Vibration of a Fluid Conveying Pipe Carrying a Discrete Mass

1974 ◽  
Vol 96 (4) ◽  
pp. 268-272 ◽  
Author(s):  
T. T. Wu ◽  
P. P. Raju
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
General Expression ◽  
Normal Modes ◽  
Critical Value ◽  
Numerical Results ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Discrete Mass

This paper presents a method to predict the dynamic response of a fluid conveying pipe carrying a discrete mass when the flow velocity is less than its critical value. A general expression for the normal modes of a vibrating pipe with various boundary conditions is newly derived herein. Also presented for a particular case are the numerical results of eigenfunctions and eigenvalues which can be used to calculate the dynamic response of a simply-supported pipe with an attached discrete mass at its mid-span.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

scholarly journals Director Fluctuations in Two-Dimensional Liquid Crystal Disclinations

Crystals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Olaf Stenull ◽  
Tom C. Lubensky
Keyword(s):  
Boundary Conditions ◽  
Normal Modes ◽  
Critical Value ◽  
Outer Radius ◽  
Two Dimensional ◽  
Free Energies ◽  
Excitation Energies ◽  
Smectic C ◽  
Inner Radius ◽  
Decay Times

We present analytical calculations of the energies and eigenfunctions of all normal modes of excitation of charge +1 two-dimensional splay (bend) disclinations confined to an annular region with inner radius R1 and outer radius R2 and with perpendicular (tangential) boundary conditions on the region’s inner and outer perimeters. Defects such as these appear in islands in smectic-C films and can in principle be created in bolaamphiphilic nematic films. Under perpendicular boundary conditions on the two surfaces and when the ratio β=Ks/Kb of the splay to bend 2D Frank constants is less than one, the splay configuration is stable for all values μ=R2/R1. When β>1, the splay configuration is stable only for μ less than a critical value μc(β), becoming unstable to a “spiral” mixed splay-bend configuration for μ>μc. The same behavior occurs in trapped bend defects with tangential boundary conditions but with Ks and Kb interchanged. By calculating free energies, we verify that the transition from a splay or bend configuration to a mixed one is continuous. We discuss the differences between our calculations that yield expressions for experimentally observable excitation energies and other calculations that produce the same critical points and spiral configurations as ours but not the same excitation energies. We also calculate measurable correlation functions and associated decay times of angular fluctuations.

Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions

2015 ◽  
Vol 32 (3) ◽  
pp. 277-287 ◽  
Author(s):  
D. S. Mashat ◽  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Thermal Buckling ◽  
Governing Equations ◽  
Linear Temperature ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Dynamic Version ◽  
Beam Theories

AbstractAnalyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

EFFECTS OF THE FOLLOWER FORCE ON THE STATIC BUCKLING OF BEAMS

2002 ◽  
Vol 02 (03) ◽  
pp. 425-430 ◽  
Author(s):  
Q. WANG
Keyword(s):  
Boundary Conditions ◽  
Cantilever Beam ◽  
Smart Materials ◽  
Piezoelectric Actuators ◽  
Critical Value ◽  
Follower Force ◽  
Cantilever Beams ◽  
Beam Structure ◽  
Different Boundary Conditions ◽  
Simply Supported

The paper discusses the effect of a follower force on the buckling capacities of a beam structure subjected to a non-follower force. The potential of the research is on the application of smart materials in the buckling enhancement of beams, since the follower force is always modeled at the interaction between the smart materials and the substrate. The buckling capacities of beams with different boundary conditions are obtained analytically. Trivial solutions are found for the simply supported beam, beam with two fixed ends, and propped cantilever beam. However, the result from the analysis of a cantilever beam shows that, when the value of follower force is small, the buckling load decreases with the increase of the follower force. Nevertheless, the buckling capacity of the cantilever beam "jumps" to a big value if the follower force on the beam is relative large and beyond a critical value. This observation indicates that by properly applying the follower force with smart materials, the buckling capacities of the beam can be enhanced dramatically for the cantilever beams. It is hoped that this work will enable designers to capitalize on the effectiveness of using piezoelectric actuators or SMA in enhancing the buckling capacities of beams.

