Quadrature of Differential Equations

 A differential quadrature element method (DQEM) based on first order shear deformation theory is developed for free vibration analysis of non-uniform beams on elastic foundations. By decomposing the system into a series of sub-domains or elements, any discontinuity in loading, geometry, material properties, and even elastic foundations can be considered conveniently. Using this method, the vibration analysis of general beam-like structures is to be studied. The governing equations of each element, natural compatibility conditions at the interface of two adjacent elements and the external boundary conditions are developed in a systematic manner, using Hamilton's principle. The present DQEM is to be implemented to Timoshenko beams resting on partially supported elastic foundations with various types of boundary conditions under the action of axial loading. The general versality, accuracy, and efficiency of the presented DQEM are demonstrated having solved different examples and compared to the exact or other numerical procedure solutions.

A1 6 112 Gb/s field transmission trial was suc- cessfully performed over legacy fiber infrastructure of Deutsche Telekom comprising partially high polarization mode dispersion (PMD) values of 8 ps. Using a commercial PMD compensator, transmission over high PMD with negligible penalty was achieved. Enabled by the maturity of 43 Gb/s components, a 112 Gb/s nonreturn to zero (NRZ) differential quadrature phase-shift keying modulation format for dense wavelength division mul- tiplexing transmissions with good system margins of 5 dB over 450 km metro distances (3 dB over 764 km) was demonstrated. By using high baud rate of 56 Gbd, penalty-free transmission is performed when copropagating with either 10.7 Gb/s NRZ or 43 Gb/s phase-shaped binary transmission signal channels. Index Terms—Copropagation with 10 and 40 Gb/s dense wavelength division multiplexing (DWDM) signals, differential quadrature phase-shift keying (DQPSK) modulation format, field trial, metro systems, polarization mode dispersion (PMD) compensation, 100 Gb/s transmission.

In this paper, two computationally efficient and accurate solution methods for transient dynamic analysis of functionally graded (FG) cylindrical shells subjected to internal dynamic pressure are presented. In order to accurately account for the thickness effects, the layerwise theory is employed to approximate the displacement components in the radial direction. In the first solution method, differential quadrature method (DQM) is implemented to discretize the resulting equations in the both spatial and time domains. In the second approach, DQM is applied to discretize equations in the axial direction while Newmark’s time integration scheme is used to solve the problem in the time domain. The fast convergence rate of the methods is demonstrated and their accuracy is verified by comparing the results with those obtained using ANSYS and also with available exact solution of a particular problem. Considerable less computational efforts of the proposed approaches with respect to the fi...

A new methodology is introduced in the differential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a different manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of difficulty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and/or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods. Copyright © 2002 John Wiley & Sons, Ltd.

This paper deals with the dynamic response of initially stressed functionally graded rectangular thin plates subjected to partially distributed impulsive lateral loads and without or resting on an elastic foundation. Material properties are assumed to be temperature-dependent, and ...

This paper reviews most of the recent research done in the field of dynamic stability/dynamic instability/parametric excitation/parametric resonance characteristics of structures with special attention to parametric excitation of plate and shell structures. The solution of dynamic stability problems involves derivation of the equation of motion, discretization, and determination of dynamic instability regions of the structures. The purpose of this study is to review most of the recent research on dynamic stability in terms of the geometry (plates, cylindrical, spherical, and conical shells), type of loading (uniaxial uniform, patch, point loading …), boundary conditions (SSSS, SCSC, CCCC …), method of analysis (exact, finite strip, finite difference, finite element, differential quadrature, and experimental …), method of determination of dynamic instability regions (Lyapunovian, perturbation, and Floquet’s methods), order of theory being applied (thin, thick, three-dimensional, nonl...