Helical Buckling of Slender Beam Structures Surrounded by an Elastic Medium

ABSTRACTThe goal of this study was to investigate analytically the buckling phenomena of slender beam structures embedded in an elastic medium. In such cases, there is a possibility that spiral-shaped buckling modes can occur due to the restraining effect of the surrounding medium. As a result of analytical investigations, helical buckling occurs radically. Furthermore the pitch of the helix does not fluctuate as the radius of the helix increases. The interesting mechanical implications of the embedding effect are demonstrated by the theoretical approach established in this study.

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Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

Applied Mathematics and Mechanics ◽

10.1007/s10483-021-2743-6 ◽

2021 ◽

Author(s):

Tuoya Sun ◽

Junhong Guo ◽

E. Pan

Keyword(s):

Elastic Medium ◽

Vibration Frequency ◽

Surrounding Medium ◽

Nonlocal Parameter ◽

Buckling Load ◽

Width Ratio ◽

Two Dimensional ◽

Coating Materials ◽

Decagonal Quasicrystal ◽

Critical Buckling Load

AbstractA mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

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Vibration Analysis of a Circular Tunnel With Jointed Liners Embedded in an Elastic Medium Subjected to Seismic Waves

Journal of Vibration and Acoustics ◽

10.1115/1.2827362 ◽

2009 ◽

Vol 131 (2) ◽

Cited By ~ 1

Author(s):

Dong-Sheng Jeng ◽

Jian-Fei Lu

Keyword(s):

Elastic Medium ◽

Seismic Waves ◽

Differential Quadrature Method ◽

Surrounding Medium ◽

Beam Theory ◽

Scattered Wave ◽

Collocation Methods ◽

Curved Beam ◽

Curved Beams ◽

Circular Tunnel

This paper presents a frequency domain analysis of a circular tunnel with piecewise liners subjected to seismic waves. In our model, the surrounding medium of the tunnel is considered as a linear elastic medium and described by the dynamic elasticity theory, while piecewise liners and connecting joints are treated as curved beams and described by a curved beam theory. Scattered wave field in the surrounding elastic medium are obtained by the wave function expansion approach. The governing equations for vibrations of a curved beam are discretized by the general differential quadrature method. We use domain decomposition methods to establish the global discrete dynamic equations for piecewise liners. Boundary least squares collocation methods, based on the continuity conditions of stresses and displacements between surrounding soil and the piecewise liners, are used to determine the response of the liners and the surrounding medium. Numerical results conclude that the presence of the joints significantly changes the distributions of the tunnel internal force, and dramatically increase shear forces and moment of the tunnel liners around joints.

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Transient Response of a Circular Cylinder of Arbitrary Thickness, in an Elastic Medium, to a Plane Dilatational Wave

Journal of Applied Mechanics ◽

10.1115/1.3625117 ◽

1966 ◽

Vol 33 (3) ◽

pp. 521-531 ◽

Cited By ~ 16

Author(s):

Hyman Garnet ◽

Jacques Crouzet-Pascal

Keyword(s):

Elastic Medium ◽

Incident Wave ◽

Surrounding Medium ◽

Time History ◽

Theory Of Elasticity ◽

Published Data ◽

Arbitrary Thickness ◽

Unstrained State ◽

History Of ◽

State Of Rest

The response of a hollow cylinder of arbitrary thickness, embedded in an elastic medium, to a transient plane pressure wave is presented. The solution is valid within the scope of the linear theory of elasticity. The technique for obtaining the solutions relies upon (a) the construction of a train of incident pulses from steady-state components, where each pulse represents the time history of the transient stress in the incident wave, and (b) the existence of a physical mechanism which, between pulses, restores the disturbed particles of the cylinder and the surrounding medium to an unstrained state of rest. The validity of the technique is demonstrated by (a) comparisons with published data for limiting cases and (b) results obtained for a broad range of values of cylinder and surrounding medium parameters. The influence on the cylinder response of liner thickness and cylinder-medium impedance mismatch, when the incident wave is a step pulse, is investigated.

