Forced Motion of Elastic Plates

1968 ◽  
Vol 35 (3) ◽  
pp. 510-515 ◽  
Author(s):  
H. Reismann
Keyword(s):  
Shear Force ◽  
Outer Boundary ◽  
Time Dependent ◽  
Elastic Plates ◽  
Normal Surface ◽  
Forced Motion ◽  
Ring Plate ◽  
Explicit Exact Solution ◽  
Surface Loads ◽  
General Method

A general method is presented for the solution of dynamic boundary-value problems of elastic plates subjected to time-dependent normal surface loads and/or time-dependent boundary conditions. As a demonstration of the method, an explicit, exact solution of the axisymmetric response of a ring plate is presented. The plate is clamped at the outer boundary and subjected to a suddenly applied transverse shear force which is uniformly distributed over the rotationally restrained inner boundary.

Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

2003 ◽  
Vol 125 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Dimitris S. Sophianopoulos ◽  
George T. Michaltsos
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Dynamic Stability ◽  
Parametric Excitation ◽  
Stability Problem ◽  
Axial Loading ◽  
Time Dependent ◽  
Analytical Treatment ◽  
Simply Supported ◽  
Forced Motion

The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.

Gravity-driven flow in a horizontal annulus

2017 ◽  
Vol 830 ◽  
pp. 479-493 ◽  
Author(s):  
Marcus C. Horsley ◽  
Andrew W. Woods
Keyword(s):  
Horizontal Well ◽  
Outer Boundary ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Two Dimensional ◽  
Narrow Gap ◽  
Dense Fluid ◽  
Annular Geometry ◽  
Gravity Driven ◽  
Gravity Driven Flow

A theory for the low-Reynolds-number gravity-driven flow of two Newtonian fluids separated by a density interface in a two-dimensional annular geometry is developed. Solutions for the governing time-dependent equations of motion, in the limit that the radius of the inner and outer boundaries are similar, and in the case that the interface is initially inclined to the horizontal, are analysed numerically. We focus on the case in which the fluid is arranged symmetrically about a vertical line through the centre of the annulus. These solutions are successfully compared with asymptotic solutions in the limits that (i) a thin film of dense fluid drains down the outer boundary of the annulus, and (ii) a thin layer of less dense fluid is squeezed out of the narrow gap between the base of the inner annulus and dense fluid. Application of the results to the problem of mud displacement by cement in a horizontal well is briefly discussed.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

scholarly journals Segmental Analysis and Design of Superstructure for Box Girder Balanced Cantilever Bridge by IRC Specification Using Midas Civil

2020 ◽  
pp. 107-114
Author(s):  
L. S. Kalaiselvan
Keyword(s):  
Shear Force ◽  
Bending Moment ◽  
Ground Level ◽  
The Other ◽  
Time Dependent ◽  
Bridge Structure ◽  
Box Girder ◽  
Segmental Analysis ◽  
Analysis And Design ◽  
Creep And Shrinkage

A bridge is a combination of substructure and superstructure that is built over a river, road, or railway to allow people and vehicles to cross from one side to the other. This paper describes about the analysis and design of box girder balanced cantilever bridge using MIDAS CIVIL by IRC loadings, characterized by central span of 130m with two symmetrical sides of 85m.Bridge deck is supported by two piers of 40m height from ground level. The bridge structure has been modelled using MIDAS CIVIL and analysis has been performed to get various output such as bending moment, shear force and time dependent properties such as creep and shrinkage at various points of the bridge. The PSC (prestressed) design of superstructure is performed as per IRC standards to get the output parameters such as principle stresses at construction stage, principle stress for prestressing tendon. While by using balanced cantilever bridge less form work has been required for this type of bridge.

Forced Motions of Timoshenko Beams

1955 ◽  
Vol 22 (1) ◽  
pp. 53-56
Author(s):  
G. Herrmann
Keyword(s):  
Free Vibration ◽  
Elastic Beam ◽  
Time Dependent ◽  
Transverse Shear Deformation ◽  
Transverse Displacement ◽  
Timoshenko Beams ◽  
Rotatory Inertia ◽  
Forced Motion ◽  
Dependent Variables ◽  
The One

Abstract Timoshenko’s theory of flexural motions in an elastic beam takes into account both rotatory inertia and transverse-shear deformation and, accordingly, contains two dependent variables instead of the one transverse displacement of classical theory of flexure. For the case of forced motions, the solution involves complications not usually encountered. The difficulties may be surmounted in several ways, one of which is presented in this paper. The method described makes use of the property of orthogonality of the principal modes of free vibration and uses the procedure of R. D. Mindlin and L. E. Goodman in dealing with time-dependent boundary conditions. Thus the most general problem of forced motion is reduced to a free-vibration problem and a quadrature.

Annular Dome Subjected to Uniform Load Over an Eccentric Circular Area

1978 ◽  
Vol 45 (4) ◽  
pp. 845-851
Author(s):  
H. Ainso
Keyword(s):  
General Solution ◽  
Shallow Shell ◽  
Outer Boundary ◽  
Uniform Load ◽  
Circular Area ◽  
Distributed Load ◽  
Load Effects ◽  
Particular Solution ◽  
Shell Equations ◽  
General Method

A general method is presented for solving shallow shell problems with finite boundaries and with an arbitrarily placed load that is uniformly distributed over a circular area of radius r0. A known solution for the distributed load on an unbounded shell is used to describe the load effects, and this particular solution is combined with Reissner’s general solution of the shallow shell equations in such a manner that all the boundary conditions are satisfied. Numerical results have been obtained for a shallow shell, clamped at the outer boundary and having a circular polar aperture free of tractions and support.

Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space

2000 ◽  
Vol 68 (2) ◽  
pp. 162-168 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Arbitrary Constant ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Poisson Effect ◽  
Wave Speeds ◽  
Wave Patterns ◽  
Infinitesimal Deformations ◽  
Surface Loads

A plane-strain study of a prestressed isotropic compressible neo-Hookean half-space subjected to shear and normal surface loads is performed. The loads are either stationary and applied for an instant, or travel at an arbitrary constant speed. The transient process is viewed as the superposition of infinitesimal deformations upon large, and exact expressions for the displacements, within and upon, the half-space are obtained. These, and the associated wave patterns, demonstrate the anisotropy induced by prestress. The wave speeds themselves are sensitive to prestress; in particular, Rayleigh waves disappear beyond a critical compressive prestress. A critical tensile prestress also exists, beyond which a negative Poisson effect occurs.

Dynamic Response of Cylindrical Shells With Initial Stress and Subjected to General Three-Dimensional Surface Loads

1971 ◽  
Vol 38 (4) ◽  
pp. 978-986 ◽  
Author(s):  
E. N. K. Liao ◽  
P. G. Kessel
Keyword(s):  
Initial Stress ◽  
Circular Cylindrical Shell ◽  
Three Dimensional ◽  
Time Dependent ◽  
Point Force ◽  
Numerical Comparison ◽  
Simply Supported ◽  
Surface Loads ◽  
Dimensional Surface ◽  
General Time

This paper presents general solutions for both Flu¨gge’s and Donnell’s equations governing the displacements of the midsurface of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial twoway stress and subjected to general time-dependent surface loads. Analytical solutions are presented to the specific problems of a stationary radial point force and a stationary point couple. A numerical comparison of Donnell’s and Flu¨gge’s theories is made for these specific problems for a wide variety of shell parameters including initial stress. It is found for the case of a dynamic point force or point couple that Donnell’s theory is satisfactory for thin and very short shells (h/a ≤ 0.01 and l/a ≤ 2).

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