On Free Vibrations of Finite Beams With Partially Fixed End Conditions Carrying Masses

1975 ◽  
Vol 42 (3) ◽  
pp. 735-736 ◽  
Author(s):  
C. L. Amba-Rao ◽  
M. Y. Hussaini
Keyword(s):  
Free Vibrations ◽  
End Conditions ◽  
Fixed End

Critical examination of various approaches used for analysing helical cables

1994 ◽  
Vol 29 (1) ◽  
pp. 43-55 ◽  
Author(s):  
M Raoof ◽  
I Kraincanic
Keyword(s):  
Large Diameter ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Critical Examination ◽  
First Order ◽  
Wide Range ◽  
End Conditions ◽  
Parametric Studies ◽  
The Individual ◽  
Fixed End

Using theoretical parametric studies covering a wide range of cable (and wire) diameters and lay angles, the range of validity of various approaches used for analysing helical cables are critically examined. Numerical results strongly suggest that for multi-layered steel strands with small wire/cable diameter ratios, the bending and torsional stiffnesses of the individual wires may safely be ignored when calculating the 2 × 2 matrix for strand axial/torsional stiffnesses. However, such bending and torsional wire stiffnesses are shown to be first order parameters in analysing the overall axial and torsional stiffnesses of, say, seven wire stands, especially under free-fixed end conditions with respect to torsional movements. Interwire contact deformations are shown to be of great importance in evaluating the axial and torsional stiffnesses of large diameter multi-layered steel strands. Their importance diminishes as the number of wires associated with smaller diameter cables decreases. Using a modified version of a previously reported theoretical model for analysing multilayered instrumentation cables, the importance of allowing for the influence of contact deformations in compliant layers on cable overall characteristics such as axial or torsional stiffnesses is demonstrated by theoretical numerical results. In particular, non-Hertzian contact formulations are used to obtain the interlayer compliances in instrumentation cables in preference to a previously reported model employing Hertzian theory with its associated limitations.

A Method for Determining the Flexural Effects of Statically Loaded Beams on Multiple Elastic Supports

1956 ◽  
Vol 23 (4) ◽  
pp. 503-508
Author(s):  
R. A. Di Taranto
Keyword(s):  
Beam Theory ◽  
Elastic Supports ◽  
Electronic Digital Computer ◽  
Simply Supported ◽  
Influence Coefficients ◽  
End Conditions ◽  
Desk Calculator ◽  
Simple Supports ◽  
Fixed End ◽  
Nonuniform Beam

Abstract Herein is presented a means for calculating the static deflections, slopes, moments, and shears of a nonuniform beam on two supports for any end conditions and on three simple supports when subjected to concentrated loads and/or concentrated moments. The method is an extension of a simple tabular procedure as used by Myklestad (1) for use on a desk calculator or electronic digital computer. The procedure is such that it may be easily carried out by one who need not have any knowledge of beam theory. Influence coefficients may be easily and directly calculated for nonuniform beams on two and three elastic supports. The two-support beam is formulated for simply supported one overhang, two supports with linear and torsional springs, and fixed-fixed end conditions. Extensions of this method to any other boundary conditions are indicated.

Force-length relation of isometric sarcomeres in fixed-end tetani

1993 ◽  
Vol 264 (1) ◽  
pp. C19-C26 ◽  
Author(s):  
A. Horowitz ◽  
G. H. Pollack
Keyword(s):  
Sarcomere Length ◽  
Production Capacity ◽  
Force Production ◽  
Length Change ◽  
Optical Diffraction ◽  
Tetanic Force ◽  
End Conditions ◽  
Linear Force ◽  
Fixed End

