A polycrystal plasticity finite–element model has been developed for nickel–base alloy C263. That is, a representative region of the material, containing about 60 grains, has been modelled using crystal plasticity, taking account of grain morphology and crystallographic orientation. With just a single material property (in addition to standard elastic properties), namely, the critical resolved shear stress, the model is shown to be capable of predicting correctly a wide range of cyclic plasticity behaviour in face–centred cubic nickel alloy C263. A fatigue crack initiation criterion is proposed, based simply on a critical accumulated slip. When this critical slip is achieved within the microstructure, crack initiation is taken to have occurred. The model predicts the development of persistent slip bands within individual grains with a width of ca. 10 μm. The model also predicts that crack initiation can occur preferentially at grain triple points under both low– (LCF) and high–cycle fatigue (HCF). For the case of HCF, this also corresponds to a free surface. The polycrystal plasticity model combined with the fatigue crack initiation criterion are shown to predict correctly the standard Basquin and Goodman correlations in HCF, and the Coffin–Manson correlation in LCF. The model predictions are based on just two material properties: the critical resolved shear stress and the critical accumulated slip. Just one experimental test is required to determine these properties, for a given temperature, which have been obtained for nickel alloy C263. Predictions of life for nickel alloy C263 are then made over a broad range of loading conditions covering both LCF and HCF. Good agreement with experiments is achieved, despite the simplicity of the proposed ‘two–parameter’ model. A simple three–dimensional form of the model has provided an estimate of the fatigue limit for HCF crack initiation in C263.
{"title":"High– and low–cycle fatigue crack initiation using polycrystal plasticity","authors":"A. Manonukul, F. Dunne","doi":"10.1098/rspa.2003.1258","DOIUrl":"https://doi.org/10.1098/rspa.2003.1258","url":null,"abstract":"A polycrystal plasticity finite–element model has been developed for nickel–base alloy C263. That is, a representative region of the material, containing about 60 grains, has been modelled using crystal plasticity, taking account of grain morphology and crystallographic orientation. With just a single material property (in addition to standard elastic properties), namely, the critical resolved shear stress, the model is shown to be capable of predicting correctly a wide range of cyclic plasticity behaviour in face–centred cubic nickel alloy C263. A fatigue crack initiation criterion is proposed, based simply on a critical accumulated slip. When this critical slip is achieved within the microstructure, crack initiation is taken to have occurred. The model predicts the development of persistent slip bands within individual grains with a width of ca. 10 μm. The model also predicts that crack initiation can occur preferentially at grain triple points under both low– (LCF) and high–cycle fatigue (HCF). For the case of HCF, this also corresponds to a free surface. The polycrystal plasticity model combined with the fatigue crack initiation criterion are shown to predict correctly the standard Basquin and Goodman correlations in HCF, and the Coffin–Manson correlation in LCF. The model predictions are based on just two material properties: the critical resolved shear stress and the critical accumulated slip. Just one experimental test is required to determine these properties, for a given temperature, which have been obtained for nickel alloy C263. Predictions of life for nickel alloy C263 are then made over a broad range of loading conditions covering both LCF and HCF. Good agreement with experiments is achieved, despite the simplicity of the proposed ‘two–parameter’ model. A simple three–dimensional form of the model has provided an estimate of the fatigue limit for HCF crack initiation in C263.","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":"91346452","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 paper reports a significant step forward in holographic velocimetry, which provides simultaneous displacement measurements in fluid and solid mechanics. Known as object conjugate reconstruction (OCR), this new approach unifies the disciplines of holographic velocimetry and holographic interferometry and provides a single measurement technique for the study of surface–flow interactions throughout a volume. Using complex–correlation processing, it enables sub–wavelength displacement resolution for all three components of a velocity field and a dynamic range exceeding 100:1. Prior to OCR, and the use of complex-correlation processing, measurement of surface-flow interactions required multiple techniques applied in a hybrid fashion, which had precluded widespread use.
