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The dynamic stability of nano-tubes is an important issue in engineering applications. Dynamic stability of anti-symmetric coupled-carbon nanotubes (C-CNTs)-systems in thermal environment is presented in this paper. In this system, the top and bottom CNTs are subjected to axial harmonic load and action of the viscous fluid, respectively.

The coupling and surrounding mediums of the CNTs are simulated by visco-Pasternak foundation containing the spring, shear and damper coefficients. Based on the Timoshenko beam theory and Hamilton’s principle, the coupled motion equations are derived considering size effects using Eringen’s nonlocal theory. Using the exact solution in conjunction with Bolotin’s method, the dynamic instability region (DIR) of the coupled structure is obtained. The effects of various parameters such as small scale parameter, Knudsen number, fluid velocity, static load factor, temperature change, surrounding medium and nanotubes aspect ratio are shown on the DIR of the coupled system.

Results indicate that considering parameters such as small scale effects, static load factor, Knudsen number and fluid velocity shifts the DIR of C-CNTs to a lower frequency zone.

To the best of our knowledge, analyses of anti-symmetric coupled CNTs have not received enough attentions so far. In order to optimize the nanostructures designing, the main purpose of the present paper is to investigate nonlocal dynamic stability of CNTs subjected to axial harmonic load coupled with CNTs conveying fluid.

The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

By extending the idea of conjugate gradient (CG) method, the authors present two iterative methods to solve the general coupled matrix equations over the generalized centro‐symmetric and central antisymmetric matrices.

When the general coupled matrix equations are consistent over the generalized centro‐symmetric and central anti‐symmetric matrices, the generalized centro‐symmetric and central anti‐symmetric solutions can be obtained within nite iterative steps. Also the least Frobenius norm generalized centrosymmetric and central anti‐symmetric solutions can be derived by choosing a special kind of initial matrices. Furthermore, the optimal approximation generalized centrosymmetric and central anti‐symmetric solutions to given generalized centro‐symmetric and central anti‐symmetric matrices can be obtained by finding the least Frobenius norm generalized centro‐symmetric and central anti‐symmetric solutions of new matrix equations. The authors employ some numerical examples to support the theoretical results of this paper. Finally, the application of the presented methods is highlighted for solving the projected generalized continuous‐time algebraic Lyapunov equations (GCALE).

By the algorithms, the solvability of the general coupled matrix equations over generalized centro‐symmetric and central anti‐symmetric matrices can be determined automatically. The convergence results of the iterative algorithms are also proposed. Several examples and an application are given to show the efficiency of the presented methods.

THE subject of flutter is universally recognised as a difficult one, and I think it will be agreed that much work remains to be done before our knowledge is sufficient for the everyday needs of the designer. It is not that our scientists and mathematicians have been found wanting, however, for the literature on the subject is extensive and the present rate of production of papers bearing on flutter is higher than ever. But, from the point of view of the man who wishes to have a broad grasp of essential principles, the sheer quantity of theoretical material alone is bewildering.

The analysis of the wing/fuselage and fuselage/tail unit interaction forces is extended to cover the case when the attached component is more conveniently analysed by the Matrix Displacement Method. The flexibility matrix of the complete aircraft, supported on the wing/fuselage attachment points, follows from the results derived in this and previous sections and takes into account the elastic interaction between the various components. The dynamical matrix of the complete free aircraft is set up and for completeness the theory and properties of the normal modes of vibration are given. A final sub‐section discusses some points of detail in the mass distribution and the definition of the forces on the aircraft.

The purpose of this paper is to demonstrate new design concepts for 24 classes of laminate, which have been derived as part of an ongoing study on the development of a unified approach to the characterization of coupled laminates. The paper presents a description of each class of coupled laminate.

The paper gives an overview of the desired performance and requirements of a smart leading edge device, its aerodynamic design for the wind tunnel tests and the structural pre‐design and sizing of the full‐scale leading edge section which will be tested in the wind tunnel.

Coupled laminates have potential applications in the design of aero‐elastic compliant rotor blades or aircraft wing structures, by introducing tailored extension‐twist and/or shear‐extension coupling at the laminate level; or in the design of thermally activated morphing structures, by exploiting more complex coupling behaviour.

These laminates contain standard cross‐ply and/or angle‐ply combinations, although double angle‐ply laminates are also considered, and correspond to any standard fibre/matrix system with a constant ply thickness throughout.

The vast majority of the laminate described possess coupling behaviour not previously identified in the literature.

The purpose of this paper is to study the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid using the Fourier expansion collocation method.

A mathematical model is developed for the analytical study on a transversely isotropic thermo-piezoelectric polygonal cross-sectional fiber immersed in fluid using a linear form of three-dimensional piezothermoelasticity theories. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the Fourier expansion collocation method (FECM) at the irregular boundary surfaces of the polygonal cross-sectional fiber. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.

From the literature survey, it is evident that the analytical formulation of thermo-piezoelectric interactions in a polygonal cross-sectional fiber contact with fluid is not discussed by any researchers. Also, in this study, a polygonal cross-section is used instead of the traditional circular cross-sections. So, the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid are studied using the FECM. The dispersion curves for non-dimensional frequency, phase velocity and attenuation coefficient are presented graphically for lead zirconate titanate (PZT-5A) material. The present analytical method obtained by the FECM is compared with the finite element method which shows a good agreement with present study.