The higher force observed in fixed-end tetani relative to sarcomere-isometric tetani is commonly attributed to sarcomere length inhomogeneity; sarcomeres in the end regions of the fiber shorten extensively at the expense of the central sarcomeres. By shortening, these sarcomeres supposedly attain higher force production capacity and can thus account for the extra force. However, the fibers could also contain sarcomeres that stay isometric throughout most of the tetanic force plateau. If such sarcomeres undergo slight shortening before their isometric phase, their force-length relation should be elevated (A. Horowitz, H. P. M Wussling, and G. H. Pollack. Biophys. J. 63: 3-17, 1992). These sarcomeres may therefore account for the higher force in fixed-end tetani. To test this possibility, single frog semitendinosus fibers were tetanized under fixed-end conditions. Sarcomere length change during the tetanus was measured at different locations along the fiber by optical diffraction. Fibers stretched to average sarcomere lengths between 2.2 and 3.2 microns contained sarcomeres that, except for some initial shortening during the early part of the tetanus, remained isometric. These sarcomeres were located between the ends and the central region of the fibers. Their force-length relation was higher than the linear force-length relation based on sarcomere length clamps by an average of 14% between sarcomere lengths of 2.4-3.2 microns. Thus slight (1-5%) shortening may explain the relatively higher fixed-end force-length relation.

Hydroelastic Instability of Uniformly Curved Pipe-Fluid Systems

1970 ◽  
Vol 37 (3) ◽  
pp. 817-822 ◽  
Author(s):  
T. E. Unny ◽  
E. L. Martin ◽  
R. N. Dubey
Keyword(s):  
Critical Velocity ◽  
Mode Shape ◽  
Flowing Fluid ◽  
Curved Pipe ◽  
Fluid Systems ◽  
End Conditions ◽  
Fixed End

This article describes an investigation of hydroelastic instability in a uniformly curved pipe containing a flowing fluid. It is found that divergence occurs with pinned-pinned and fixed-fixed end conditions. The angular length of the pipe is found to influence the critical velocity and the mode shape at instability.

Vibration of an elastic strip with varying curvature

1992 ◽  
Vol 339 (1655) ◽  
pp. 587-625 ◽  
Keyword(s):  
Total Internal Reflection ◽  
Normal Modes ◽  
Mode Shapes ◽  
Elastic Strip ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
End Conditions ◽  
The One ◽  
Fixed End ◽  
Good Agreement

The vibrational behaviour of an elastic strip with varying curvature is investigated. The case of vibration which is predominantly transverse is considered, and it is shown that when the strip is S-shaped, certain of the normal modes may be confined to the vicinity of the inflection point of the S by a process of total internal reflection from points where the curvature reaches critical values. This confinement can produce modes with extraordinarily low damping factors. Asymptotic analysis is compared with experimental measurements on a strip in several S-shaped configurations, and very good agreement is demonstrated for modal frequencies and shapes. Mathematically, the lower modes turn out to be analogous to those of the one-dimensional harmonic oscillator in quantum mechanics. This mode confinement behaviour occurs for all waveguide branches except the lowest, ‘bending beam ’, branch. In this particular case, wave propagation is insensitive to curvature. However, an interesting phenomenon associated with curvature is found : the successive mode shapes do not display the normal alternation of symmetry and antisymmetry with respect to the centre of the strip. The effect is shown to result from the constraint on axial movement produced by fixed end conditions. For the geometry of the experiments, this constraint raises the frequencies of antisymmetric modes in a characteristic way while leaving the symmetric modes unaltered, thus changing the mode sequence. Theory is developed which gives reasonable quantitive agreement with the observations.

Structural Abstraction in Snap-fit Analysis

2000 ◽  
Vol 122 (4) ◽  
pp. 395-402 ◽  
Author(s):  
Gaurav Suri ◽  
Anthony F. Luscher
Keyword(s):  
Finite Element ◽  
Accurate Estimation ◽  
Test Cases ◽  
Finite Element Models ◽  
Feature Models ◽  
Engineering Activity ◽  
End Conditions ◽  
Unrealistic Assumption ◽  
Fixed End ◽  
Plastic Parts

Snap-fit design has always been more of an art instead of an engineering activity. Research in this area focuses on generating finite element models for predicting the performance of snap-fit features. Such research typically uses fixed-end conditions at the base of the snap-fit feature. Often this is an unrealistic assumption, because snap-fits are usually molded on plastic parts with significant flexibility. The performance of snap-fits can be significantly influenced by this additional flexibility. To predict this performance of snap-fits it often becomes necessary to analyze the entire part, which can be a costly and time consuming process. There is no general methodology in the open literature to incorporate base-part flexibility into the design of snap-fit features. Existing work in this area is inaccurate and limited to certain base-part and snap-fit topologies. This paper proposes a new methodology called structural abstraction for incorporating base-part flexibility into snap-fit feature models. This methodology abstracts base-parts as spring elements with various stiffnesses. The underlying theory and the relevant relationships are developed and the approach is validated using several test cases. Independence of the approach to both base-part and snap-fit topologies is established and shown to be a major advantage of this technique. Use of this methodology will improve snap-fit analysis and give a more accurate estimation of retention strength. It is shown that in certain cases the improvement in accuracy over conventional finite element models of snap-fits can be as high as 70 percent. [S1050-0472(00)02504-6]

