Stochastic response determination of structural systems modeled via dependent coordinates: a frequency domain treatment based on generalized modal analysis

Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis framework is challenging due to the presence of singular matrices, and thus, the machinery of generalized matrix inverses needs to be employed. An efficient frequency domain response analysis methodology for structural dynamical systems modeled via dependent coordinates is developed herein. This is done by resorting to the Moore–Penrose generalized matrix inverse in conjunction with a recently proposed extended modal analysis treatment. It is shown that not only the formulation is efficient in drastically reducing the computational cost when compared to a straightforward numerical evaluation of the involved generalized inverses, but also facilitates the derivation and implementation of the celebrated random vibration input–output frequency domain relationship between the excitation and the response power spectrum matrices. The validity of the methodology is demonstrated by considering a multi-degree-of-freedom shear type structure and a multi-body structural system as numerical examples.

     

A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm

The Vehicle Routing Problem (VRP) is one of the most well studied problems in operations research, both in real life problems and for scientific research purposes. During the last 50 years a number of different formulations have been proposed, together with an even greater number of algorithms for the solution of the problem. In this paper, the VRP is formulated as a problem of two decision levels. In the first level, the decision maker assigns customers to the vehicles checking the feasibility of the constructed routes (vehicle capacity constraints) and without taking into account the sequence by which the vehicles will visit the customers. In the second level, the decision maker finds the optimal routes of these assignments. The decision maker of the first level, once the cost of each routing has been calculated in the second level, estimates which assignment is the better one to choose. Based on this formulation, a bilevel genetic algorithm is proposed. In the first level of the proposed algorithm, a genetic algorithm is used for calculating the population of the most promising assignments of customers to vehicles. In the second level of the proposed algorithm, a Traveling Salesman Problem (TSP) is solved, independently for each member of the population and for each assignment to vehicles. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the average quality is less than 1%. More specifically in the set with the 14 classic instances proposed by Christofides, the quality is 0.479% and in the second set with the 20 large scale vehicle routing problems, the quality is 0.826%. The algorithm is ranked in the tenth place among the 36 most known and effective algorithms in the literature for the first set of instances and in the sixth place among the 16 algorithms for the second set of instances. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the Expanding Neighborhood Search Strategy is used.     

Polarity formation by a higher order interaction Markov-like chain

Vector property generation is discussed for chain growth by higher order interactions. Because of a deterministic property evolution a state space approach was used. Although not strictly Markovian, the system shows ergodic properties and convergence for a large number of attachment steps. For reasonable interaction energies attributed to increasing order, the main extra contribution to polarity formation results from interactions up to next nearest neighbours. Nonlinear equations up to third order were solved by an iterative procedure.     

A liquid derivative of 12-tungstophosphoric acid with unusually high conductivity

Surface functionalization of the solid heteropolyacid H3PW12O40 with a bulky PEG-containing quaternary ammonium cation through partial proton exchange leads to a polyoxometalate-based liquid salt with high-temperature proton conductivity ( approximately 10-3 S cm-1 at 140 degrees C) under dry conditions. The proton conductivity of the liquid salt is 4 orders of magnitude higher than that of the solid analogue under identical conditions and shows super ionic behavior as defined by Walden plot.     

Front initiation on microdesigned composite catalysts

We first briefly review the subject of spatiotemporal pattern formation on microdesigned composite catalysts. One of the most significant interaction mechanisms between different reacting domains (consisting of different metal catalysts such as Pt and Rh, coupled through surface diffusion) is the initiation of reaction fronts at the interface between them. We then explore in some detail the effect of two-dimensional composite geometry on this basic building block of composite catalyst dynamics. (c) 2002 American Institute of Physics.     

Vibration quenching in a large scale rotor-bearing system using journal bearings with variable geometry

In large scale rotating machinery the resonance amplitude during the passage through resonance is a matter of consideration because of its influence in the surrounding environment of the rotational system and foundation. In this paper, a variable geometry journal bearing (VGJB), recently patented, is applied for the mounting of a large scale rotor bearing system operating at the range of medium speed. The simulation of the rotor-bearing system incorporates a recent method for simulation of a multi-segment continuous rotor in combination with nonlinear bearing forces. The use of the current bearing gives results that encourage the use of such a bearing in rotating machinery since the vibration amplitude during the passage through the critical speed can be reduced up to 60–70%. In the presented study, the developed amplitude and the rotor stresses are severely reduced compared to those of the system with normal cylindrical journal bearings during a virtual start up of the system.     

Some combinatorial principles for trees and applications to tree families in Banach spaces

Suppose that is a normalized family in a Banach space indexed by the dyadic tree S. Using Stern's combinatorial theorem we extend important results from sequences in Banach spaces to tree‐families. More precisely, assuming that for any infinite chain β of S the sequence is weakly null, we prove that there exists a subtree T of S such that for any infinite chain β of T the sequence is nearly (resp., convexly) unconditional. In the case where is a family of continuous functions, under some additional assumptions, we prove the existence of a subtree T of S such that for any infinite chain β of T, the sequence is unconditional. Finally, in the more general setting where for any chain β, is a Schauder basic sequence, we obtain a dichotomy result concerning the semi‐boundedly completeness of the sequences .     

Nanomaterials in Cementitious Composites: An Update

This review is an update about the addition of nanomaterials in cementitious composites in order to improve their performance. The most common used nanomaterials for cementitious materials are carbon nanotubes, nanocellulose, nanographene, graphene oxide, nanosilica and nanoTiO₂. All these nanomaterials can improve the physical, mechanical, thermal and electrical properties of cementitious composites, for example increase their compressive and tensile strength, accelerate hydration, decrease porosity and enhance fire resistance. Cement based materials have a very complex nanostructure consisting of hydration products, crystals, unhydrated cement particles and nanoporosity where traditional reinforcement, which is at the macro and micro scale, is not effective. Nanomaterials can reinforce the nanoscale, which wasn’t possible heretofore, enhancing the performance of the cementitious matrix.     

A quantitative western blot technique using TMB: Comparison with the conventional technique

Numerous molecular biological experiments performed throughout the world require the detection or quantification of a protein of interest. Western blotting is one of the most popular techniques used for this purpose and offers quantitative information with the aid of specialized software. However, its dependence on the picture that is captured, and the background and the absence of a common protocol prevent the technique from being completely quantitative. To overcome these obstacles, we present a simple and reliable assay that is similar to the regular technique, with the exception of the last stage of band visualization and quantification. We propose that small pieces of the blot that include the protein of interest can be cut and dipped in a small volume of 3,3',5,5'-tetramethylbenzidine solution, giving a colorimetric signal with linear dependence on the quantity of the protein. The reaction is stopped with H₂SO₄, and the signal is measured in a plate reader. This modification shows high linearity without additional costs and can be applied for both purified proteins and proteins found in a lysate. The results obtained with our proposed technique were compared with those obtained by the conventional method and proved to be more reliable.