Theoretical and Experimental Analysis of the Forced Response of Sagged Cable/Mass Suspensions

1993 ◽  
Author(s):  
S.-P. Cheng ◽  
N. C. Perkins
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Forced Response ◽  
Integral Representations ◽  
Asymptotic Model ◽  
Ocean Engineering ◽  
Solution Strategy ◽  
Matrix Formulation ◽  
State Response ◽  
Natural Frequency Spectrum

Abstract This study examines the forced response of a sagged elastic cable supporting an array of discrete masses. Such systems arise, for instance, in ocean engineering applications employing cable hydrophone arrays. The excitation considered is harmonic and normal to the cable and may, for instance, approximate prescribed environmental loading. An asymptotic model is presented that describes the linear forced response of a cable/mass suspension having small equilibrium curvature. Closed-form expressions for the Green’s function to an associated boundary-value problem are obtained using a transfer matrix formulation. The derived Green’s function is utilized to construct integral representations for steady-state response under boundary and/or domain excitation. Solutions obtained for a variety of domain loading distributions demonstrate the utility and efficiency of this solution strategy. The theoretical response predictions are verified through experimental measurements of the natural frequency spectrum and frequency response of laboratory cable/mass suspensions.

Theoretical and Experimental Analysis of the Forced Response of Sagged Cable/Mass Suspensions

1994 ◽  
Vol 61 (4) ◽  
pp. 944-948 ◽  
Author(s):  
S.-P. Cheng ◽  
N. C. Perkins
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Forced Response ◽  
Integral Representations ◽  
Asymptotic Model ◽  
Ocean Engineering ◽  
Solution Strategy ◽  
Matrix Formulation ◽  
State Response ◽  
Natural Frequency Spectrum

This study examines the forced response of a sagged elastic cable supporting an array of discrete masses. Such systems arise, for instance, in ocean engineering applications employing cable hydrophone arrays. The excitation considered is harmonic and normal to the cable and may, for instance, approximate prescribed environmental loading. An asymptotic model is presented that describes the linear forced response of a cable/mass suspension having small equilibrium curvature. Closed-form expressions for the Green’s function to an associated boundary value problem are obtained using a transfer matrix formulation. The derived Green’s function is utilized to construct integral representations for steady-state response under boundary and/or domain excitation. Solutions obtained for a variety of domain loading distributions demonstrate the utility and efficiency of this solution strategy. The theoretical response predictions are verified through experimental measurements of the natural frequency spectrum and frequency response of laboratory cable/mass suspensions.

scholarly journals Cones of localized shear strain in incompressible elasticity with prestress: Green's function and integral representations

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140423 ◽  
Author(s):  
L. P. Argani ◽  
D. Bigoni ◽  
D. Capuani ◽  
N. V. Movchan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ad Hoc ◽  
Shear Failure ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Representations ◽  
Element Formulation ◽  
Infinite Body ◽  
Incompressible Elasticity

The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney–Rivlin elasticity and the J 2 -deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup–cone rupture of ductile metal bars.

On Green's functions for small disturbances of plane Couette flow

1977 ◽  
Vol 79 (3) ◽  
pp. 525-534 ◽  
Author(s):  
Philip S. Marcus ◽  
William H. Press
Keyword(s):  
Green’S Function ◽  
Couette Flow ◽  
Green's Function ◽  
Integral Representations ◽  
Plane Couette Flow ◽  
Linearized Stability ◽  
Transcendental Functions ◽  
Complete Set ◽  
The Stability ◽  
Sommerfeld Equation

The linearized stability of plane Couette flow is investigated here, without using the Orr–Sommerfeld equation. Rather, an unusual symmetry of the problem is exploited to obtain a complete set of modes for perturbations of the unbounded (no walls) flow. An explicit Green's function is constructed from these modes. The unbounded flow is shown to be rigorously stable. The bounded case (with walls) is investigated by using a ‘method of images’ with the unbounded Green's function; the stability problem in this form reduces to an algebraic characteristic equation (not a differential-equation eigenvalue problem), involving transcendental functions defined by integral representations.

Alternative Methods of Evaluating Green’s Function in Three-Dimensional Ship-Wave Problems

1977 ◽  
Vol 21 (02) ◽  
pp. 89-93
Author(s):  
Grant E. Hearn
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Three Dimensional ◽  
Integral Representations ◽  
Alternative Methods ◽  
Ship Wave ◽  
Integral Forms ◽  
Finite Integral ◽  
Efficiency Comparison ◽  
Wave Problems

This paper introduces new alternative forms of Green's function, and its derivatives, suitable for the calculations associated with three-dimensional ship-wave problems. Rather than infinite-range integral forms, new finite integral representations of Green's function for harmonic motions are derived for the "single-body" and "double-body" descriptions of the interactive problem. The usefulness of these finite integral descriptions is illustrated by carrying out a computing efficiency comparison with other alternative, but mathematically equivalent, descriptions of the Green's function. The calculations carried out indicate that the proposed forms of the Green function are numerically more efficient than the standard forms without affecting accuracy.

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method
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