7,725 research outputs found
Computation of a combined spherical-elastic and viscous-half-space earth model for ice sheet simulation
This report starts by describing the continuum model used by Lingle & Clark
(1985) to approximate the deformation of the earth under changing ice sheet and
ocean loads. That source considers a single ice stream, but we apply their
underlying model to continent-scale ice sheet simulation. Their model combines
Farrell's (1972) elastic spherical earth with a viscous half-space overlain by
an elastic plate lithosphere. The latter half-space model is derivable from
calculations by Cathles (1975). For the elastic spherical earth we use
Farrell's tabulated Green's function, as do Lingle & Clark. For the half-space
model, however, we propose and implement a significantly faster numerical
strategy, a spectral collocation method (Trefethen 2000) based directly on the
Fast Fourier Transform. To verify this method we compare to an integral formula
for a disc load. To compare earth models we build an accumulation history from
a growing similarity solution from (Bueler, et al.~2005) and and simulate the
coupled (ice flow)-(earth deformation) system. In the case of simple isostasy
the exact solution to this system is known. We demonstrate that the magnitudes
of numerical errors made in approximating the ice-earth system are
significantly smaller than pairwise differences between several earth models,
namely, simple isostasy, the current standard model used in ice sheet
simulation (Greve 2001, Hagdorn 2003, Zweck & Huybrechts 2005), and the Lingle
& Clark model. Therefore further efforts to validate different earth models
used in ice sheet simulations are, not surprisingly, worthwhile.Comment: 36 pages, 16 figures, 3 Matlab program
Evolution of constrained layer damping using a cellular automaton algorithm
Constrained layer damping (CLD) is a highly effective passive vibration control strategy if optimized adequately. Factors controlling CLD performance are well documented for the flexural modes of beams but not for more complicated mode shapes or structures. The current paper introduces an approach that is suitable for locating CLD on any type of structure. It follows the cellular automaton (CA) principle and relies on the use of finite element models to describe the vibration properties of the structure. The ability of the algorithm to reach the best solution is demonstrated by applying it to the bending and torsion modes of a plate. Configurations that give the most weight-efficient coverage for each type of mode are first obtained by adapting the existing 'optimum length' principle used for treated beams. Next, a CA algorithm is developed, which grows CLD patches one at a time on the surface of the plate according to a simple set of rules. The effectiveness of the algorithm is then assessed by comparing the generated configurations with the known optimum ones
Exact 3D solution for static and damped harmonic response of simply supported general laminates
The state-space method is adapted to obtain three dimensional exact solutions
for the static and damped dynamic behaviors of simply supported general
laminates. The state-space method is written in a general form that permits to
handle both cross-ply and antisymmetric angle-ply laminates. This general form
also permits to obtain exact solutions for general laminates, albeit with some
constraints. For the general case and for the static behavior, either an
additive term is added to the load to simulate simply supported boundary
conditions, or the plate bends in a particular way. For the dynamic behavior,
the general case leads to pairs of natural frequencies for each order, with
associated mode shapes. Finite element simulations have been performed to
validate most of the results presented in this study. As the boundary
conditions needed for the general case are not so straightforward, a specific
discussion has been added. It is shown that these boundary conditions also work
for the two aforementioned laminate classes. The damped harmonic response of a
non symmetrical isotropic sandwich is studied for different frequencies around
the fundamental frequency. The static and undamped dynamic behaviors of the
[-15/15], [0/30/0] and [-10/0/40] laminates are studied for various
length-to-thickness ratios
Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid
Integral balance solution employing entire domain approximation and the
penetration dept concept to the Stokes' first problem of a viscoelastic
generalized second grade fluid has been developed. The solution has been
performed by a parabolic profile with an unspecified exponent allowing
optimization through minimization of the norm over the domain of the
penetration depth. The closed form solution explicitly defines two
dimensionless similarity variables and, responsible for the viscous and the
elastic responses of the fluid to the step jump at the boundary. The solution
was developed with three forms of the governing equation through its two
dimensional forms (the main solution and example 1) and the dimensionless
version showing various sides of the flow field and how the dimensionless
groups control it: mainly the effect of the Deborah number. Numerical
simulations demonstrating the effect of the various operating parameter and
fluid properties on the developed flow filed have been performed.Comment: 19 pages, 6 figures; in press Thermal Science, volume 16, 2012, issue
A boundary integral equation method in the frequency domain for cracks under transient loading
Acknowledgments The financial support of the German Academic Exchange Service (DAAD), Engineering and Physical Sciences Research Council (EPSRC) and Advanced Research Collaboration (ARC) Programme (funded by the British Council and DAAD) is gratefully acknowledged.Peer reviewedPublisher PD
Dynamic Instability of Viscoelastic Plate in Supersonic Flow
The present work is investigating the aero-elastic instability of a viscoelastic plates under compressive forces. The Bubnov-Galerkin method used to solve the governing equations. The quasi-steady aerodynamic loadings are determined using linear piston theory. The nonlinear integro-differential equation of the plate is transformed into a set of nonlinear algebraic equations through a Galerkin approach. The resulting system of the equations is analytically solved. The influence of elastic and viscoelastic properties and the compressive load characteristicsof the plate material on the value of critical parameters are discussed
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