International Journal of Structural Stability and Dynamics

This paper deals with the geometrical nonlinear analyses of buckled columns. Differential equations governing the elasticas of buckled columns are derived, in which both the effects of taper type and shear deformation are included. Three kinds of taper types are considered, i.e. breadth, depth and square tapers. Differential equations are solved numerically to obtain the deflection of elasticas and the buckling loads of such columns. Both clamped ends and hinged ends are considered. The effects of shear deformation on the deflection of elasticas of buckled columns and on the buckling loads of columns are investigated extensively. The buckling load equations for uniform columns are expressed as a function of the implicit shear effect. Experimental studies are presented that complement the theoretical results of nonlinear responses of the elasticas.

This paper is concerned with the plastic buckling of moderately thick annular plates under a uniform compressive stress state. The analysis is based on the incremental theory of plasticity which employs the Prandtl–Reuss equations and the plate material is assumed to obey the Ramberg–Osgood stress–strain relation. The effect of transverse shear deformation is taken into consideration by adopting the Mindlin plate theory. The governing differential equations for the plastic buckling problem are solved analytically and the plastic buckling stress factors for annular plates with the allowance of transverse shear deformation are presented for the first time. The influences of the boundary conditions, thickness to outer radius ratios, and inner to outer radius ratios on the buckling stress factors are also examined.

By the variational principle, the chaotic vibrations of deterministic geometrically nonlinear elastic spherical and conical axially symmetric shells with non-homogeneous thickness subjected to a transversal harmonic load are analyzed. The material of the shells is assumed to be isotropic and of the Hookean type. Inertial forces tangent to the averaged surface and inertia of rotation of the cross-section are neglected. By the Ritz procedure, the original PDEs are transferred to the ODEs (Cauchy problem), which are then solved by the fourth-order Runge–Kutta method. In the numerical studies, scenarios of transitions from harmonic to chaotic states for vibrations of flexible spherical and conical shells are detected. Various vibrational states for different combinations of the following control parameters: shell's deflection arrow, the amplitude and frequency of the exciting force, number of modes considered, boundary conditions, and the thickness and shape of the shell cross-section are studied. By adjusting the above parameters, we can detect the transition of a continuous system to the lumped one, and the transition from the harmonic to chaotic vibrations.

This paper is concerned with the axisymmetric vibration problem of polar orthotropic circular plates of quadratically varying thickness and resting on an elastic foundation. The problem is solved by using the Rayleigh–Ritz method with boundary characteristic orthonormal polynomials for approximating the deflection function. Numerical results are computed for frequencies, nodal radii and mode shapes. Three-dimensional graphs are also plotted for the first four normal modes of axisymmetric vibration of plates with free, simply-supported and clamped edge conditions for various values of taper, orthotropy and foundation parameters.

Presented here is an analytical solution to the free vibration problem of an isotropic cylindrical panel with SS2-type simply supported boundary conditions based on Reddy's third order shear deformation shell theory. Using the principle of virtual work, the Reddy's shell theory generates five highly coupled partial differential equations in terms of three unknown displacements and two unknown rotations. The partial differential equations in conjunction with the prescribed boundary conditions are solved using displacement functions expressed in terms of double Fourier series expansion. Cylindrical panels with various aspect and thickness ratios are considered in the study of convergence behavior and parametric variation of the eigenvalues. The eigenvalues and mode shapes obtained in this study are compared with those obtained from the finite element software package ANSYS. The hitherto unavailable analytical solutions can be used as benchmarks for checking the accuracy of various approximate methods such as the Rayleigh–Ritz, finite element and finite difference methods.

In this paper, the need for testing of transmission line towers is emphasized. The failure of cross arms that constitute a part of the tower body is analyzed by the nonlinear finite element method. The finite element analysis results are compared with the test results and the reasons for failure are discussed in detail. The cross arm is modeled using beam and plate elements. Four different types of towers with cross arms are considered. The effect of inner triangulation formed by the redundant patterns on the cross arm performance is studied. The effect of staggering secondary bracings in elevation and plan of the cross arm and detailing of cross arm tips (loading points) are also studied.

This paper presents the research on the analysis of the van der Waals (vdW) interaction on double-walled carbon nanotubes (DWNTs) via an elastic beam model. The parametric studies on the size of DWNTs are conducted to show the effect of vdW interaction on the analysis of both a cantilever DWNT subjected to force at the free tip and a DWNT subjected to pure bending. In addition, the kink instability for the cantilever DWNT is analyzed based on the proposed beam model. It is hoped that the research will provide mechanical models for the analysis of both single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs), as well as for kink instability analysis of carbon nanotubes (CNTs).

In contrast with the odd number based multiple tuned mass dampers (ON-MTMD) used conventionally, which is targeted at the central natural frequency, the arbitrary integer based multiple tuned mass dampers (AI-MTMD) is proposed for the convenient applications of MTMD by giving up the central natural frequency hypothesis. The total number of the TMD units constituting the AI-MTMD may be selected as an arbitrary integer according to the practical requirements. In terms of the dynamic magnification factors (DMF) of the AI-MTMD structure system, the criterion for evaluating the optimum parameters and effectiveness of the AI-MTMD is selected as the minimization of the minimum values of the maximum DMF of the structure with the AI-MTMD. Employing the maximum DMF of every mass block in the AI-MTMD, the stroke of the AI-MTMD is simultaneously evaluated. The results indicate that both the AI-MTMD and the ON-MTMD can practically render the same performance, thus demonstrating that the former can be more convenient in mitigating structural oscillations with respect to the ON-MTMD stuck to the central natural frequency hypothesis.