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10 Equivalent Statistical Linearization
The solution of non-linear vibration problems in terms of probabilistic characteristics of the response is a complex task, since no general methods...
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12 Stability Analysis of Cylindrical Shells with Random Imperfections
As an example of imperfection sensitive structures, the axially compressed cylindrical shell is analyzed in the subsequent sections. Despite of its...
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2 Outline
The monograph is structured as follows: Part I including Chapts. 3–6 reviews briefly the theoretical background of the deterministic methods and...
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Review of Different Instability Types and Regimes
The three major types of “ideal„ instabilities studied here are [92]:
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Two Methods for Analysis of Continuum Mechanics of Elastic Structures
There are two basic methods to analyze the continuum elastic structural mechanics: One is by applying Newton’s law of motion to a free body element...
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Vibrations of Inclined Bars with End Constraint
Considered are the vibrations of inclined bars with the bottom end flxed in space and the top end having a constraint which requires that this end...
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Buckling of Inclined Columns
The stability of a simple truss subjected to a single force, P, as shown in Fig. 8.1 was investigated by Mises [40] as a basic model to illustrate...
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Membrane Vibrations of Conical Shells
The vibrations of conical shells are due to the inertial and external forces acting the transverse, circumferential and meridional directions of the...
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Introduction
Many Dam applications involve phenomena of hydrodynamic mixing instabilities at interfaces between different materials. Simulation codes must include...
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Reconstruction by Awe's Two‐Fluid Model of Developed Mixing Instabilities
The self‐similar incompressible “0D„ approach can be used to estimate the performance of Awe's two‐fluid model in the three cases of simple mixing...
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Asymptotic Solutions of Conical Shells of Constant Thickness
The solutions of conical shells with linearly varying thickness presented in the last chapter have suggested a new approach to obtain asymptotic...
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Effect of Rotatory Inertia and Shear Deformation on Vibration of Inclined Bars with End Constraint
The effect of rotatory inertia and shear deformation on the vibration of the inclined bar with the end constraint studied in Chap. 2 is examined...
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Buckling of Conical Shells under a Single Axial Load
The buckling of conical shells subjected to external loads is a classic problem in shell structures. Since the theoretical predications could not...
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Some Perspectives on Further Developments of Models1
Faced with the insufficiencies of the basic single‐fluid models, such as Dam's к‐ε, several authors [13–26,167] have rightly identified the source of...
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8 Karhunen-Loève Expansion
In the following, second order stochastic processes are considered, i.e. random functions x(t) satisfying E{x(t)2}<∞,...
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Reconstruction by Dam's к‐ε Model of Developed Mixing Instabilities
According to the literature, the calibration of coefficients of the incompressible к‐ε model (listed in Table 2.1, p. 14) is based on the...
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13 Random Vibrations of Multi-Story Structures
The procedure described in Sec.11 is now applied to both a multi degree of freedom system (12-story building, 36 degrees of freedom) and a large...
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1 Objectives
Complex deterministic systems under deterministic loading are generally analyzed by the finite element method. This is mainly due to the most...
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B Lyapunov Matrix Differential Equation
The state space equation of the system defined in (6.18) is given by, see e.g. [91],...