Book contents
- Frontmatter
- PREFACE
- Contents
- ART. 142 On the Maintenance of Vibrations by Forces of Double Frequency, and on the Propagation of Waves through a Medium endowed with a Periodic Structure
- ART. 143 On the Existence of Reflection when the Relative Refractive Index is Unity
- ART. 144 On the Stability or Instability of Certain Fluid Motions, II
- ART. 145 Diffraction of Sound
- ART. 146 On the Relative Densities of Hydrogen and Oxygen. (Preliminary Notice)
- ART. 147 On Point-, Line-, and Plane-Sources of Sound
- ART. 148 Wave Theory of Light
- ART. 149 On the Reflection of Light at a Twin Plane of a Crystal
- ART. 150 On the Remarkable Phenomenon of Crystalline Reflexion described by Prof. Stokes
- ART. 151 Is the Velocity of Light in an Electrolytic Liquid influenced by an Electric Current in the Direction of Propagation?
- ART. 152 On the Bending and Vibration of Thin Elastic Shells, especially of Cylindrical Form
- ART. 153 On the Composition of Water
- ART. 154 The History of the Doctrine of Radiant Energy
- ART. 155 Note on the Free Vibrations of an Infinitely Long Cylindrical Shell
- ART. 156 On the Free Vibrations of an Infinite Plate of Homogeneous Isotropic Elastic Matter
- ART. 157 On the Limit to Interference when Light is Radiated from Moving Molecules
- ART. 158 Iridescent Crystals
- ART. 159 The Sailing Flight of the Albatross
- ART. 160 On the Character of the Complete Radiation at a Given Temperature
- ART. 161 On the Visibility of Faint Interference-Bands
- ART. 162 On the Uniform Deformation in Two Dimensions of a Cylindrical Shell of Finite Thickness, with Application to the General Theory of Deformation of Thin Shells
- ART. 163 On Achromatic Interference-Bands
- ART. 164 On Bells
- ART. 165 The Clark Standard Cell
- ART. 166 On the Vibrations of an Atmosphere
- ART. 167 On the Tension of Recently Formed Liquid Surfaces
- ART. 168 Measurements of the Amount of Oil Necessary in Order to Check the Motions of Camphor upon Water
- ART. 169 Foam
- ART. 170 On the Superficial Viscosity of Water
- ART. 171 On Huygens's Gearing in Illustration of the Induction of Electric Currents
- ART. 172 The Bourdon Gauge
- ART. 173 On Defective Colour Vision
- ART. 174 Instantaneous Photographs of Water Jets
- ART. 175 On the Tension of Water Surfaces, Clean and Contaminated, Investigated by the Method of Ripples
- ART. 176 On the Theory of Surface Forces
- ART. 177 Clerk-Maxwell's Papers
- ART. 178 On Pin-Hole Photography
- ART. 179 Some Applications of Photography
- ART. 180 On the Sensitiveness of the Bridge Method in its Application to Periodic Electric Currents
- ART. 181 On Van der Waals' Treatment of Laplace's Pressure in the Virial Equation: Letters to Prof. Tait
- ART. 182 On the Virial of a System of Hard Colliding Bodies
- ART. 183 Dynamical Problems Illustration of the Theory of Gases
- ART. 184 Experiments in Aërodynamics. [Review of Langley's]
- ART. 185 On Reflexion from Liquid Surfaces in the Neighbourhood of the Polarizing Angle
- ART. 186 On the Theory of Surface Forces. II. Compressible Fluids
- ART. 187 On the Relative Densities of Hydrogen and Oxygen. II
- ART. 188 Superheated Steam
- ART. 189 Aberration
- ART. 190 Remarks on Maxwell's Investigation respecting Boltzmann's Theorem
- ART. 191 On the Physics of Media that are composed of Free and Perfectly Elastic Molecules in a State of Motion. [Introduction to Waterston's Memoir]
- ART. 192 Experiments upon Surface-Films
- ART. 193 On the Theory of Surface Forces. III.—Effect of Slight Contaminations
- ART. 194 On the Question of the Stability of the Flow of Fluids
- ART. 195 On the Instability of a Cylinder of Viscous Liquid under Capillary Force
- ART. 196 On the Instability of Cylindrical Fluid Surfaces
- Plate section
ART. 155 - Note on the Free Vibrations of an Infinitely Long Cylindrical Shell
Published online by Cambridge University Press: 05 July 2011
Book contents
- Frontmatter
- PREFACE
- Contents
- ART. 142 On the Maintenance of Vibrations by Forces of Double Frequency, and on the Propagation of Waves through a Medium endowed with a Periodic Structure
- ART. 143 On the Existence of Reflection when the Relative Refractive Index is Unity
- ART. 144 On the Stability or Instability of Certain Fluid Motions, II
- ART. 145 Diffraction of Sound
- ART. 146 On the Relative Densities of Hydrogen and Oxygen. (Preliminary Notice)
- ART. 147 On Point-, Line-, and Plane-Sources of Sound
- ART. 148 Wave Theory of Light
- ART. 149 On the Reflection of Light at a Twin Plane of a Crystal
- ART. 150 On the Remarkable Phenomenon of Crystalline Reflexion described by Prof. Stokes
- ART. 151 Is the Velocity of Light in an Electrolytic Liquid influenced by an Electric Current in the Direction of Propagation?
