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

1983 ◽  
Vol 50 (4a) ◽  
pp. 723-726 ◽  
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.

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

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.

scholarly journals Comprehensive vibrational dynamics of half-open fluid-filled shells

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190207
Author(s):  
Markus Lendermann ◽  
Jin Ming Koh ◽  
Joel Shi Quan Tan ◽  
Kang Hao Cheong
Keyword(s):  
Elastic Shell ◽  
Acoustic Properties ◽  
Vibrational Dynamics ◽  
Closed Form Solutions ◽  
Vibrational Response ◽  
Solid Objects ◽  
Engineered Structures ◽  
Physical Insight ◽  
Fluid Levels ◽  
Shell Geometry

Fluid-filled shells are near-ubiquitous in natural and engineered structures—a familiar example is that of glass harps comprising partially filled wineglasses or glass bowls, whose acoustic properties are readily noticeable. Existing theories modelling the mechanical properties of such systems under vibrational load either vastly simplify shell geometry and oscillatory modal shapes to admit analytical solutions or rely on finite-element black-box computations for general cases, the former yielding poor accuracy and the latter offering limited tractability and physical insight. In the present study, we derive a theoretical framework encompassing elastic shell deformation with structural and viscous dissipation, accommodating arbitrary axisymmetric shell geometries and fluid levels; reductions to closed-form solutions under specific assumptions are shown to be possible. The theory is extensively verified against a range of geometries, fluid levels and fluid viscosities in experiments; an extension of the model encompassing additional solid objects within the fluid-filled shell is also considered and verified. The presented theoretical advance in describing vibrational response is relevant in performance evaluation for engineered structures and quality validation in manufacturing.

Parametric Influences on the Response of Structural Shells

1975 ◽  
Vol 97 (4) ◽  
pp. 1311-1316 ◽  
Author(s):  
N. J. Huffington ◽  
J. D. Wortman
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Empirical Model ◽  
Difference Method ◽  
Large Deflection ◽  
Structural Response ◽  
Impulsive Loading ◽  
Relative Importance ◽  
Rapid Estimation ◽  
System Parameters

The effects on structural response produced by variation of geometric, loading, and material property parameters have been investigated for the specific case of a fixed-ended cylinder subjected to a “frontal cosine” distribution of impulsive loading (although many qualitative results can be expected to apply to other cases). Responses were determined using the REPSIL code, which employs a finite difference method to solve the partial differential equations for large deflection, anelastic shell motions. Graphical representations of results in terms of six nondimensional quantities make it possible to obtain an overview of the influence of various system parameters on structural response and to draw certain conclusions regarding their relative importance. An empirical model based on REPSIL code data has been developed which permits rapid estimation of cylinder responses over a useful range of system parameters.

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

2009 ◽  
Vol 131 (2) ◽  
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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