{"title":"Holographic velocimetry with object conjugate reconstruction (OCR): simultaneous velocity mapping in fluid and solid mechanics","authors":"D. Barnhart, N. Halliwell, J. Coupland","doi":"10.1098/rspa.2003.1265","DOIUrl":"https://doi.org/10.1098/rspa.2003.1265","url":null,"abstract":"This paper reports a significant step forward in holographic velocimetry, which provides simultaneous displacement measurements in fluid and solid mechanics. Known as object conjugate reconstruction (OCR), this new approach unifies the disciplines of holographic velocimetry and holographic interferometry and provides a single measurement technique for the study of surface–flow interactions throughout a volume. Using complex–correlation processing, it enables sub–wavelength displacement resolution for all three components of a velocity field and a dynamic range exceeding 100:1. Prior to OCR, and the use of complex-correlation processing, measurement of surface-flow interactions required multiple techniques applied in a hybrid fashion, which had precluded widespread use.","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":"91372698","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 governing equations for the deformation and the fluid flow in a poroelastic medium are derived under (i) a moderately small ratio of external load to elastic stiffness which is of O(ε), where ε = l/l′ is the ratio of the microscale to the macroscale lengths, and (ii) a moderately small pore- (or grain-) size-based Reynolds number which is of O(ε1/2), by employing the theory of homogenization. The macroscale governing equations are nonlinear in general and several canonical boundary–value problems are defined in a unit cell with a periodic structure on the microscale. However, to determine the effects of inertia and deformation on the macroscale seepage flow, only a few cell problems need to be solved. The correction to Darcy's law in deformable media is shown to be cubic in the seepage velocity as in the case of a rigid medium but with modified permeability and inertial effect due to deformation. It is also shown that Darcy's law is stated with permeability which is dependent on the state of elastic strain of the medium throughout the consolidation process. While the changes due to fluid inertia and medium deformation are small but as important as the inertial effects in rigid media, the porosity and permeability changes for a medium isotropic on the macroscale are shown to be linearly proportional to the volume strain of the medium, and also modify the inertial effect in Darcy's law accordingly, as compared with the case for a rigid medium.
{"title":"Flow and deformation in poroelastic media with moderate load and weak inertia","authors":"C. Lee","doi":"10.1098/rspa.2003.1250","DOIUrl":"https://doi.org/10.1098/rspa.2003.1250","url":null,"abstract":"The governing equations for the deformation and the fluid flow in a poroelastic medium are derived under (i) a moderately small ratio of external load to elastic stiffness which is of O(ε), where ε = l/l′ is the ratio of the microscale to the macroscale lengths, and (ii) a moderately small pore- (or grain-) size-based Reynolds number which is of O(ε1/2), by employing the theory of homogenization. The macroscale governing equations are nonlinear in general and several canonical boundary–value problems are defined in a unit cell with a periodic structure on the microscale. However, to determine the effects of inertia and deformation on the macroscale seepage flow, only a few cell problems need to be solved. The correction to Darcy's law in deformable media is shown to be cubic in the seepage velocity as in the case of a rigid medium but with modified permeability and inertial effect due to deformation. It is also shown that Darcy's law is stated with permeability which is dependent on the state of elastic strain of the medium throughout the consolidation process. While the changes due to fluid inertia and medium deformation are small but as important as the inertial effects in rigid media, the porosity and permeability changes for a medium isotropic on the macroscale are shown to be linearly proportional to the volume strain of the medium, and also modify the inertial effect in Darcy's law accordingly, as compared with the case for a rigid medium.","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":"81863564","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}
An exact expression for the torsional rigidity of a cylindrical bar with arbitrary transverse cross–section filled with an assemblage of multicoated inclusions is derived. The exact formula depends on the constituent shear rigidities, the area fractions and the size distribution of the multicoated inclusions, but is independent of the assembly microstructure. The analysis is based on a successive construction of neutral multicoated inclusions under Saint–Venant's torsion. We show how to design permissible multicoated inclusions, with phase–shear rigidities and area fractions appropriately balanced, so that after its introduction into a homogeneous host bar the warping field in the host bar will not be disturbed. What makes the neutral inclusion under torsion particularly intriguing is that both the constraint conditions and the torsional rigidity are independent of the location of the neutral inclusion. One can thereby add many neutral inclusions to fill up the cross–section without further derivations. Without solving any field equations, we prove that the torsional rigidity of a given cross–section filled with an assemblage of multicoated inclusion can be exactly determined in a simple, explicit form.
{"title":"An exactly solvable microgeometry in torsion: assemblage of multicoated cylinders","authors":"Tungyang Chen","doi":"10.1098/rspa.2003.1268","DOIUrl":"https://doi.org/10.1098/rspa.2003.1268","url":null,"abstract":"An exact expression for the torsional rigidity of a cylindrical bar with arbitrary transverse cross–section filled with an assemblage of multicoated inclusions is derived. The exact formula depends on the constituent shear rigidities, the area fractions and the size distribution of the multicoated inclusions, but is independent of the assembly microstructure. The analysis is based on a successive construction of neutral multicoated inclusions under Saint–Venant's torsion. We show how to design permissible multicoated inclusions, with phase–shear rigidities and area fractions appropriately balanced, so that after its introduction into a homogeneous host bar the warping field in the host bar will not be disturbed. What makes the neutral inclusion under torsion particularly intriguing is that both the constraint conditions and the torsional rigidity are independent of the location of the neutral inclusion. One can thereby add many neutral inclusions to fill up the cross–section without further derivations. Without solving any field equations, we prove that the torsional rigidity of a given cross–section filled with an assemblage of multicoated inclusion can be exactly determined in a simple, explicit form.","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":"83425171","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}
Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.
