In this study, free vibration analysis of conical and cylindrical shells and annular plates made of composite laminated and functionally graded materials (FGMs) is investigated. Carbon nanotubes reinforced (CNTR) composite case is also taken consideration for FGM. The equations of motion for conical shell are obtained via Hamilton's principle using the transverse shear deformation theory. To obtain the eigenvalue problem of the system, the method of discrete singular convolution is employed. Material properties are graded in the thickness direction according to a volume fraction power law and four-parameter power law indexes for FGM cases. Five types of distributions of CNTR material are also considered. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. Free vibrations of cylindrical shells and annular plates with FGM are treated as special cases. Results are also presented for carbon nanotubes reinforced (CNTR) composite cylindrical shells and annular plates. It is found that the convergence and accuracy of the present DSC method is very good for vibration problem of shells with functionally graded materials (FMG) and CNTR functionally graded materials.

Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method

Introduction T purpose of this Survey is to review and bring together in an orderly fashion some of the principal contributions to the field of structural mechanics of structures containing composite materials. The topics of micromechanics and fracture, while quite important, are not considered in this Survey. Emphasis is given to the macromechanical structural analysis of various structural elements, including response under conditions of stable static loading, buckling, and dynamics. The Survey unfolds in the following sequence: Straight and Curved Laminated Bars, Laminated Plates, Laminated Shells, Sandwich Structures, Applications to Practical Structural Systems, and Future Trends. The authors hope that this contribution will be a useful reference tool for researchers and engineers already involved in structural aspects of advanced composites, as well as for those who are just entering the field. No Survey can do full justice to such a wide field as compositematerial structural mechanics. The references cited give only a glimpse of the extensive literature in this field. The authors apologize for not citing a number of important contributions in the field.

Composite Material Mechanics: Structural Mechanics

Free vibration of orthotropic conical shells

This paper presents a 4-node facet type quadrangular shell finite element, based on a layerwise theory, developed for dynamic modelling of laminated structures with viscoelastic damping layers. The bending stiffness of the facet shell element is based on the Reissner–Mindlin assumptions and the plate theory is enriched with a shear locking protection adopting the MITC approach. The membrane component is corrected by using incompatible quadratic modes and the drilling degrees of freedom are introduced through a fictitious stiffness stabilization matrix. Linear static tests, using several pathological tests, showed good and convergent results. Dynamic analysis evaluation is provided by using two eigenproblems with exact analytical solution, as well as a conical sandwich shell with a closed-form analytical solution and a semi-analytical ring finite element solution. The applicability of the proposed finite element to viscoelastic core sandwich plates is assessed through experimental validation.

A generalized layerwise finite element for multi-layer damping treatments

We experimentally examine the amplitude of a bluff body undergoing vortex-induced vibration (VIV) supported by linear and various nonlinear structural forces. This investigation is made possible by our Cyber-Physical Fluid Dynamics force-feedback technique; using it, we can impose arbitrary nonlinear restoring forces on a circular cylinder in our water channel. For the range of nonlinearities examined, detailed analysis allows one to understand and predict the response of the nonlinear structural system using knowledge of a standard, linear VIV system. We also present a case study examining the potential of nonlinear springs to aid in a VIV-based energy harvesting device. Appropriate choices of the spring's nonlinearity allow the hypothetical energy harvester to operate at high performance over a much larger range of Reynolds number than a standard system.

D.J. Wilkins

Papers

Free vibrations of orthotropic sandwich conical shells with various boundary conditions

Optimal design of a non-linear dynamic absorber