ 1. We obtain results concerning the evolution of reaction–diffusion wavefronts and accelerating wavefronts, which extend to systems those results which have been previously established for an analogous scalar problem. We provide an alternative approach to studying this system (via comparison theorems) to that given by Malham & Oliver in 2000 (using weighted L2 estimates), which enables a considerable extension of the results therein.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90710734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Triply periodic minimal surfaces are objects of great interest to physical scientists, biologists and mathematicians. It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. More importantly, here we further establish the multifunctionality of such two-phase systems by showing that they are also extremal when a competition is set up between the effective bulk modulus and the electrical (or thermal) conductivity of the composite. The implications of our findings for materials science and biology, which provides the ultimate multifunctional materials, are discussed.
{"title":"Minimal surfaces and multifunctionality","authors":"S. Torquato, A. Donev","doi":"10.1098/rspa.2003.1269","DOIUrl":"https://doi.org/10.1098/rspa.2003.1269","url":null,"abstract":"Triply periodic minimal surfaces are objects of great interest to physical scientists, biologists and mathematicians. It has recently been shown that triply periodic two-phase bicontinuous composites with interfaces that are the Schwartz primitive (P) and diamond (D) minimal surfaces are not only geometrically extremal but extremal for simultaneous transport of heat and electricity. More importantly, here we further establish the multifunctionality of such two-phase systems by showing that they are also extremal when a competition is set up between the effective bulk modulus and the electrical (or thermal) conductivity of the composite. The implications of our findings for materials science and biology, which provides the ultimate multifunctional materials, are discussed.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89544733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. T. Xing, R. Shenoi, Philip A. Wilson, J. T. Xing
Analytical solutions defining flow through porous media subjected to a boundary condition of variable pressure are developed in this paper. The traditional solutions of flow through porous media subjected to a boundary condition of constant pressure are special cases of the generalized solutions given herein. The gravitational effect is also considered and a moving–coordinate system with a flow velocity caused by the gravitation is chosen to investigate the form of the wet domain. Applications of the developed theory to permeability measurement in resin–transfer moulding are described.
{"title":"Fluid flow through porous media subjected to a boundary condition of variable pressure","authors":"J. T. Xing, R. Shenoi, Philip A. Wilson, J. T. Xing","doi":"10.1098/rspa.2003.1122","DOIUrl":"https://doi.org/10.1098/rspa.2003.1122","url":null,"abstract":"Analytical solutions defining flow through porous media subjected to a boundary condition of variable pressure are developed in this paper. The traditional solutions of flow through porous media subjected to a boundary condition of constant pressure are special cases of the generalized solutions given herein. The gravitational effect is also considered and a moving–coordinate system with a flow velocity caused by the gravitation is chosen to investigate the form of the wet domain. Applications of the developed theory to permeability measurement in resin–transfer moulding are described.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81151009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pseudo–rigid bodies are regarded here as globally constrained three–dimensional homogeneous continua. The constraint reaction stresses play a fundamental role in maintaining the homogeneity of the deformation field in pseudo–rigid bodies, and the theory is formulated in a manner that makes this role explicit. Our derivation of Lagrange's equations is patterned after geometrical derivations recently given for particle systems and rigid bodies. The pseudo–rigid body is represented by an abstract particle P moving in a higher–dimensional Euclidean space, called Hertzian space, the metric of which is determined by the radius of gyration of the body. The dynamical equations for the pseudo–rigid body are transformed into a single balance equation in Hertzian space. In the presence of holonomic constraints, the particle P is confined to move in a manifold, the configuration manifold, imbedded in Hertzian space. The geometry of the configuration manifold is Riemannian. Lagrange's equations emerge as the covariant components of the balance equation taken along the coordinate directions in the configuration manifold. Non–holonomic constraints are also considered.
