International Journal of Structural Stability and Dynamics

This paper presents a detailed treatment of the formulation of static, bucking and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. The theory is limited to small strains, moderate deflections and small rotations. The torsional shear strain on the middle surface of the beam wall is zero for an open contour while it corresponds to constant shear flow for a closed contour. Rigorous expressions for strains based on membrane theory of shells are obtained through which the effect of nonlinear tapering is considered. Solutions for classical buckling and vibration analysis by the finite element method are discussed. Numerical integration by using Gaussian quadrature on the cross-sections for the computation of sectorial properties and stress resultants and over the length for the computation of flexural, geometric and mass matrices is suggested. Some examples are solved and critical bucking loads, natural frequencies and the corresponding buckled and mode shapes are obtained by the Jacobi iteration procedure.

Cable structures are lightweighted, simple to fabricate and reusable. They provide effective solutions for large-span structures. Analysis of cables is complex because of their highly geometrically nonlinear behavior. Based on the Lagrangian formulation and a fourth-order polynomial displacement function, the tangent stiffness matrix for a five-node curved cable element is derived and statically condensed to a simple form readily for incorporation into a frame analysis computer program. The program uses the pointwise–equilibrium–polynomial (PEP) element with initial imperfection and the "Nonlinear Integrated Design and Analysis (NIDA)" method for design and nonlinear analysis of cabled structures. Numerical examples demonstrate the robustness and practicality of the proposed method.

In this study, an attempt has been made to incorporate the effect of transverse shear on the stability analysis of moderately thick/very thick composite laminated plates under in-plane compressive loading using a "Simple Higher-Order Shear Deformation Theory" based on four unknown displacement functions (u₀, v₀, w_b, w_s) instead of five which is commonly used in most of the higher-order theories. The finite element method is employed to study the initial buckling load of laminated plates. The change in initial buckling response of thick rectangular anti-symmetric laminates with respect to the fiber orientation angle has been studied. The interaction curves (between N_x and N_y for different parameters of the laminates) are studied in detail. The interaction curves for N_x and N_y are either linear or piecewise linear. There are some combinations of biaxial in-plane loads for which laminates with different lay-up sequences have the same initial buckling loads.

This paper presents accurate elastic solutions for rotating annular disks. A new material properties and density profile in exponential form containing four geometric parameters is proposed. Analytical solutions using this profile are obtained in terms of Whittaker's functions for the elastic deformation of rotating annular disks. The inner and outer edges of the disk are considered to have combinations of clamped and free boundary conditions. Special cases of rotating annular disks are investigated, which include annular disks with constant thickness and constant density, exponentially variable elastic properties and density, and exponentially graded disks. For all cases studied, closed form solutions are obtained and numerical results are presented. The results include the radial displacement, circumferential and radial stresses of the four annular disk configurations for combinations of homogeneous and exponentially graded cases. The distributions of stresses and displacement are obtained and comparisons between different cases are made at the same angular velocity.

Stability analysis of carbon nanotubes (CNT) under initial bend is conducted using continuum elastic beam models for both single wall nanotube (SWNT) and double wall nanotube (DWNT). A discrete beam model is proposed for simulating the mechanism of kink instability, a local buckling phenomenon, of CNTs. Theoretical analysis of the critical axial load for kink instability is carried out with the elastic beam model. Based on the theoretical analysis, the size effect of CNTs on the critical axial force is studied. By setting the initial bend to be zero, the current model can be used to predict the buckling load of a straight CNT as well.

The present paper deals with dynamic nonlinear systems loaded by badly defined forcing actions. As an improvement on the first approximate procedure developed by the authors, a more feasible and reliable alternative entropic closure approach is presented herein. Such a procedure allows one to deal with high order nonlinearities, and it can be suitably generalized to treating multi-degree of freedom (MDOF) systems. In fact, the effectiveness of the proposed approach is intricately linked to the exact calculation of some multiple integrals related to the approximate expression of the chosen response probability function. To this end, a procedure that can guarantee high accuracy in the computation of integrals is also studied, which helps in validating the whole approach.

This paper is concerned with the problem of occurrence of combination resonances in parametrically excited doubly curved panels. The dynamic instability of doubly curved panels, subjected to non-uniform in-plane harmonic loading is investigated. Sander's first-order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory can be reduced to Love's and Donnell's theories by means of tracers. Analytical expressions for the instability regions are obtained at Ω = ω_m + ω_n (Ω is the excitation frequency and ω_m and ω_n are the natural frequencies of the system), by using the method of multiple scales. It is shown that besides the principal instability region at Ω =2ω₁, where ω₁ is the fundamental frequency, other cases of Ω = ω_m + ω_n which are related to other modes, can be of major importance and yield a significantly enlarged instability region. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. The effects of edge loading, curvature, shallowness ratio, edge length to thickness ratio, aspect ratio, boundary conditions and the static load factor on dynamic instability regions are considered.

The lever-type multiple tuned mass dampers (LT-MTMD), consisting of several lever-type tuned mass dampers (LT-TMDs) with a uniform distribution of natural frequencies, are proposed for the vibration control of long-span bridges. Using the analytical expressions for the dynamic magnification factors (DMF) of the LT-MTMD structure system, an evaluation, with inclusion of the LT-MTMD stroke, is conducted on the performance of the LT-MTMD with identical stiffness and damping coefficients but unequal masses for mitigating harmonically forced vibrations. The LT-MTMD is found to possess the near-zero optimum average damping ratio regimen when the total number of dampers exceeds a certain value. In comparison, the LT-MTMD without the near-zero optimum average damping ratio and the traditional hanging-type multiple tuned mass dampers (HT-MTMD) without the near-zero optimum average damping ratio can achieve approximately the same optimum frequency spacing (an indicator for robustness), effectiveness, and stroke. Compared with the HT-MTMD, the LT-MTMD needs lesser optimum average damping ratio but significantly higher optimum tuning frequency ratio. Its main advantage is that the static stretching of the spring may be adjusted to meet the practical requirements through the support movement, while maintaining the same robustness, effectiveness, and stroke. Consequently, the LT-MTMD is a better choice for suppressing the vibration of long-span bridges as the static stretching of the spring required is not large.