This paper contributes the analytical model to find the solution of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid. The dispersion curves of the non-dimensional frequency, phase velocity and attenuation coefficient are more prominent in flexural modes. Also, the surrounding fluid on the various considered wave characteristics is more significant and dispersive in the hexagonal cross-sections. The aspect ratio (a/b) of polygonal cross-sections is critical to industry or other fields which require more flexibility in design of materials with arbitrary cross-sections.

To predict the occurrence of the combination resonances in parametrically excited, simply supported laminated composite plates in contrast to the simple resonances by using first‐order shear deformation lamination theory considering the effects of shear deformation and rotary inertia.

Finite element technique is applied to obtain the equilibrium equation of a plate. Modal transformation is applied to transform the equilibrium equation into a suitable form for the application of the method of multiple scales (MMS). The MMS is applied to obtain the boundaries of the simple and combination resonances.

The combination resonance zones contribute a considerable amount to the local instability region and the widths of combination resonance zones are comparable to those of the simple resonance zones for the loading of the small bandwidth at one end or for the concentrated edge loading.

Aircrafts, spacecrafts and many other structures such as ships, bridges, vehicles and offshore structures use the plate type elements, which are susceptible to dynamic instability.

It will assist the researchers of stability behavior of elastic systems.

Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin‐walled structures are prone to acoustic emissions, or in shape control approaches to suppress unwanted vibrations. Also in Lamb wave based health monitoring systems piezoelectric patches are applied to excite and to receive ultrasonic waves. The purpose of this paper is to develop a higher order finite element with piezoelectric capabilities in order to simulate smart structures efficiently.

In the paper the development of a new fully three‐dimensional piezoelectric hexahedral finite element based on the p‐version of the finite element method (FEM) is presented. Hierarchic Legendre polynomials in combination with an anisotropic ansatz space are utilized to derive an electro‐mechanically coupled element. This results in a reduced numerical effort. The suitability of the proposed element is demonstrated using various static and dynamic test examples.

In the current contribution it is shown that higher order coupled‐field finite elements hold several advantages for smart structure applications. All numerical examples have been found to agree well with previously published results. Furthermore, it is demonstrated that accurate results can be obtained with far fewer degrees of freedom compared to conventional low order finite element approaches. Thus, the proposed finite element can lead to a significant reduction in the overall numerical costs.

To the best of the author's knowledge, no piezoelectric finite element based on the hierarchical‐finite‐element‐method has yet been published in the literature. Thus, the proposed finite element is a step towards a holistic numerical treatment of structural health monitoring (SHM) related problems using p‐version finite elements.

This study aims to construct a mathematical model to study the dispersion analysis of magneto-electro elastic plate of arbitrary cross sections immersed in fluid by using the Fourier expansion collocation method (FECM).

The analytical formulation of the problem is designed and developed using three-dimensional linear elasticity theories. As the inner and outer boundaries of the arbitrary cross-sectional plate are irregular, the frequency equations are obtained from the arbitrary cross-sectional boundary conditions by using FECM. The roots of the frequency equation are obtained using the secant method, which is applicable for complex solutions.

The computed physical quantities such as radial stress, hoop strain, non-dimensional frequency, magnetic potential and electric potential are plotted in the form of dispersion curves, and their characteristics are discussed. To study the convergence, the non-dimensional wave numbers of longitudinal modes of arbitrary (elliptic and cardioid) cross-sectional plates are obtained using FECM and finite element method and are presented in a tabular form. This result can be applied for optimum design of composite plates with arbitrary cross sections.

This paper contributes the analytical model for the role of arbitrary cross-sectional boundary conditions and impact of fluid loading on the dispersion analysis of magneto-electro elastic plate. From the graphical patterns of the structure, the effects of stress, strain, magnetic, electric potential and the surrounding fluid on the various considered wave characteristics are more significant and dominant in the cardioid cross sections. Also, the aspect ratio (a/b) and the geometry parameters of elliptic and cardioids cross sections are significant to the industry or other fields that require more flexibility in design of materials with arbitrary cross sections.

The transverse shear deformation and rotary inertia effects need to be included for an accurate analysis in the response of the relatively thick plates. This paper seeks to use, one of the refined theories which takes into account those effects, The First Order Shear Deformation Theory, to obtain linear and non‐linear responses for anti‐symmetric angle‐ply composite plates under random excitation.

The random excitation is assumed to be stationary, ergodic and Gaussian with zero‐mean. A Monte Carlo Simulation of stationary random process is used. A multi‐mode Galerkin approach and numerical integration procedure are employed to find linear and non‐linear response solutions. Laminated composite plate is taken to be simply‐supported along four edges.

The vibration of composite plates at elevated temperatures is also investigated. The linear and non‐linear deflections root‐mean‐square (RMS) are obtained for various input levels, the different lamination angles and the number of layers.

Further, case studies might lead to a lighter design of thick panels used in high‐performance systems such as aerospace structures.

The paper provides information on the linear and more realistic non‐linear vibrations of thick composite plates in time domain so that it would be possible to obtain key statistical information directly from time‐response history.