{"title":"Pseudo-rigid continua: basic theory and a geometrical derivation of Lagrange's equations","authors":"J. Casey","doi":"10.1098/rspa.2003.1274","DOIUrl":"https://doi.org/10.1098/rspa.2003.1274","url":null,"abstract":"Pseudo–rigid bodies are regarded here as globally constrained three–dimensional homogeneous continua. The constraint reaction stresses play a fundamental role in maintaining the homogeneity of the deformation field in pseudo–rigid bodies, and the theory is formulated in a manner that makes this role explicit. Our derivation of Lagrange's equations is patterned after geometrical derivations recently given for particle systems and rigid bodies. The pseudo–rigid body is represented by an abstract particle P moving in a higher–dimensional Euclidean space, called Hertzian space, the metric of which is determined by the radius of gyration of the body. The dynamical equations for the pseudo–rigid body are transformed into a single balance equation in Hertzian space. In the presence of holonomic constraints, the particle P is confined to move in a manifold, the configuration manifold, imbedded in Hertzian space. The geometry of the configuration manifold is Riemannian. Lagrange's equations emerge as the covariant components of the balance equation taken along the coordinate directions in the configuration manifold. Non–holonomic constraints are also considered.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74789589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.
{"title":"A continuum anisotropic model of sea-ice dynamics","authors":"A. Wilchinsky, D. Feltham","doi":"10.1098/rspa.2004.1282","DOIUrl":"https://doi.org/10.1098/rspa.2004.1282","url":null,"abstract":"We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85257328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In recent years, relativism has been the object of yet another campaign of criticism, this time from scientists who consider it antithetical to the practice of science. In this context, the 2002 publication by Beven of an article in which (between the lines) he advocates a kind of relativism associated with environmental modelling is particularly noteworthy. In the present commentary, it is argued that cognitive relativism is unavoidable in environmental sciences and that it has been recognized as such for over two decades by a number of researchers in the field. It is also pointed out, however, that the kind of relativism alluded to by Beven expands the scope of the debate significantly, and has serious implications for the practice of environmental policy making.
{"title":"The emergence of a new kind of relativism in environmental modelling: a commentary","authors":"P. Baveye","doi":"10.1098/rspa.2003.1256","DOIUrl":"https://doi.org/10.1098/rspa.2003.1256","url":null,"abstract":"In recent years, relativism has been the object of yet another campaign of criticism, this time from scientists who consider it antithetical to the practice of science. In this context, the 2002 publication by Beven of an article in which (between the lines) he advocates a kind of relativism associated with environmental modelling is particularly noteworthy. In the present commentary, it is argued that cognitive relativism is unavoidable in environmental sciences and that it has been recognized as such for over two decades by a number of researchers in the field. It is also pointed out, however, that the kind of relativism alluded to by Beven expands the scope of the debate significantly, and has serious implications for the practice of environmental policy making.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90604486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deformation studies at grain level have been performed in order to model how individual crystals in a polycrystalline material deform. The experiment was carried out by plane–strain compression of a high–purity polycrystalline aluminium with columnar grain structure with near ⟨100⟩ fibre texture parallel to the constrained direction in the channel die. This structure was chosen to allow a fully three–dimensional characterization of the grain structure. The grain orientations were mapped by orientation image microscopy, as the directionally solidified material was deformed in steps of 10% to a total height reduction of 40%. The grains were found either to show nearly uniform rotations or to split into two types of deformation bands, either with repeating orientation fields or with non–repeating orientation fields. The Taylor model and the finite–element method (FEM) were, as usual, quite successful in predicting the average deformation texture, but the Taylor model failed totally to predict the rotation of individual grains. The FEM was more successful in predicting the individual grain rotations but did not, as in a previous study, predict the morphology of the deformation bands. The significant discovery, made here, was that it appeared possible to model the local deformation at a grain scale, from the observed individual deviations of the grain rotations from those predicted if each grain underwent just the plane–strain conditions imposed on the sample. Plastic work rates were computed allowing four shears (two shears in each of the two contact planes) that are compatible with the channel–die geometry. It was found that in all the ‘hard’ grains (those with high Taylor factors), the additional shears (in type and magnitude) that minimized the plastic energy dissipation rate were the same shears that were needed to match the observed grain rotations. Adjacent Taylor ‘soft’ grains were found to have been subjected to the additional shears imposed by their neighbouring hard grains. This was true even when these shears raised the plastic work of the soft grains. This effect was most marked when the soft grains were small in size. These additional shears found by this plastic work analysis were consistent with the observed additional shear seen in the overall shape change of the sample. The grains forming non–repeating orientation fields had low initial Taylor factors and were surrounded by high–Taylor–factor grains, usually of larger size, but which had adopted somewhat different extra shears. The grains showing repeating orientation fields were found to have an orientation, near ‘cube’, (001) ⟨100⟩, which was initially unstable, leading to a break–up into different orientation fields when deformed. These differing deformation bands in the cube grains followed different strain paths, which also minimized their plastic work.
