Thomas G. Chondros

Identification of cracks in welded joints of complex structures

Abstract The problem of the influence of a crack in a welded joint on the dynamic behaviour of a structural member is discussed in this work. Analytical and experimental investigation gave the relation between the change in natural frequency of vibration of a cantilever beam and the crack depth that appears at the built-in edge which is clamped by way of a weld. Measurement of the change of the natural frequency of the beam thus can give information for crack appearance and furthermore make possible the estimation of its depth. The results have been used to determine the behaviour of beams with different boundary conditions and can be extended to formed structures with complicated geometries.

Dynamic Sensitivity of Structures to Cracks

Cracks that develop on machine members and structures influence their dynamic behavior. The Rayleigh principle is used for an estimation of the change in the natural frequencies and modes of vibation of the structure if the crack geometry is known, assuming that the eigenvalue problem for the uncracked structure has been solved in advance. The method reduces the computational effort needed for the full eigensolution of cracked structures and gives acceptable accuracy. It can be extended to higher modes and to decompose degenerate modes found in symmetric structures. To demonstrate the change in the dynamic behavior of linear structures with the crack depth, a cylindrical shaft and a plane frame consisting of prismatic bars were analyzed for dynamic sensitivity to surface cracks.

LONGITUDINAL VIBRATION OF A BAR WITH A BREATHING CRACK

Abstract The dynamics of a cracked fixed-free bar with a breathing crack in longitudinal vibration is investigated. The Hu–Washizu–Barr variational formulation was used to develop the equation of motion and the boundary conditions of the cracked bar as a one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The eigenfrequency changes due to a single open-edge breathing crack, are shown to depend on the bilinear character of the system. The associated linear problems are solved over their respective domain of definition and then the solutions are matched through the initial conditions. These changes are smaller than the ones caused by open cracks. The method has been tested for different bar configurations corresponding to crack location, crack depths, cross-section dimensions, and Poisson’s ratio. The natural frequencies obtained from this model agree well with experimental results.

Longitudinal vibration of a continuous cracked bar

Abstract A continuous cracked bar vibration theory is developed for longitudinal vibration of rods with an edge crack. The Hu–Washizu–Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked bar as a one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of longitudinal vibrations of a bar with a single edge crack are presented: the continuous cracked bar vibration theory, the lumped crack bar vibration analysis, and experimental results obtained on aluminum bars with fatigue cracks. Experimental results fall between the values predicted by the two analytical methods. Moreover, the continuous bar theory agrees better with the experimental results than the lumped crack flexibility theory for small cracks. For larger cracks, a / h >0.4, experimentation was difficult due to the co-existence of several coupled modes and no reliable results could be obtained.

Variational formulation of a rod under torsional vibration for crack identification

In Chap. 10 the Hu-Washizu-Barr variational formulation is used for the development of the differential equation and boundary conditions for a cracked rod. Based on the general variational principle and independent assumptions about displacement, momentum, strain and stress fields of the cracked rod with one or more pairs of transverse symmetrically disposed open edge cracks along its length, the equations of motion in torsional vibration were derived. Crack is introduced as a stress disturbance function, and stress field is determined by fracture mechanics methods. Strain energy density theory has been used for an accurate evaluation of the stress disturbance function. The strain energy density criterion is based on local density of the energy field in the crack tip region, and no special assumptions on the direction in which the energy released by the separating crack surfaces is required.

The Development of Machine Design as a Science from Classical Times to Modern Era

Developments in natural philosophy and the scientific method in the 6th and 5th Centuries BCled to rapid development of engineering design in the 4th to 1st Centuries BCin the Greek and Hellenistic world, reaching maturity in the Roman Empire after the 2nd Century ADwhen Greek mathematical works started being translated into Latin. Design rules and concepts were practiced extensively by the engineers of ancient times leading to machine design from machine elements to the design of a machine as a system. Purely mechanical treatises on machinery go back to the 4th century BC.For the solution of mechanical problems and the design of equipment many basic scientific principles had to be explained at this time, and also trial and experimentation was established. The process of engineering design evolution from the 4th century BCup to modern era is discussed here.

“Deus-Ex-Machina” Reconstruction and Dynamics

In some ancient Greek drama, an apparently insoluble crisis was solved by the intervention of a god often brought on stage by an elaborate piece of equipment. This “god from the machine” was literally a Deus Ex Machina. Archaeological evidences and descriptions of mechanisms used in the ancient Greek theatre were investigated in an attempt to reconstruct the Deus Ex Machina. None of these machines, made of perishable materials is extant. However, from the numerous references to such machines in extant tragedies or comedies and vase paintings, information about its design and operation is available. Static and dynamic analysis and simulation of the mechanism kinematics were performed. The reconstructed mechanism is a spatial three or four bar linkage designed for path generation.

Archimedes (287–212 BC)

Archimedes (ca. 287–212 BC) was born in Syracuse, in the Greek colony of Sicily. He studied mathematics at the Museum in Alexandria. Archimedes systematized the design of simple machines and the study of their functions. He was probably the inventor of the compound pulley and developed a rigorous theory of levers and the kinematics of the screw. He is the founder of statics and of hydrostatics, and his machine designs fascinated subsequent writers. Archimedes was both a great engineer and a great inventor, but his books concentrated on applied mathematics and mechanics and rigorous mathematical proofs. Archimedes was also known as an outstanding astronomer; his observations of solstices were used by other astronomers of the era.

Reliability of hot water solar systems in Greece

Ten thousand domestic hot water solar systems were surveyed in Greece to assess component and system reliability. Data concerning the functioning condition of the systems was collected, a computerized data base was established and statistical analysis was performed. This work is part of a solar system evaluation program within the European Community. Greece was selected due to the high concentration of solar collector systems and the fact that these systems have reached maturity, the average lifespan being five years.

DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK BASED FAULT DIAGNOSTIC SYSTEM OF AN ELECTRIC CAR

In this paper, the authors describe the development of a fault diagnostic system for an electric vehicle based on artificial neural networks (ANN). The system is able to compare measured and predicted temperatures from the two motors of the electric vehicle and then give an error reading when a difference greater than a user defined tolerance results.