An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part II: Applications

doi:10.1016/j.compstruct.2015.07.022

Composite Structures

Volume 132, 15 November 2015, Pages 1288-1302

https://doi.org/10.1016/j.compstruct.2015.07.022 Get rights and content

Abstract

An exact spectral-dynamic stiffness method (S-DSM) for free vibration analysis of composite plates and plate assemblies has been proposed in Part I of this two-part paper. The main purpose of this Part II paper is twofold: (i) To validate and demonstrate the superiority of the proposed S-DSM and (ii) To establish exact benchmark solutions for free vibration of composite plate-like structures. The S-DSM is applied to a number of problems covering orthotropic composite plates and plate assemblies. It is demonstrated that the S-DSM gives exact solutions with high computational efficiency within low as well as high frequency ranges. The applications are completely general and the new development can handle complex plate shapes with any boundary conditions.

Introduction

In Part I of this two-part paper [1], a novel method called the spectral-dynamic stiffness method (S-DSM) has been developed for exact free flexural vibration analysis of composite plate-like structures. The proposed method has no restrictions and is completely general to handle any boundary conditions covering any frequency range.

The intended aim of this Part II paper is to examine critically the elegance of the S-DSM presented in the Part I companion paper, particularly in terms of its efficiency, accuracy and versatility. Since the S-DSM provides flexibility to consider general composite plate-like structures with different geometries and material properties when subjected to different boundary conditions, a vast quantity of results can be computed. However, the main aim of this paper, which is basically a result paper, is to illustrate the benefits of the S-DSM in free vibration analysis of composite plate-like structures. A selective and carefully chosen sample of examples are given in this paper for composite plates and plate assemblies. The results computed by using the S-DSM are compared and contrasted with finite element solutions and other published results wherever possible. All of the S-DSM results presented are accurate up to all figures given in order to serve as benchmarks. It should be kept in mind that even through the theory in Part I paper allows consideration of rotatory inertia, results in this Part II paper are computed without the rotatory inertia effects for the convenience of validation (with existing results) and benchmarking purposes.

For notational convenience, Part I of this two-part paper is referred to as Part I paper. The reference of sections and equations in the Part I paper will be denoted as Section I-(section number) and Eq. I-(equation number) respectively. For example, Eq. (1) in the Part I paper is written in short form as Eq. I-(1) in this Part II paper and so on.

This Part II paper is organised as follows. In Section 2, the convergence, computational efficiency and numerical stability of the proposed spectral dynamic stiffness method (S-DSM) is examined and results are demonstrated quite comprehensively. More specifically, Section 2.1 illustrates the enormously high computational efficiency and numerical accuracy of the S-DSM, whereas Section 2.2 discusses the numerical stability of the method covering low to high frequency ranges. In Section 3, the S-DSM is applied to composite plates with different boundary conditions including classical and non-classical elastic constraints. The S-DSM applications for different practical engineering plate-like structures are illustrated in Section 4. This Part II paper is completed with conclusions in Section 5.

Section snippets

Convergence, efficiency and numerical stability analysis

As expected, the S-DSM gives highly accurate results very efficiently by using a relatively small number of terms in the series expansion. This is due to the completeness as well as the strong orthogonality of the series solution applied. Moreover, the series solution satisfies the governing differential equation exactly and provides complete flexibility to describe any arbitrary boundary conditions. The reason was explained in detail in Ref. [2] in the context of isotropic plates. It will be

Individual composite plates with different boundary conditions

Having demonstrated its high accuracy, efficiency and numerical stability, the S-DSM is now applied for free vibration analysis of composite plates against the background that the subject has been covered extensively in the literature. It appears that almost all of the existing results for composite plates in the literature are not sufficiently accurate in general. To address this issue, four representative problems are investigated here to provide exact results as benchmark solutions. These

Complex engineering structures with practical applications

In the previous section, the current S-DSM was applied to four cases of individual composite plates. These cases are clearly for non-Levy type plates. Such analyses in an exact sense prior to this research were not possible earlier by using the conventional DSM. The current results have demonstrated the exactness, high efficiency of the S-DSM for any frequency range. In this section, the assembly procedure (another important advantage of the S-DSM) is illustrated by applying the method to three

Conclusions

The spectral-dynamic stiffness method (S-DSM) developed in Part I of this two-part paper has been applied to a variety of plate-like structures including individual composite plates and complex plate assemblies with arbitrary boundary conditions. The comprehensive set of results obtained by the S-DSM are compared and contrasted with different other methods wherever possible, e.g., exact solution, finite element method, analytical methods like the superposition method, Ritz method and etc. These

Acknowledgements

The authors appreciate the support given by EPSRC (United Kingdom) through a Grant EP/J007706/1 which made this work possible.

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An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part II: Applications

Abstract

Introduction

Section snippets

Convergence, efficiency and numerical stability analysis

Individual composite plates with different boundary conditions

Complex engineering structures with practical applications

Conclusions

Acknowledgements

Compos Struct

Int J Solids Struct

J Sound Vibr

Thin-Walled Struct

J Sound Vibr

J Sound Vibr

J Sound Vibr

J Sound Vibr

J Sound Vibr

Int J Solids Struct

J Sound Vibr

J Sound Vibr

J Sound Vibr

Compos Struct

Compos Struct