Research On Modeling Theories And Computation Methods For The Vibration Of Multilayered Structures

With the rapid development of new industries,traditional structures made form single homogeneous materials can not satisfy the diversified demands of engineering applications because of the limitations of environment resources or their own inability in comprehensive performance.Instead of the traditional structures,multilayered structures made by composite are increasingly used in many fields of modern engineering applications,such as surface warships,underwater vehicles,marine risers,due to their high modulus and specific strength,outstanding designability characteristic etc.Compared with the traditional structure,the dynamic characteristics of multilayered structures are rare complex due to the laminarity and the anisotropy of material.Therefore,it is necessary to consider not only the individual characteristics of each layer,but also the coupling between displacement and stress fields.After extensive literature review,it is found that most researchers modeled the multilayered structure using the equivalent single layer(ESL)theories thus reduce the 3-D problems to a variety of 2-D or 1-D representations.In the ESL theories,an equivalent layer is studied and consequently,the displacements are considered continuous and differentiable through the interface,which no-doubt violates the interlaminate stress continuity conditions.To analyze thick laminated structures,more advanced theories accounts for all the transverse stress and strain components are need to provide reliable and accurate solutions to ensure safe and successful structure designs.Moreover,in engineering applications,the boundary conditions and lamination of a multilayered structure may not always be classical and cross-ply in nature.A variety of possible boundary conditions and lamination cases can be encountered in practical.The existing solution methods are often only customized for a specific lamination and a set of different classical boundary conditions,and thus typically require constant modifications of the solution procedures to adapt to different boundary and lamination cases which may result in very tedious calculations.Therefore,it is necessary to develop more accurate,efficient theories and methods which are capable of universally dealing with multilayered structures with different boundary conditions,general laminations as well as arbitrary thickness.Against this background,the following research work has been carried out in this dissertation.Taking aim at the shortage of the existing two-dimensional methods that are often only customized for a specific set of classical boundary conditions such as free,simply-supported and clamped cases,a general two-dimensional spectral method which are capable of universally dealing with multilayered structures with different boundary conditions is proposed.In this method,the displacement field of a structure is approximated by the traditional spectral method and the boundary conditions are then stated in a variational form by the aid of penalty parameters and Lagrange multipliers which provides complete flexibility to describe any arbitrary boundary conditions.It should be remarked here that present method makes the choice of admissible functions quite flexible;any linearly independent,complete basis functions may be employed.Moreover,the proposed method offers an easy analysis operation for the entire restraining conditions and the change of boundary conditions from one case to another is as easy as changing structure parameters without the need of making any change to the solution procedure.Numerical verification shows that the proposed method converge rapidly and has better numerical stability.In order to overcome the drawback of the existing three-dimensional methods that are only confined for very limited cases such as cross-ply laminated rectangular plates under simply-supported boundary conditions,a general three-dimensional spectral-differential quadrature method which are capable of universally dealing with multilayered structures with different boundary conditions and arbitrary layout is proposed.This method is undertaken by the exact 3-D elasticity theory so that it’s able to study very well the dynamic behavior of thick multilayered structures.In each individual layer,the transverse domain is discretized by the differential quadrature technique.The displacement fields of discretized surfaces are selected as the fundamental unknowns.Then,each fundamental unknown is invariantly expanded by the general spectral method and the problems are stated in a variational form by the aid of penalty parameters and Lagrange multipliers which provides complete flexibility to describe any prescribed boundary conditions.The current method successfully avoids solving a highly nonlinear transcendental equation that is rely on roots-locating numerical method and all the modal information can be obtained just by solving linear algebraic equation systems.Numerical verification shows that the proposed method has high calculation precision.In view of low modeling precision of the ESL theories and high computation cost of the three-dimensional elasticity laminated theory,a Chebyshev polynomials based high order layerwise theory is proposed.The theory has an ability of achieving arbitrary modeling precision according to practical requirements.The displacement field in each discrete layer through the thickness of the laminate includes Chebyshev polynomial distributions of the in-plane displacements,in addition to the linear approximations assumed by linear layerwise theories.The proposed theory also offers an easy analysis operation to realize different modeling precision requirements only by changing the truncation order without the need of reprogramming form case to case.From the large amount of the literature survey,this work appears to be the first time to obtain 2-D elasticity solution for laminated curved beams with variable curvatures,arbitrary lamination schemes and general restraints as well as 3-D elasticity solution for laminated plates and cylindrical shells with arbitrary lamination schemes and general boundary conditions which may fill a gap in the literature.