Stability of Stochastic Elastic and Viscoelastic Systems

Stability of Stochastic Elastic and Viscoelastic Systems V. D. Potapov Moscow State University of Railway Communication, Russia Numerous structures assembled by civil and mechanical engineers are driven by external forces randomly changing in time and space. These forces include, for example, seismic and wind loads, transport loads and acoustic pressures. The parameters of these forces cannot be precisely measured, but they may have critical effects on fundamental structural characteristics, and hence have significant design implications. Materials used in construction also have an effect on structural behaviour. This book proposes a new approach for the analysis of the stability of different stochastic systems using both analytic (including asymptotic) and numerical methods. For example, constitutive equations used for the description of viscoelastic materials, which can be employed to take account of internal friction in an elastic material are examined, offering new opportunities for analysing the behaviour of real structures. Problems addressed include:
* stability of columns and rods subjected to longitudinal random stationary forces
* stability of plates in a gas flow subjected to in-plane loads, which are assumed as random stationary processes
* stability of cylindrical shells and panels under the action of longitudinal random stationary loads
* behaviour of flexible rods, plates and cylindrical panels, subjected to random stationary force and loads, under finite deflections
Furthermore, this text develops methods for estimating critical loads, resulting in an accessible and unified account of reliability theory and techniques as applied to engineering structures. All postgraduate students and practitioners of mechanical engineering (applied mechanics), civil engineering (structural mechanics), applied mathematics, and designers of mechanical and civil structures will find this not only a valuable, but an extremely useful book.

Numerous structures assembled by civil and mechanical engineers are driven by external forces randomly changing in time and space. These forces include, for example, seismic and wind loads, transport loads and acoustic pressures. The parameters of these forces cannot be precisely measured, but they may have critical effects on fundamental structural characteristics, and hence have significant design implications. Materials used in construction also have an effect on structural behaviour. This book proposes a new approach for the analysis of the stability of different stochastic systems using both analytic (including asymptotic) and numerical methods. For example, constitutive equations used for the description of viscoelastic materials, which can be employed to take account of internal friction in an elastic material are examined, offering new opportunities for analysing the behaviour of real structures. Problems addressed include:

• stability of columns and rods subjected to longitudinal random stationary forces
• stability of plates in a gas flow subjected to in-plane loads, which are assumed as random stationary processes
• stability of cylindrical shells and panels under the action of longitudinal random stationary loads
• behaviour of flexible rods, plates and cylindrical panels, subjected to random stationary force and loads, under finite deflections

Furthermore, this text develops methods for estimating critical loads, resulting in an accessible and unified account of reliability theory and techniques as applied to engineering structures. All postgraduate students and practitioners of mechanical engineering (applied mechanics), civil engineering (structural mechanics), applied mathematics, and designers of mechanical and civil structures will find this not only a valuable, but an extremely useful book.