In this study Trapezon’s result is generalized on bending oscillation of beams of constant thickness whose width varies in accordance with a fourth order parabola. The existence of a closed formula is shown, which offers solution not only for a fourth order parabola but for every power function describing the width of the beam. In particular, if the exponent is a power of 2 then also the closed form of the general solution can be given.
In this paper Maple general-purpose computer algebra system is used to find closed-form solution for the vibration of inhomogeneous beam with a translational spring at one of its end and clamped at the other end. Instead of using linear algebra to find the form of acceptable mode shape and flexural rigidity, calculus tools are introduced to find the general solution of the differential equation. In the second part of the article it is shown how Maple can be used in the course of engineering calculations.
Sub corona vendere. Quellenkritische Studien zu Kriegsgefangenschaft und Sklaverei in Rom bis zum Ende des Hannibalkrieges. Von Karl-Wilhelm Welwei; Pierre Sanchez: L'Amphictionie des Pyles et de Delphes
The aim of this paper is to find a closed form of the integrals ∫
= 0, 1, 2, … using the Maple computer algebra system. Although Maple 10 is not capable to calculate these integrals in one step, it turns out to be a very useful tool to solve this and similar kind of complex mathematical problems. During the problem solving process Maple proves that it is useful and, what is more, it is an indispensable partner. Maple helps us to formulate our conjecture, acts as an advisor and, last but not least, performs complex symbolic calculation instead of us.
In his study Aydogdu analyzed the vibration and buckling of axially functionally graded simply supported beams. By using pre-defined frequency and buckling loads he determined the Young’s modulus in axial direction as a function of axial coordinate. In this study it is demonstrated that there is error in his calculation; moreover, corrected computation is presented and the right solution of the ODE is visualized. It is pointed out that the method used by Aydogdu is apparently not applicable for the solution of the problem at hand.