- ART. 152 On the Bending and Vibration of Thin Elastic Shells, especially of Cylindrical Form
- ART. 153 On the Composition of Water
- ART. 154 The History of the Doctrine of Radiant Energy
- ART. 155 Note on the Free Vibrations of an Infinitely Long Cylindrical Shell
- ART. 156 On the Free Vibrations of an Infinite Plate of Homogeneous Isotropic Elastic Matter
- ART. 157 On the Limit to Interference when Light is Radiated from Moving Molecules
- ART. 158 Iridescent Crystals
- ART. 159 The Sailing Flight of the Albatross
- ART. 160 On the Character of the Complete Radiation at a Given Temperature
- ART. 161 On the Visibility of Faint Interference-Bands
- ART. 162 On the Uniform Deformation in Two Dimensions of a Cylindrical Shell of Finite Thickness, with Application to the General Theory of Deformation of Thin Shells
- ART. 163 On Achromatic Interference-Bands
- ART. 164 On Bells
- ART. 165 The Clark Standard Cell
- ART. 166 On the Vibrations of an Atmosphere
- ART. 167 On the Tension of Recently Formed Liquid Surfaces
- ART. 168 Measurements of the Amount of Oil Necessary in Order to Check the Motions of Camphor upon Water
- ART. 169 Foam
- ART. 170 On the Superficial Viscosity of Water
- ART. 171 On Huygens's Gearing in Illustration of the Induction of Electric Currents
- ART. 172 The Bourdon Gauge
- ART. 173 On Defective Colour Vision
- ART. 174 Instantaneous Photographs of Water Jets
- ART. 175 On the Tension of Water Surfaces, Clean and Contaminated, Investigated by the Method of Ripples
- ART. 176 On the Theory of Surface Forces
- ART. 177 Clerk-Maxwell's Papers
- ART. 178 On Pin-Hole Photography
- ART. 179 Some Applications of Photography
- ART. 180 On the Sensitiveness of the Bridge Method in its Application to Periodic Electric Currents
- ART. 181 On Van der Waals' Treatment of Laplace's Pressure in the Virial Equation: Letters to Prof. Tait
- ART. 182 On the Virial of a System of Hard Colliding Bodies
- ART. 183 Dynamical Problems Illustration of the Theory of Gases
- ART. 184 Experiments in Aërodynamics. [Review of Langley's]
- ART. 185 On Reflexion from Liquid Surfaces in the Neighbourhood of the Polarizing Angle
- ART. 186 On the Theory of Surface Forces. II. Compressible Fluids
- ART. 187 On the Relative Densities of Hydrogen and Oxygen. II
- ART. 188 Superheated Steam
- ART. 189 Aberration
- ART. 190 Remarks on Maxwell's Investigation respecting Boltzmann's Theorem
- ART. 191 On the Physics of Media that are composed of Free and Perfectly Elastic Molecules in a State of Motion. [Introduction to Waterston's Memoir]
- ART. 192 Experiments upon Surface-Films
- ART. 193 On the Theory of Surface Forces. III.—Effect of Slight Contaminations
- ART. 194 On the Question of the Stability of the Flow of Fluids
- ART. 195 On the Instability of a Cylinder of Viscous Liquid under Capillary Force
- ART. 196 On the Instability of Cylindrical Fluid Surfaces
- Plate section
Summary
In a recent memoir Mr Love has considered this question among others; but he has not discussed his result {equation (95)}, except in its application to a rather special case involving the existence of a free edge. When the cylinder is regarded as infinitely long, the problem is naturally of a simpler character; and I have thought that it might be worth while to express more fully the frequency equation, as applicable to all vibrations, independent of the thickness of the shell, which are periodic with respect both to the length and the circumference of the cylinder.
In order to prevent misunderstanding, it may be well to premise that the vibrations, whose frequency is to be determined, do not include the gravest of which a thin shell is capable. If the middle surface be simply bent, the potential energy of deformation is of a higher order of magnitude than in the contrary case, and according to the present method of treatment the frequency of vibration will appear to be zero. It is known, however, that the only possible modes of bending of a cylindrical shell are such as are not periodic along the length, or rather have the wave-length in this direction infinitely long. When the middle surface is stretched, as well as bent, the potential energy of bending may be neglected, except in certain very special cases.
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- Scientific Papers , pp. 244 - 248Publisher: Cambridge University PressPrint publication year: 2009First published in: 1902