M. Cengiz Dökmeci

Bio: M. Cengiz Dökmeci is an academic researcher from Istanbul Technical University. The author has contributed to research in topics: Variational principle & Boundary value problem. The author has an hindex of 16, co-authored 43 publications receiving 676 citations. Previous affiliations of M. Cengiz Dökmeci include Yıldız Technical University & Northwestern University.

Theory of vibrations of coated, thermopiezoelectric laminae

Abstract: This study presents a theory for dynamic problems of coated laminae in which there is coupling between mechanical and electrical as well as thermal fields. The laminae is coated completely with perfectly conducting electrodes on both its faces, and it may comprise any number of bonded layers, each with a distinct but uniform thickness, curvature and electromechanical properties. First, a generalized variational theorem is derived so as to describe the complete set of the fundamental equations of thermopiezoelectricity. Next, by the use of this theorem, a system of two‐dimensional, approximate governing equations of the coated laminae is constructed for the case when the mechanical displacement, electric potential, and temperature fields vary linearly across the laminae thickness. The effects of elastic stiffnesses of, and the interactions between, layers of the laminae and its electrodes are all taken into account. Also, the uniqueness of the governing equations is examined, and a theorem which includes the conditions sufficient for the uniqueness is given.

About heat waves

Abstract: In 1982, the Belgian Pilots' Guild raised the question of what effect exposure to radar radiation--for example, that encountered in passing a pilot launch's radar--might have on the human body. Recapitulating investigations of this question, this article states that in 25 years of experience with radar, there have been no known incidents of pilots being affected by radar waves. In the future, however, involvement by some pilots with Vessel Traffic Service shore-based radar could affect pilots somewhat differently from limited exposure to pilot launch radar. Pilots who find themselves in new working conditions close to an emitting source should exercise care all times.

Variational Principles in Mechanics

Abstract: The recognition that minimizing an integral function through variational methods (as in the last chapters) leads to the second-order differential equations of Euler-Lagrange for the minimizing function made it natural for mathematicians of the eighteenth century to ask for an integral quantity whose minimization would result in Newton’s equations of motion. With such a quantity, a new principle through which the universe acts would be obtained. The belief that “something” should be minimized was in fact a long-standing conviction of natural philosophers who felt that God had constructed the universe to operate in the most efficient manner—but how that efficiency was to be assessed was subject to interpretation. However, Fermat (1657) had already invoked such a principle successfully in declaring that light travels through a medium along the path of least time of transit. Indeed, it was by recognizing that the brachistochrone should give the least time of transit for light in an appropriate medium that Johann Bernoulli “proved” that it should be a cycloid in 1697. (See Problem 1.1.) And it was Johann Bernoulli who in 1717 suggested that static equilibrium might be characterized through requiring that the work done by the external forces during a small displacement from equilibrium should vanish. This “principle of virtual work” marked a departure from other minimizing principles in that it incorporated stationarity—even local stationarity—(tacitly) in its formulation. Efforts were made by Leibniz, by Euler, and most notably, by Lagrange to define a principle of least action (kinetic energy), but it was not until the last century that a truly satisfactory principle emerged, namely, Hamilton’s principle of stationary action (c. 1835) which was foreshadowed by Poisson (1809) and polished by Jacobi (1848) and his successors into an enduring landmark of human intellect, one, moreover, which has survived transition to both relativity and quantum mechanics. (See [L], [Fu] and Problems 8.11 8.12.)