Triangular Plates Analyzed by Point Matching

1962 ◽  
Vol 29 (4) ◽  
pp. 755-756 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Numerical Results ◽  
Point Matching ◽  
Simply Supported ◽  
Special Adaptation ◽  
Matching Technique

This brief note analyzes uniformly loaded triangular plates with either clamped or simply supported edges using a special adaptation of the point-matching technique, the functions satisfying the differential equation, also being chosen to satisfy exactly the boundary conditions on one edge. Numerical results are tabulated for three geometries.

A Reduction Method for Buckling Problems of Orthotropic Plates

1957 ◽  
Vol 8 (2) ◽  
pp. 145-156 ◽  
Author(s):  
P. Shuleshko
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Reduction Method ◽  
Isotropic Plate ◽  
Axial Loading ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Plate Buckling

SummarySeveral plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.

A New 3D Finite Element for Sandwich Beams With a Viscoelastic Core

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Kamel Amichi ◽  
Noureddine Atalla
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Results ◽  
Sandwich Beams ◽  
3D Finite Element ◽  
Various Boundary Conditions ◽  
The Core ◽  
Viscoelastic Core ◽  
Displacement Approach

A sandwich finite element for laminated steels is presented. It is based on a discrete displacement approach and allows for both symmetrical and unsymmetrical configurations. The three-layer sandwich model is built assuming a Timoshenko hypothesis for the viscoelastic core and Euler–Bernoulli hypotheses for the elastic faces, but the latter is modified to account for the rotational influence of the transversal shearing in the core. The validity and accuracy of the presented element are assessed through comparisons with numerical results of sandwich beams and sandwich rings with a variety of geometrical and mechanical properties and various boundary conditions. The present results are also compared with analytical, finite element, and experimental solutions for various boundary conditions.

Finite element method and analytical analysis of static and dynamic pull-in instability of a functionally graded microplate

2020 ◽  
pp. 107754632098020
Author(s):  
Arang Pazhouheshgar ◽  
Yashar Haghighatfar ◽  
Amirhossein Moghanian
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Power Laws ◽  
Functionally Graded ◽  
Numerical Results ◽  
Damping Coefficient ◽  
Various Boundary Conditions ◽  
Crucial Effect ◽  
Fringing Field ◽  
Material Power

The static and dynamic pull-in phenomenon of a functionally graded Al/Al2O3 microplate, considering the damping coefficient and fringing field effects, has been analyzed because of its crucial effect in micro-electromechanical systems application, especially in microswitches. The nonlinear equation of motion of functionally graded microplate has been derived using Hamilton’s principle, and solved analytically. Furthermore, a finite element code has been developed to solve the problem. Comparing the theoretical and numerical results for specific boundary conditions demonstrates that the numerical solution predicts the pull-in phenomenon with the least errors; and it can be used for various material power laws, damping coefficients, and initial gaps between the microplate and the substrate. The numerical results for various boundary conditions demonstrate that by increasing the damping coefficient, the dynamic pull-in voltage is also increased, and pull-in time will slow down. Moreover, the effect of power law and applied voltage on the pull-in instability is investigated.

scholarly journals Nonlocal FEM Formulation for Vibration Analysis of Nanowires on Elastic Matrix with Different Materials

2019 ◽  
Vol 24 (2) ◽  
pp. 38 ◽  
Author(s):  
Büşra Uzun ◽  
Ömer Civalek
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity Theory ◽  
Silver Nanowire ◽  
Small Scale ◽  
Weighted Residual Method ◽  
Simply Supported ◽  
Scale Parameters ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation ◽  
Foundation Model

In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped–clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study.

Sign in / Sign up

Export Citation Format

Share Document