Probabilistic stability of uncertain composite plates and stochastic irregularity in their buckling mode shapes: A semi-analytical non-intrusive approach

In this study, the mechanical properties of the composite plate were considered Gaussian random fields and their effects on the buckling load and corresponding mode shapes were studied by developing a semi-analytical non-intrusive approach. The random fields were decomposed by the Karhunen−Loève method. The strains were defined based on the assumptions of the first-order and higher-order shear-deformation theories. Stochastic equations of motion were extracted using Euler–Lagrange equations. The probabilistic response space was obtained by employing the non-intrusive polynomial chaos method. Finally, the effect of spatially varying stochastic properties on the critical load of the plate and the irregularity of buckling mode shapes and their sequences were studied for the first time. Our findings showed that different shear deformation plate theories could significantly influence the reliability of thicker plates under compressive loading. It is suggested that a linear relationship exists between the mechanical properties’ variation coefficient and critical loads’ variation coefficient. Also, in modeling the plate properties as random fields, a significant stochastic irregularity is obtained in buckling mode shapes, which is crucial in practical applications.     

REVIEW OF APPLIED PARTICLE SHAPE DESCRIPTORS AND PRODUCED PARTICLE SHAPES IN GRINDING ENVIRONMENTS. PART II: THE INFLUENCE OF COMMINUTION ON THE PARTICLE SHAPE

In this article the literature on the shape of particles produced by comminution methods and the grinding condition is reviewed and presented. Some agreement and disagreement among workers for the shapes that are produced by comminution are presented. In addition, the important factors affecting the shape of particles in different comminution methods are also described.     

LOSS MINIMIZATION OF A DC MOTOR DRIVE

ABSTRACT

This paper presents a practical method for operation of a semi-converter-fed DC motor drive at the point of maximum efficiency while maintaining any particular torque-speed load point. Design and operation of an economical, microprocessor-based adaptive controller used to retrofit a commercially available SCR drive for minimum loss operation of a DC motor is described. Experimental and simulation results are presented in graphical forms, giving comparison of overall drive system efficiencies between loss minimization adaptive control and conventional constant field current operation for a standard-efficiency DC motor with a 7½ hp rating for both separately excited and shunt connected configurations. The greatest potential for energy savings is found to exist for the case of light load at low speeds.     

RELATIONSHIP BETWEEN TRUE AND ESTIMATED POSSIBILISTIC SYSTEMS AND THEIR RECONSTRUCTIONS†

This paper is a theoretical contribution to reconstructability analysis of possibilistic systems. A method to estimate a given possibility distribution from the associated observations is derived based on the one-to-one correspondence between possibility distributions and their basic probability assignments. It is shown that in this estimation the possibility value for a state is proportional to the frequency of the state in the observations which are drawn from nested state subsets. The order preservation relationship between a given (true) possibility distribution and its estimation is derived. Based on this preservation property, it is shown that the order in the distance from an original possibilistic overall system of their unbiased reconstructions from two alternative reconstruction hypotheses (structures) is preserved in the estimated systems domain. Particularly, it is proved that systems conceptualized in terms of possibility theory possess an important property: if a possibilistic system is perfectly reconstructable from a specific reconstruction hypothesis, then a system estimated from any data produced by the former system is also perfectly reconstructable from the same hypothesis.     

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.