Three-Dimensional Solutions for Free Vibrations of Initially-Stressed Thermoelectroelastic Multilayered Plates

Author(s):  
Kangming Xu ◽  
Ahmed K. Noor ◽  
Yvette Y. Tang
2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.


2018 ◽  
Vol 33 ◽  
pp. 02033
Author(s):  
Vladimir Agapov

The necessity of new approaches to the modeling of rods in the analysis of high-rise constructions is justified. The possibility of the application of the three-dimensional superelements of rods with rectangular cross section for the static and dynamic calculation of the bar and combined structures is considered. The results of the eighteen-story spatial frame free vibrations analysis using both one-dimensional and three-dimensional models of rods are presented. A comparative analysis of the obtained results is carried out and the conclusions on the possibility of three-dimensional superelements application in static and dynamic analysis of high-rise constructions are given on its basis.


1996 ◽  
Vol 49 (3) ◽  
pp. 155-199 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton ◽  
Charles W. Bert

The focus of this review is on the hierarchy of computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters. The literature reviewed is devoted to the following application areas: heat transfer problems; thermal and mechanical stresses (including boundary layer and edge stresses); free vibrations and damping; transient dynamic response; bifurcation buckling, local buckling, face-sheet wrinkling and core crimping; large deflection and postbuckling problems; effects of discontinuities (eg, cutouts and stiffeners), and geometric changes (eg, tapered thickness); damage and failure of sandwich structures; experimental studies; optimization and design studies. Over 800 relevant references are cited in this review, and another 559 references are included in a supplemental bibliography for completeness. Extensive numerical results are presented for thermally stressed sandwich panels with composite face sheets showing the effects of variation in their geometric and material parameters on the accuracy of the free vibration response, and the sensitivity coefficients predicted by eight different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the analytic three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of sandwich plates and shells are outlined.


2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.


1998 ◽  
Vol 65 (4) ◽  
pp. 820-828 ◽  
Author(s):  
E. Carrera

This paper presents the dynamic analysis of multilayered plates using layer-wise mixed theories. With respect to existing two-dimensional theories at the displacement formulated, the proposed models a priori fulfill the continuity of transverse shear and normal stress components at each interface between two adjacent layers. A Reissner’s mixed variational equation is employed to derive the differential equations, in terms of the introduced stress and displacement variables, that govern the dynamic equilibrium and compatibility of each layer. The continuity conditions at the interfaces are used to write corresponding equations at multilayered level. Related standard displacement formulations, based on the principle of virtual displacements, are given for comparison purposes. Numerical results are presented for the free-vibration response (fundamental and higher order frequencies are calculated) of symmetrically and unsymmetrically laminated cross-ply plates. Several comparisons to three-dimensional elasticity analysis and to some available results, related to both layer-wise and equivalent single-layer theories, have shown that the presented mixed models: (1) match the exact three-dimensional results very well and (2) lead to a better description in comparison to results related to other available analysis.


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