Buckling Characteristics of Laminated Functionally-Graded CNT-Reinforced Composite Plate under Nonuniform Uniaxial and Biaxial In-Plane Edge Loads

In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.

Generalized eigenvalues of the (P, 2)-Laplacian under a parametric boundary condition

In this paper we study a general eigenvalue problem for the so called (p, 2)-Laplace operator on a smooth bounded domain Ω ⊂ ℝN under a nonlinear Steklov type boundary condition, namely \[\left\{ \begin{aligned} -\Delta_pu-\Delta u & =\lambda a(x)u \quad {\rm in}\ \Omega,\\ (|\nabla u|^{p-2}+1)\dfrac{\partial u}{\partial\nu} & =\lambda b(x)u \quad {\rm on}\ \partial\Omega . \end{aligned} \right.\] For positive weight functions a and b satisfying appropriate integrability and boundedness assumptions, we show that, for all p>1, the eigenvalue set consists of an isolated null eigenvalue plus a continuous family of eigenvalues located away from zero.

Dynamic stability of non-dilute fiber shear suspensions

Temporal stability analysis of fiber suspended shear flow is performed. After introducing the second order structure tensor to determine the Folgar-Tucker inter-fiber interactions based on the Langevin?s equation, a system governing the flow stability is derived in conjunction with the fiber orientation closure. Effect of the inter-fiber interactions on the dynamic stability is studied by solving the general eigenvalue problem. Results show that fiber interaction has significant stabilizing effects on the flow. The most unstable wave number changes with the interaction coefficient. For given interaction coefficient, wave number and other relevant parameters, there is a Re number which corresponds to the critical flow. This Re number is related to the wave number.

Prediction of natural frequencies for thin circular cylindrical shells

In this paper an analytical procedure is given to study the free-vibration characteristics of thin circular cylindrical shells. Ritz polynomial functions are assumed to model the axial modal dependence and the Rayleigh-Ritz variational approach is employed to formulate the general eigenvalue problem. Influence of some commonly used boundary conditions, viz. simply supported-simply supported, clamped-clamped and clamped-free, and also the effects of variations of shell parameters on the vibration frequencies are examined. Natural frequencies for a number of particular cases are evaluated and compared with some available experimental and other analytical results in the literature on this topic. These results are given in the form of tables and figures. A very good agreement between the results of the present analysis and the corresponding experimental and analytical results available in the literature is obtained to confirm the validity and accuracy as well as the efficiency of the method.

Transverse Vibrations of a Rotating Twisted Timoshenko Beam Under Axial Loading

Transverse bending vibrations of a rotating twisted beam subjected to an axial load and spinning about its axial axis are established by using the Timoshenko beam theory and applying Hamilton’s Principle. The equations of motion of the twisted beam are derived in the twist nonorthogonal coordinate system. The finite element method is employed to discretize the equations of motion into time-dependent ordinary differential equations that have gyroscopic terms. A symmetric general eigenvalue problem is formulated and used to study the influence of the twist angle, rotational speed, and axial force on the natural frequencies of Timoshenko beams. The present model is useful for the parametric studies to understand better the various dynamic aspects of the beam structure affecting its vibration behavior.