In-Plane Flexural Vibrations of Circular Rings

1969 ◽  
Vol 36 (3) ◽  
pp. 620-625 ◽  
Author(s):  
S. S. Rao ◽  
V. Sundararajan
Keyword(s):  
Natural Frequencies ◽  
Classical Equation ◽  
Circular Ring ◽  
Classical Formula ◽  
Free Ring ◽  
Circular Arcs ◽  
End Conditions ◽  
Circular Rings ◽  
Experimental Values ◽  
Fixed End

An equation of motion governing the free, in-plane vibrations of a circular ring is developed to include the effects of shear deformation and rotatory inertia. This equation is solved to find the natural frequencies of vibration of free rings and stiffened rings and the results compared with those given by a classical formula. The frequencies for a free ring are found to compare well with the experimental values of Kuhl [5]. Natural frequencies of circular arcs are calculated from the classical equation with hinged and fixed end conditions and the results compared with the approximate values given by Den Hartog [8, 9].

scholarly journals Post-Buckling Behavior of a Circular Rod Constrained Within a Circular Cylinder

1986 ◽  
Vol 53 (4) ◽  
pp. 929-934 ◽  
Author(s):  
K. G. Sorenson ◽  
J. B. Cheatham
Keyword(s):  
Circular Cylinder ◽  
Solution Procedure ◽  
Initial Contact ◽  
Cylinder Wall ◽  
Infinite Length ◽  
Buckling Behavior ◽  
Constant Pitch ◽  
End Conditions ◽  
Post Buckling ◽  
Fixed End

An axially loaded weightless circular rod buckles helically when constrained within a circular cylinder. The effects of pinned and fixed-end conditions are investigated. Both end conditions locate the rod end on the cylinder axis, and are found to perturb the helix in an exponentially decaying manner for a distance of less than one helix pitch length. Far from the end, the rod behaves as an undisturbed constant-pitch helix. The distance from the rod end to the point of initial contact with the cylinder wall is calculated. Closed-form analytical solutions are obtained for the deflected shapes and internal reactions of the end sections. The solution procedure applies to rods of either finite or infinite length.

Structural Abstraction in Snap-Fit Analysis

1999 ◽  
Author(s):  
Gaurav Suri ◽  
Anthony F. Luscher
Keyword(s):  
Science Research ◽  
Accurate Estimation ◽  
Test Cases ◽  
Finite Element Models ◽  
Q Factor ◽  
Feature Models ◽  
End Conditions ◽  
Unrealistic Assumption ◽  
Fixed End ◽  
Plastic Parts

Abstract Snap-fit design has always been more of an art rather than a pure engineering science. Research in this area focuses on generating finite element models for predicting the performance of snap-fit features. Such research typically uses fixed end conditions at the base of the snap-fit feature. Often this is an unrealistic assumption, because snap-fits are usually molded on plastic parts with significant flexibility. The performance of snap-fits can be significantly influenced by this additional flexibility. To predict the performance of snap-fits in complex plastic parts, it has often been necessary to analyze the entire part, which can be a costly and time consuming process. There is no general methodology in the open literature to incorporate base-part flexibility into the design of snap-fit features. Existing work in this area such as Q-Factor charts, is inaccurate and specific to certain base-part and snap-fit topologies. This paper proposes a new methodology called structural abstraction for incorporating base-part flexibility into feature models. This methodology abstracts base-parts as spring elements with various stiffnesses. The theory behind this approach and the relevant relationships are developed and the approach is validated using several test cases. Independence of the approach to both base-part and snap-fit topologies is established and shown to be a major advantage of this technique. Use of this methodology will improve snap-fit analysis and give a more accurate estimation of retention strength. It is shown that in certain cases the improvement in accuracy can be as high as 70 percent or more.

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