{"title":"A study of the characteristics of white noise using the empirical mode decomposition method","authors":"Zhaohua Wu, N. Huang","doi":"10.1098/rspa.2003.1221","DOIUrl":"https://doi.org/10.1098/rspa.2003.1221","url":null,"abstract":"Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.","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":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74607769","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}
It is shown that the cross–sectional area of a non–uniform axially vibrating rod can be reconstructed from one of its mode shapes, and that the solution, up to a scale factor, is unique. The conditions, which allow construction of a physical rod with positive smooth cross–sectional area, are given. The problem is addressed for the discrete and the continuous models of the rod. Examples demonstrate the various results.
{"title":"Reconstructing the cross–sectional area of an axially vibrating non–uniform rod from one of its mode shapes","authors":"Y. Ram, I. Elishakoff","doi":"10.1098/rspa.2003.1214","DOIUrl":"https://doi.org/10.1098/rspa.2003.1214","url":null,"abstract":"It is shown that the cross–sectional area of a non–uniform axially vibrating rod can be reconstructed from one of its mode shapes, and that the solution, up to a scale factor, is unique. The conditions, which allow construction of a physical rod with positive smooth cross–sectional area, are given. The problem is addressed for the discrete and the continuous models of the rod. Examples demonstrate the various results.","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":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77401209","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 free–space Green function for a two–dimensional exponentially graded elastic medium is derived. The shear modulus Âμ is assumed to be an exponential function of the Cartesian coordinates (x,y), i.e. μ ≡ μ(x,y) = μ0e2(β1x+β2y), where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel functions, and a non–singular term. The non–singular component is expressed in terms of one–dimensional Fourier–type integrals that can be computed by the fast Fourier transform.
{"title":"Green's function for a two–dimensional exponentially graded elastic medium","authors":"Youn-Sha Chan, L. Gray, T. Kaplan, G. Paulino","doi":"10.1098/rspa.2003.1220","DOIUrl":"https://doi.org/10.1098/rspa.2003.1220","url":null,"abstract":"The free–space Green function for a two–dimensional exponentially graded elastic medium is derived. The shear modulus Âμ is assumed to be an exponential function of the Cartesian coordinates (x,y), i.e. μ ≡ μ(x,y) = μ0e2(β1x+β2y), where μ0, β1, and β2 are material constants, and the Poisson ratio is assumed constant. The Green function is shown to consist of a singular part, involving modified Bessel functions, and a non–singular term. The non–singular component is expressed in terms of one–dimensional Fourier–type integrals that can be computed by the fast Fourier transform.","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":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80646120","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 describe a simple two–parameter analytic model, based on the embedded–atom–method formalism, that extends a short range Lennard–Jones potential into the many–body regime. We demonstrate that this is a first step toward a minimalist treatment of real materials with negligible angular forces. The ground–state structures in this model include all the common phases. In this framework, properties of a face–centred cubic (FCC) material such as temperature dependence of free energy, melting point, thermal expansion coefficients, Grüneisen parameters, elastic constants and defect properties are calculated as a function of the many–body parameters A and β. These properties are then expressed as analytic functions of A and β, as perturbations of the classical Lennard–Jones pair potential. Addition of the many–body effects to the classical Lennard–Jones pair potential brings the computed material properties to within the range of their experimental values for many FCC metals.