{"title":"Detailed analyses of grain–scale plastic deformation in columnar polycrystalline aluminium using orientation image mapping and crystal plasticity models","authors":"S. Kalidindi, A. Bhattacharyya, R. Doherty","doi":"10.1098/rspa.2003.1260","DOIUrl":"https://doi.org/10.1098/rspa.2003.1260","url":null,"abstract":"Deformation studies at grain level have been performed in order to model how individual crystals in a polycrystalline material deform. The experiment was carried out by plane–strain compression of a high–purity polycrystalline aluminium with columnar grain structure with near ⟨100⟩ fibre texture parallel to the constrained direction in the channel die. This structure was chosen to allow a fully three–dimensional characterization of the grain structure. The grain orientations were mapped by orientation image microscopy, as the directionally solidified material was deformed in steps of 10% to a total height reduction of 40%. The grains were found either to show nearly uniform rotations or to split into two types of deformation bands, either with repeating orientation fields or with non–repeating orientation fields. The Taylor model and the finite–element method (FEM) were, as usual, quite successful in predicting the average deformation texture, but the Taylor model failed totally to predict the rotation of individual grains. The FEM was more successful in predicting the individual grain rotations but did not, as in a previous study, predict the morphology of the deformation bands. The significant discovery, made here, was that it appeared possible to model the local deformation at a grain scale, from the observed individual deviations of the grain rotations from those predicted if each grain underwent just the plane–strain conditions imposed on the sample. Plastic work rates were computed allowing four shears (two shears in each of the two contact planes) that are compatible with the channel–die geometry. It was found that in all the ‘hard’ grains (those with high Taylor factors), the additional shears (in type and magnitude) that minimized the plastic energy dissipation rate were the same shears that were needed to match the observed grain rotations. Adjacent Taylor ‘soft’ grains were found to have been subjected to the additional shears imposed by their neighbouring hard grains. This was true even when these shears raised the plastic work of the soft grains. This effect was most marked when the soft grains were small in size. These additional shears found by this plastic work analysis were consistent with the observed additional shear seen in the overall shape change of the sample. The grains forming non–repeating orientation fields had low initial Taylor factors and were surrounded by high–Taylor–factor grains, usually of larger size, but which had adopted somewhat different extra shears. The grains showing repeating orientation fields were found to have an orientation, near ‘cube’, (001) ⟨100⟩, which was initially unstable, leading to a break–up into different orientation fields when deformed. These differing deformation bands in the cube grains followed different strain paths, which also minimized their plastic work.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73074322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reliable life–prediction models for the durability of thermal barrier coatings require the identification of the relative importance of various mechanisms responsible for the failure of the coatings at high temperatures. Studies of these mechanisms in subsystems of thermal barrier coatings can provide valuable information. In the present work, we undertake an experimental study of ‘rumpling’, or progressive roughening of the bond–coat (BC) surface in the bond coat–superalloy systems upon high–temperature exposure. Thermal cycling and isothermal experiments are carried out on a platinum aluminide BC, a nickel aluminide BC, and an NiCoCrAlY BC deposited on an Ni–based superalloy in air and in vacuum. Cyclic experiments are conducted in air for different levels of initial roughness of the BC surface. Upon thermal cycling in air, the BC surfaces with a wide range of initial roughness rumple to comparable characteristic wavelengths and amplitudes, indicating the insensitivity of the rumpling phenomenon to the initial surface fluctuations. Observations of the rumpled BC surfaces show that the stresses in the BC provide driving force for the rumpling process. On comparing the experimental observations with existing rumpling models in the literature, it is concluded that the thermally grown aluminium oxide and the microstructural changes in the BC have a limited role in inducing rumpling. Plausibility of several possible deformation mechanisms is discussed. It is shown that several of the rumpling observations in the current work can be explained by a BC stress–driven surface–diffusion model from the literature.