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Power Law of Critical Buckling in Structural Members Supported by a Winkler Foundation

Journal of Mechanics ◽

10.1017/jmech.2016.112 ◽

2016 ◽

Vol 33 (3) ◽

pp. 369-374

Author(s):

M. Sato ◽

S. Harasawa ◽

Y. Konishi ◽

T. Maruyama ◽

S. J. Park

Keyword(s):

Elastic Medium ◽

Power Law ◽

Axial Loading ◽

Elastic Buckling ◽

Winkler Foundation ◽

Structural Members ◽

Spherical Shells ◽

Buckling Modes ◽

Plates And Shells ◽

Critical Buckling Strain

AbstractIn the fields of engineering, nanoscience, and biomechanics, thin structural members, such as beams, plates, and shells, that are supported by an elastic medium are used in several applications. There is a possibility that these thin structures might buckle under severe loading conditions; higher-order, complicated elastic buckling modes can be found owing to the balance of rigidities between the thin members and elastic supports. In this study, we have shown a new and simple ‘power law’ relation between the critical buckling strain (or loads) and rigidity parameters in structural members supported by an elastic medium, which can be modelled as a Winkler foundation. The following structural members have been considered in this paper: i) a slender beam held by an outer elastic support under axial loading, ii) cylindrical shells supported by an inner elastic core under hydrostatic pressure (plane strain condition), and iii) complete spherical shells that are filled with an inner elastic medium.

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Blast Loading of a Spherical Container Surrounded by an Infinite Elastic Medium

Journal of Applied Mechanics ◽

10.1115/1.3167136 ◽

1983 ◽

Vol 50 (4a) ◽

pp. 723-726 ◽

Cited By ~ 13

Author(s):

L. A. Glenn ◽

R. E. Kidder

Keyword(s):

Finite Difference ◽

Elastic Medium ◽

Surrounding Medium ◽

Elastic Shell ◽

Impulsive Loading ◽

Closed Form Solutions ◽

Interfacial Separation ◽

Infinite Extent ◽

Spherical Elastic Shell ◽

Spherical Container

Closed-form solutions are derived for the response of a spherical elastic shell, surrounded by a different elastic medium of infinite extent, and subjected to Heaviside or impulsive loading. The results are compared with earlier solutions in which the surrounding medium was a fluid. The importance of interfacial separation is also investigated by comparing the impulsive loading results with finite difference calculations in which it was possible for the shell to decouple from the surroundings when radial tensile stresses occurred at the shared boundary.

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The Fine Structure of Rat Granulosa Cell Cultures Correlated with Progestin Secretion

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100073209 ◽

1973 ◽

Vol 31 ◽

pp. 552-553

Author(s):

T. M. Crisp ◽

F.R. Denys

Keyword(s):

Fine Structure ◽

Granulosa Cell ◽

Cell Cultures ◽

Single Injection ◽

Surrounding Medium ◽

Petri Dish ◽

Female Rats ◽

Vaginal Smear ◽

Immature Female ◽

Serum Gonadotropin

The purpose of this paper is to present observations on the fine structure of rat granulosa cell cultures grown in the presence of an adenohypophyseal explant and to correlate the morphology of these cells with progestin secretion. Twenty-six day old immature female rats were given a single injection of 5 IU pregnant mares serum gonadotropin (PMS) in order to obtain ovaries with large vesicular follicles. At 66 hrs. post-PMS administration (estrus indicated by vaginal smear cytology), the ovaries were removed and placed in a petri dish containing medium 199 and 100 U penicillin/streptomycin (P/S)/ml. Under a 20X magnification dissecting microscope, some 5-8 vesicular follicles/ovary were punctured and the granulosa cells were expressed into the surrounding medium. The cells were transferred to centrifuge tubes and spun down at 1000 rpm for 5 mins.

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Differential polarization imaging of sickled cells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100102390 ◽

1988 ◽

Vol 46 ◽

pp. 62-63

Author(s):

Marcos F. Maestre

Keyword(s):

Optical Properties ◽

Theoretical Approach ◽

Polarized Light ◽

Polarization Microscopy ◽

Spectroscopic Techniques ◽

Polarization Imaging ◽

Circularly Polarized Light ◽

Circularly Polarized ◽

Microscopic Scale ◽

Chiral Structures

Recently we have developed a form of polarization microscopy that forms images using optical properties that have previously been limited to macroscopic samples. This has given us a new window into the distribution of structure on a microscopic scale. We have coined the name differential polarization microscopy to identify the images obtained that are due to certain polarization dependent effects. Differential polarization microscopy has its origins in various spectroscopic techniques that have been used to study longer range structures in solution as well as solids. The differential scattering of circularly polarized light has been shown to be dependent on the long range chiral order, both theoretically and experimentally. The same theoretical approach was used to show that images due to differential scattering of circularly polarized light will give images dependent on chiral structures. With large helices (greater than the wavelength of light) the pitch and radius of the helix could be measured directly from these images.

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