Analysis Of Dynamic Performances For Composite Laminated Structures Subjected To Arbitrary Boundary And Coupling Conditions

With the rapid development of the manufacturing process and the continuous increase of the requirements of structure design,the composite laminated structures,having excellent properties,have been extensively used with single or coupling forms in various engineering fields,such as aviation,aerospace,naval vessels,automobile,sports equipment and civil industries and so on.In all these practical engineering,the dynamic performances of composite laminated structures are the decisive factor for guaranteeing the safety and reliable of the whole equipment constructed by such structures.From the review for the existing modelling theories and analysis methods,one can found that most of them are confined to the classical boundary and coupling conditions,i.e.,free,simply-supported and clamped boundary as well as rigid coupling conditions.However,instead of the ideal classical boundary and coupling conditions which are unrealistic in many engineering applications,the arbitrary boundary and coupling conditions are more universal.Therefore,presenting an complete understanding of the dynamic performances of composite laminated structures with arbitrary boundary and coupling conditions,and performing an detail parametric study for such the engineering structures are of great theoretical significance and has practical importance.In this paper,focused on modelling theory and the method of reverberation ray matrix,the following research contents are carried out:First of all,on the basis of the macromechanics theory and the orthotropic elasticity theory,the kinematic equations of three-dimension elastic body and the constitutive equations are obtained.Moreover,a unified procedure for deducing the governing differential equations and the appropriate boundary conditions are presented via the Hamilton’s principle.Thus,the modelling theory of composite laminated structures is given in the generalized view.At the same time,the MRRM is extended to analyze the dynamic performance of composite laminated structures subjected to arbitrary boundary and coupling conditions.For the different analysis projects,the MRRM equation is combined with various appropriate solving schemes to calculate the dynamic results.Furthermore,a basic process for the dynamic analysis of composite laminated structures with arbitrary boundary and coupling conditions is summarized.Secondly,a unified analysis model for the dynamic performances of composite laminated beam structures with arbitrary lamination schemes and boundary conditions,on aPasternak elastic foundation is presented by using different plane assumptions,in which the Pasternak elastic foundation consists of Winkler-type and shear layers.The wave solutions are constructed by the exact closed-form solutions of the governing differential equations on the basis of the classical beam theory and the first-order shear deformation beam theory.At the ends of beam,the artificial virtual boundary technique is applied with arranging two groups of linear displacement springs and one group of rotation springs.By adjusting the stiffness values of these boundary springs,arbitrary boundary conditions can be achieved.The natural frequencies and the transient responses of composite laminated beam structures subjected to the arbitrary external excitations are obtained by the means of the MRRM.The excellent accuracy,reliability and efficiency of the current unified analysis model and solution methods are fully demonstrated and verified through numerical examples.Meanwhile,a systematic parametric investigation is performed regarding the effects of shear deformation and inertia rotary,elastic restraint parameters,foundation stiffnesses,plane assumptions,lamination schemes,material properties,geometry parameters.Thirdly,the MRRM is further extended to analyze the dynamic performances of composite laminated panel structures on a Pasternak elastic foundation and subjected to arbitrary boundary conditions.According to the characteristics of curvatures for laminated panel structures,some addition assumptions are adopted to the traditional shell theories,and then the classical shallow shell theory and the first-order shear deformation shallow shell theory are presented.In order to employed the MRRM for the two-dimension structures,the Lévy’s exact closed-form solutions are used to perform a dimension reduction process on the governing differential equations,and construct the wave solutions which are suitable for the MRRM formulations.By applying the artificial virtual boundary technique,the non-simply-supported edges are restrained by linear springs and rotational springs,which are distributed along the two edges continuously and have the directions corresponding to the generalized displacements.Thus,the generalized forces along the two edges are simulated and the arbitrary boundary conditions can be imitated.Several numerical cases are presented to test and verify the accuracy,reliability and efficiency of the present modelling theories and method.Moreover,the influences of the shallow shell theories and foundation parameters on the free vibration characteristic,as well as the boundary parameters,lamination schemes,material properties,geometry parameters and load types on transient response are discussed indetail.Fourthly,for the first time,a simple first-order shear deformation shell theory(S-FSDST)is presented for the dynamic analysis of composite laminated stiffened open cylindrical shells with arbitrary boundary and coupling conditions.Unlike the existing first-order shear deformation shell theory,the S-FSDST contains only four unknowns and has strong similarities with the classical shell theory in many aspects such as governing differential equations,boundary conditions,strains and stress resultant expressions.Hence,the S-FSDST can also be regarded as an enhanced classical shell theory with the consideration of the effects of shear deformation and rotary inertia terms.Based on the present theory,the extended MRRM is employed to analyze the free vibration characteristic of the non-stiffened open cylindrical shells and the steady state response of the stiffened open cylindrical shells.Under the current framework,the artificial virtual boundary technique and the artificial virtual coupling technique are used to separately simulate the arbitrary boundary and coupling conditions.And the stiffeners are treated as the composite laminated curved beams on a Pasternak elastic foundation.Numerical comparison studies show that the S-FSDST has a better performance than the existing theories,on both the accuracy and efficiency aspects.Simultaneously,parametric studies regarding the influences of boundary parameters and stiffener parameters on non-stiffened or stiffened open cylindrical shells are carried out respectively.Finally,based on the above research,the dynamic performances of composite laminated coupled plates structures with arbitrary boundary and coupling conditions are further analyzed.Many researchers have studied the dynamic performances for the coupled plate structure of traditional materials,but no work related to the considered topic has been published.In this paper,the free vibration characteristic and the propagation of power flow are studied by utilized the extended MRRM.Along the edges of such structure,the artificial virtual boundary technique is used to achieve the arbitrary boundary conditions.Along the coupling edges of the substructures,the generalized forces and displacements are firstly transformed into the global coordinate system according to the coordinate transformation relations.Then,the artificial virtual coupling technique are applied,where certain supporting springs and coupling springs are adopted along the directions of the generalized displacements in the global coordinate system.By changing the stiffness values of these springs,the generalized displacement continuity and generalized force equilibrium conditions can be adjustedarbitrarily,which lead to the arbitrary coupling conditions.The numerical simulations for the common “L”,“T” and “ 口 ”-type coupled plates verify that the present method has the superior computing performance and won’t limited by the number and coupling angle of the coupled plates.On this basis,the effects of the material properties and coupling parameters on the power flow and its transmission efficiency are also investigate respectively.