{"title":"Experimental investigation of the bond-coat rumpling instability under isothermal and cyclic thermal histories in thermal barrier systems","authors":"R. Panat, K. Hsia","doi":"10.1098/rspa.2003.1262","DOIUrl":"https://doi.org/10.1098/rspa.2003.1262","url":null,"abstract":"Reliable life–prediction models for the durability of thermal barrier coatings require the identification of the relative importance of various mechanisms responsible for the failure of the coatings at high temperatures. Studies of these mechanisms in subsystems of thermal barrier coatings can provide valuable information. In the present work, we undertake an experimental study of ‘rumpling’, or progressive roughening of the bond–coat (BC) surface in the bond coat–superalloy systems upon high–temperature exposure. Thermal cycling and isothermal experiments are carried out on a platinum aluminide BC, a nickel aluminide BC, and an NiCoCrAlY BC deposited on an Ni–based superalloy in air and in vacuum. Cyclic experiments are conducted in air for different levels of initial roughness of the BC surface. Upon thermal cycling in air, the BC surfaces with a wide range of initial roughness rumple to comparable characteristic wavelengths and amplitudes, indicating the insensitivity of the rumpling phenomenon to the initial surface fluctuations. Observations of the rumpled BC surfaces show that the stresses in the BC provide driving force for the rumpling process. On comparing the experimental observations with existing rumpling models in the literature, it is concluded that the thermally grown aluminium oxide and the microstructural changes in the BC have a limited role in inducing rumpling. Plausibility of several possible deformation mechanisms is discussed. It is shown that several of the rumpling observations in the current work can be explained by a BC stress–driven surface–diffusion model from the literature.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85509526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is a response to a comment by Baveye in which he invites me to expand on the use of the word relativism in the context of environmental models. Limitations to a classical statistical approach to model (as realist hypothesis) falsification are discussed. It is concluded that environmental modelling must necessarily be operator dependent and relativist, even while being conducted in a context of pragmatic realism.
{"title":"Reply to ‘The emergence of a new kind of relativism in environmental modelling: a commentary’ by Philippe Baveye","authors":"K. Beven","doi":"10.1098/rspa.2003.1257","DOIUrl":"https://doi.org/10.1098/rspa.2003.1257","url":null,"abstract":"This article is a response to a comment by Baveye in which he invites me to expand on the use of the word relativism in the context of environmental models. Limitations to a classical statistical approach to model (as realist hypothesis) falsification are discussed. It is concluded that environmental modelling must necessarily be operator dependent and relativist, even while being conducted in a context of pragmatic realism.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73499965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dynamics of a resonantly excited thin cantilever with an active controller are investigated experimentally. The controller mimics a passive wideband absorber discussed in the accompanying theory paper. Lead-zirconate-titanate patches are bonded to both sides of the beam to actuate it, while an electromagnetic shaker drives the beam near resonance. An active controller consisting of an array of coupled controllers is developed, such that the governing equations for the controller are quadratically coupled to the resonating system. The control signal, in terms of the motion of the controllers, is quadratically nonlinear. It is shown that the slow time-scale equations of this physical system are identical in form to those for the passive wideband vibration absorber. The controller is implemented using modelling software and a controller hardware board. Two sets of experiments are performed: one with a constant excitation frequency and the other with a linearly varying excitation frequency at a slow sweep rate (non-stationary excitation). The experimental results verify the analysis presented for the passive wideband autoparametric vibration absorber. The experiments also demonstrate the effectiveness of the absorber in reducing the response amplitude of structures, and its robustness to frequency mistuning.
{"title":"Dynamics of structures with wideband autoparametric vibration absorbers: experiment","authors":"A. Vyas, A. Bajaj, A. Raman","doi":"10.1098/rspa.2003.1205","DOIUrl":"https://doi.org/10.1098/rspa.2003.1205","url":null,"abstract":"The dynamics of a resonantly excited thin cantilever with an active controller are investigated experimentally. The controller mimics a passive wideband absorber discussed in the accompanying theory paper. Lead-zirconate-titanate patches are bonded to both sides of the beam to actuate it, while an electromagnetic shaker drives the beam near resonance. An active controller consisting of an array of coupled controllers is developed, such that the governing equations for the controller are quadratically coupled to the resonating system. The control signal, in terms of the motion of the controllers, is quadratically nonlinear. It is shown that the slow time-scale equations of this physical system are identical in form to those for the passive wideband vibration absorber. The controller is implemented using modelling software and a controller hardware board. Two sets of experiments are performed: one with a constant excitation frequency and the other with a linearly varying excitation frequency at a slow sweep rate (non-stationary excitation). The experimental results verify the analysis presented for the passive wideband autoparametric vibration absorber. The experiments also demonstrate the effectiveness of the absorber in reducing the response amplitude of structures, and its robustness to frequency mistuning.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78615599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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