J.B. Roberts

Bio: J.B. Roberts is an academic researcher from University of Sussex. The author has contributed to research in topics: Random vibration & Parametric statistics. The author has an hindex of 3, co-authored 3 publications receiving 1608 citations.

Random vibration and statistical linearization

Abstract: Interest in the study of random vibration problems using the concepts of stochastic process theory has grown rapidly due to the need to design structures and machinery which can operate reliably when subjected to random loads, for example winds and earthquakes. This is the first comprehensive account of statistical linearization - powerful and versatile methods with related techniques allowing the solution of a very wide variety of practical non-linear random vibration problems. The principal value of these methods is that unlike other analytical methods, they are readily generalized to deal with complex mechanical and structural systems and complex types of excitation such as earthquakes.

Stochastic averaging: An approximate method of solving random vibration problems

Abstract: Results obtained by applying the method of stochastic averaging to random vibration problems are discussed. This method is applicable to a variety of problems involving the response of lightly damped systems to broad-band random excitations. Solutions pertaining to both linear and non-linear vibrations are reviewed, and it is shown that the technique enables, in the case of parametric excitation, stability criteria to be established. Some results which have been obtained relating to the first-passage reliability problems are also surveyed. Various applications of the theory to engineering problems are outlined.

Multiple solutions generated by statistical linearization and their physical significance

Abstract: Three cases are examined where the statistical linearization (SL) procedure can yield multiple solutions for the first and second moments of the response. The first is an oscillator with a hardening non-linear stiffness excited by a narrow-band random excitation, the second is an oscillator with two potential wells excited by wide-band random excitation, and the third is an oscillator where the non-linear features present in the first two problems are combined. The results of an SL analysis are quantitatively compared with the behaviour of digitally simulated sample functions of the displacement response. In all cases a definite correspondence is found between the occurrence of multiple solutions generated by the SL method and the appearance of noticeable jumps in sample functions of the response. In some cases a quantitative agreement exists between the first and second moment values of the multiple solutions and the magnitude of “local” moments of the response.

Physics of liquid jets

Abstract: Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Liquid Sloshing Dynamics

Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

Galerkin finite element approximations of stochastic elliptic partial differential equations

Abstract: We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the com- putations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the computation of the expected value of the solution. The first method gener- ates independent identically distributed approximations of the solution by sampling the coefficients of the equation and using a standard Galerkin finite element variational formulation. The Monte Carlo method then uses these approximations to compute corresponding sample averages. The sec- ond method is based on a finite dimensional approximation of the stochastic coefficients, turning the original stochastic problem into a deterministic parametric elliptic problem. A Galerkin finite element method, of either the h -o rp-version, then approximates the corresponding deterministic solution, yielding approximations of the desired statistics. We present a priori error estimates and include a comparison of the computational work required by each numerical approximation to achieve a given accuracy. This comparison suggests intuitive conditions for an optimal selection of the numerical approximation.