In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical METHOD of GENERALIZED DIFFERENTIAL squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equations and boundary conditions are derived in the Cartesian coordinates. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinate into a new computational coordinates. GENERALIZED DIFFERENTIAL QUADRATURE METHOD (GDQM) is selected as a strong METHOD and natural frequencies and corresponding modes are derived. The accuracy and convergence of the proposed solution are confirmed using results presented by other authors. Finally, the effect of the power law index, angles and thickness of the plate on the natural frequencies are investigated.

In this research, behavior of a cylindrical sandwich panel with the flexible core in different boundary conditions, under the influence of follower force are studied. For this purpose, using the theory of the first-order shear deformation, and the principle of Hamilton, the governing equations have been extracted and by using GENERALIZED DIFFERENTIAL QUADRATURE METHOD (GDQM) are solved. The obtained results indicate that by considering simplicity of present METHOD compared to the other METHODs in the analysis of stability problems of the cylindrical sandwich panel, the present results have the acceptable accuracy. Also, the results review show that the flutter phenomenon occurs in the free and clamp boundary conditions and for other boundary conditions only the divergence phenomenon or static buckling occurs. Another significant result is that increasing the number of composite layers, makes the flutter phenomenon in the cylindrical sandwich panel with the flexible core occurs later.

This paper presents the application of the GENERALIZED DIFFERENTIAL QUADRATURE (GDQ) METHOD for the hydrodynamic analysis of circular and noncircular, two lobe and three lobe, journal bearings. GDQ is a simple, efficient, high-order numerical technique and it uses the information on all grid points to approach the derivatives of the unknown function. The effectiveness of the solution technique is verified by comparing the GDQ computed results with that of analytical solutions and FDM results from the published literature. It is found that GDQ METHOD can easily compete with the existing METHODs of solution of lubrication problems for its analytical simplicity, smaller computer storage requirements and capability of producing accurate results with very high computational efficiency. Also the effects of design and assemble parameters, namely the eccentricity ratio, preload factor, mount and tilt angles on the performance parameters of these bearings have been investigated using GDQ METHOD. Results show that the variation of mount and tilt angles can has variable effects on noncircular lobed journal bearing performance parameters. Among the two types of noncircular bearings considered, the effect of the mount and tilt angles is more significant for two lobe bearings in comparison with the three lobe bearings.

In this paper the GENERALIZED DIFFERENTIAL QUADRATURE METHOD (GDQM) is presented for easy and effective bending analysis of composite sandwich plates with symmetric angle-ply face sheets under static loading based on the first order shear deformation theory (FSDT). The bending behavior of composite sandwich plates with various combinations of boundary conditions is studied. The effects of fiber orientation, ratio of thickness to length of the plate, the ratio of thickness of core to thickness of the face sheet are studied on the transverse displacement rotation about mid-plane and moment resultants. Comparisons are made with the existing solutions. The obtained graphs give very good results due to optimum design of sandwich plates. It has been found that a fast convergent rate can be achieved by the GDQM with non-uniform grids and very accurate results are obtained.

This paper presents the application of GENERALIZED DIFFERENTIAL QUADRATURE (GDQ) METHOD for analysis of circular and non-circular (two-lobe) journal bearings, lubricated with micro polar fluid. GENERALIZED DIFFERENTIAL QUADRATURE is a simple, efficient, and high-order numerical technique, which uses the information on all sample grid points to approach the derivatives of the unknown function. The effectiveness of the solution technique is verified by comparing the GDQ computed results with previous results of circular journal bearing. It is seen from the results that GDQ METHOD can easily compete with existing METHODs of solution of lubrication problems for its analytical simplicity, less computer storage requirements, and capability of producing accurate results with a very high computational efficiency. Also, GDQ results for two-lobe journal bearing, lubricated with micro polar fluids, show an increase in load carrying capacity and decrease in the coefficient of friction, attitude angle, and side leakage for bearing in comparison with the same bearing lubricated with Newtonian fluid.

This study aims to determine the global buckling load of stiffened composite conical shells under axial compression. Stringers stiffen the conical shells in longitudinal and rings in circumferential directions. The boundary conditions are assumed to be simply supported at both ends. At first, the equilibrium equations are obtained using the first-order shear deformation theory and the principle of minimum potential energy. Effects of stiffeners (longitudinal and circumferential directions) are considered using the smearing technique. The resulting equations are solved using the GENERALIZED DIFFERENTIAL QUADRATURE METHOD to obtain the critical buckling load. The acquired results are compared with the finite element METHOD results and other researcher's results available in the literature, and good agreement is observed. The influence of the number of stiffeners and rings, length, radius, semi-vertex angle of the cone, and shear deformation on the shell's buckling behavior is studied. Finally, the optimum number of stiffeners (longitudinal and circumferential directions) to achieve the maximum global buckling load in a cross-ply composite conical shell with various stacking sequences for a specific weight and overall geometry is investigated.