{"title":"On the Lennard–Jones EAM potential","authors":"S. G. Srinivasan, M. Baskes","doi":"10.1098/rspa.2003.1190","DOIUrl":"https://doi.org/10.1098/rspa.2003.1190","url":null,"abstract":"We describe a simple two–parameter analytic model, based on the embedded–atom–method formalism, that extends a short range Lennard–Jones potential into the many–body regime. We demonstrate that this is a first step toward a minimalist treatment of real materials with negligible angular forces. The ground–state structures in this model include all the common phases. In this framework, properties of a face–centred cubic (FCC) material such as temperature dependence of free energy, melting point, thermal expansion coefficients, Grüneisen parameters, elastic constants and defect properties are calculated as a function of the many–body parameters A and β. These properties are then expressed as analytic functions of A and β, as perturbations of the classical Lennard–Jones pair potential. Addition of the many–body effects to the classical Lennard–Jones pair potential brings the computed material properties to within the range of their experimental values for many FCC metals.","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":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74228290","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}
Changes in the wettability characteristics of an alumina bioceramic occasioned by high–power diode–laser (HPDL) surface treatment were apparent from the observed reduction in the contact angle. Such changes were due to the HPDL bringing about reductions in the surface roughness, increases in the surface O2 content and increases in the polar component of the surface energy. Additionally, HPDL treatment of the alumina–bioceramic surface was found to effect an improvement in the bonding characteristics by increasing the work of adhesion. An electronic approach was used to elucidate the bonding characteristics of the alumina bioceramic before and after HPDL treatment. It is postulated that HPDL–induced changes to the alumina bioceramic produced a surface with a reduced band–gap energy, which consequently increased the work of adhesion by increasing the electron transfer at the metal–oxide interface and thus the metal–oxide interactions. Furthermore, it is suggested that the increase in the work of adhesion of the alumina bioceramic after HPDL treatment was due to a correlation existing between the wettability and ionicity of the alumina bioceramic, for it is believed that the HPDL–treated surface is less ionic in nature than the untreated surface and therefore exhibits better wettability characteristics.
{"title":"Wetting and bonding characteristics of selected liquid metals with a high–power diode–laser–treated alumina bioceramic","authors":"J. Lawrence","doi":"10.1098/rspa.2003.1228","DOIUrl":"https://doi.org/10.1098/rspa.2003.1228","url":null,"abstract":"Changes in the wettability characteristics of an alumina bioceramic occasioned by high–power diode–laser (HPDL) surface treatment were apparent from the observed reduction in the contact angle. Such changes were due to the HPDL bringing about reductions in the surface roughness, increases in the surface O2 content and increases in the polar component of the surface energy. Additionally, HPDL treatment of the alumina–bioceramic surface was found to effect an improvement in the bonding characteristics by increasing the work of adhesion. An electronic approach was used to elucidate the bonding characteristics of the alumina bioceramic before and after HPDL treatment. It is postulated that HPDL–induced changes to the alumina bioceramic produced a surface with a reduced band–gap energy, which consequently increased the work of adhesion by increasing the electron transfer at the metal–oxide interface and thus the metal–oxide interactions. Furthermore, it is suggested that the increase in the work of adhesion of the alumina bioceramic after HPDL treatment was due to a correlation existing between the wettability and ionicity of the alumina bioceramic, for it is believed that the HPDL–treated surface is less ionic in nature than the untreated surface and therefore exhibits better wettability characteristics.","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":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87785940","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}
Wave propagation in slowly varying elastic waveguides is analysed in terms of mutually uncoupled quasi–modes. These are a generalization of the Lamb modes that exist in a uniform guide to a weakly non–uniform guide. Quasi–modal propagation is dependent upon the wavelength and two geometrical length–scales, that of the longitudinal variations and the guide thickness. By changing these length–scales one enters different asymptotic regimes. In this paper the emphasis is on the mid–frequency regime, where only a few propagating modes can exist. Our aim is to present an asymptotic theory for quasi–modal propagation in a canonical geometry, an arbitrarily curved two–dimensional plate of constant thickness. We derive practically useful asymptotic expressions of the quasi–modes of a weakly curved plate; these are particularly important since an adiabatic approximation for this problem coincides with the expression for the Lamb modes of a flat plate of the same thickness.
{"title":"Lamb quasi–modes in curved plates","authors":"D. Gridin, R. Craster","doi":"10.1098/rspa.2003.1254","DOIUrl":"https://doi.org/10.1098/rspa.2003.1254","url":null,"abstract":"Wave propagation in slowly varying elastic waveguides is analysed in terms of mutually uncoupled quasi–modes. These are a generalization of the Lamb modes that exist in a uniform guide to a weakly non–uniform guide. Quasi–modal propagation is dependent upon the wavelength and two geometrical length–scales, that of the longitudinal variations and the guide thickness. By changing these length–scales one enters different asymptotic regimes. In this paper the emphasis is on the mid–frequency regime, where only a few propagating modes can exist. Our aim is to present an asymptotic theory for quasi–modal propagation in a canonical geometry, an arbitrarily curved two–dimensional plate of constant thickness. We derive practically useful asymptotic expressions of the quasi–modes of a weakly curved plate; these are particularly important since an adiabatic approximation for this problem coincides with the expression for the Lamb modes of a flat plate of the same thickness.","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":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79554780","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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