In this paper, the analytical solution of the SH wave propagation problems in shear modulus and density continuous nonhomogeneous medium is given based on the complex variable function method, and the scattering
Fig. 10 shows the scatter plot of the TRE, in millimeters, with respect to the angle, ϕ, in degrees, obtained using the internal system of reference and cylindrical coordinates. Using real values for describing the angle the correlation is R=0.34. When the ϕ is considered in absolute ...
Because the current is restricted to flow on the surface of a cylinder of radius a and has only angular and axial dependence, the relation between the current density and the stream function in cylindrical coordinates is: ##EQU6## and Spis found from: ##EQU7## The contour plots of the ...
We introduce a Cartesian coordinate system Oxyz with the z-direction along the axis of the cylindrical beam and parallel to its generators. The beam is assumed to be of length L and one of its bases is taken to lie on the xy-plane, where z=0. The beam is loaded in torsion by ...
To obtain the unknown vertex coordinates, the Poisson equation requires a discrete guidance vector field for each of the three coordinates. Once a discrete guidance vector field is introduced over the parameterization mesh, its divergence, defined in (4), at a vertex of the parameterization mesh ...
Find the unit vector in the xy-plane that is perpendicular to vector A. What is the sum of the following four vectors in unit-vector notation? Write the vector F = 4x + 6y + 2z In cylindrical coordinates at point (x=2, y=3, z=4). Determine if the following...
For this, based on the proposed example in Sect. 4.1 in the work by Reese et al. [107], we propose a notched cylindrical shell subjected to an extreme bending load. Fig. 2 Isommetric view from the deformed of the benchmark problem run with (a) Q1 and (b) Q1P0 algorithms, ...
In this section, we develop a general method for smoothing functions on surfaces, which are represented by triangular meshes. The proposed algorithm consists of several steps: optimization of the SF, extraction of the surface mesh information, a smoothing of the operator structuring, a smoothing pro...
where, δ and 𝑡t are variation operator and time coordinate respectively, which the latter one changes between interval 𝑡0t0 to 𝑡1t1. According to Equation (13), the equations of motion of the sandwich composite plate are derived by variational calculation of 𝜑𝑥φx, 𝜑𝑦φy...