International Journal of Structural Stability and Dynamics

Considered herein is the vibration and stability problems of a slender column subjected to generalized load with a force directed toward the positive pole. The load is developed by heads composed of circular profile elements. The geometrically nonlinear problem of stability and free vibrations is formulated on the basis of Hamilton's principle, and due to nonlinearity, the problem is solved by applying the small parameter method. Vibration and stability results show the influence of chosen parameters that characterize the considered column (including initial prestressing). The assumed mathematical model is validated by experimental results.

In this paper, the principal resonance is investigated for a cantilever with a contact end. The cantilever is modeled as an Euler–Bernoulli beam, and the contact is modeled by the Derjaguin–Müller–Toporov theory. The problem is formulated as a linear nonautonomous partial-differential equation with a nonlinear autonomous boundary condition. The method of multiple scales is applied to determine the steady-state response. The equation of response curves is derived from the solvability condition of eliminating secular terms. The stability of steady-state responses is analyzed by using the Lyapunov-linearized stability theory. Numerical examples are presented to highlight the effects of the excitation amplitude, the damping coefficient, and the coefficients related to the contact.

In this paper, the dynamic stability of a disk rotating in air has been modeled and analyzed numerically as well as observed from experiments. A simple expression on the aerodynamic loading acting on the rotating disk is applied in the modeling, and the dynamic stability results of the disks are evaluated based on the eigenvalues for the vibration modes. The disk critical speeds and the flutter speeds are calculated and compared with the results from experiments, which are conducted on two steel disks with different diameters and thicknesses. The modeling predicts that the rotating disk flutter starts with the mode (0, 3)B, which agrees with the results reported in the literature and the observation in the present experimental study.

The present study deals with the dynamic stability of laminated composite pre-twisted cantilever panels. The effects of various parameters on the principal instability regions are studied using Bolotin's approach and finite element method. The first-order shear deformation theory is used to model the twisted curved panels, considering the effects of transverse shear deformation and rotary inertia. The results on the dynamic stability studies of the laminated composite pre-twisted panels suggest that the onset of instability occurs earlier and the width of dynamic instability regions increase with introduction of twist in the panel. The instability occurs later for square than rectangular twisted panels. The onset of instability occurs later for pre-twisted cylindrical panels than the flat panels due to addition of curvature. However, the spherical pre-twisted panels show small increase of nondimensional excitation frequency.

This paper presents a three-dimensional (3D) moving least-square Ritz (MLS-Ritz) formulation for the free vibration analysis of homogeneous elastic thick plates with mixed boundary constraints. The analysis is based on the linear elasticity theory. The Ritz trial functions are established through the moving least-square technique for the displacement fields of the plates. Vibration frequencies for thick square plates and right-angled isosceles triangular plates are obtained by the MLS-Ritz method. The reliability and accuracy of the presented method are examined by extensive convergence and comparison studies and it is established herein that the MLS-Ritz method is a powerful and effective numerical method for the 3D analysis of thick plates.

In this paper, the effects of randomness in the material properties and foundation stiffness parameters on the elastic buckling of laminated composite plate resting on elastic foundation subjected to uniform in-plane edge compression are studied. Higher order shear deformation theory has been used for the plates. The interaction between the plate and foundation is included in the formulation of a two-parameter Pasternak model. A C⁰ finite element method is used for treating the random eigenvalue problem. The uncertain lamina material properties and the foundation stiffness parameters are modeled as independent basic random variables. A mean-centered first order perturbation technique is adopted to examine the stochastic characteristics of the buckling load. From the results presented for laminated composite plates resting on elastic foundations with different boundary conditions, the influence of variation of material constant, foundation stiffness parameters, edge in-plane forces, side-to-thickness ratio, plate aspect ratio, and variation in standard deviation of material properties on the buckling response has been investigated. The results have been compared with those available in the literature and from an independent Monte Carlo simulation.

Geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out in this paper. The Green–Lagrange strain tensor in its entirety is used in the analysis. The locally effective material properties are evaluated using homogenization method which is based on the Mori–Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness is determined by solving a steady-state heat transfer (i.e. energy) equation. As an example, a functionally gradient material circular plate composed of zirconium and aluminum is used and results are presented in graphical form.

The performance-based design of coupled core wall systems offers a number of advantages over conventional strength-based methods in terms of constructability and structural performance. Under large seismic loads, the expected degradation of the coupling beams in coupled wall structures results in an evolution of the lateral force resisting system from a coupled wall system to a system of linked cantilever wall piers. The present study focuses on the performance of the eventually obtained linked wall pier systems and defines their performance in a novel way: as the minimization of transmissibility of horizontal ground motion. In this paper, fixed point theory (FPT) is used to establish initial design values for the coupling beams required to optimize the dynamic response of the linked wall pier system. An initial parametric study of the application of FPT to optimizing the behavior of linked wall piers is presented. The resulting optimized wall systems are compared with practically obtainable, rigid and uncoupled systems subject to a linear time history analysis to assess the extent and practicality of optimization obtained.

In this paper, the dynamic performance of a controlled high building is numerically investigated considering the effects of different numbers of mass dampers and their interconnection. The numerical analysis is conducted on a 20-story building considered as a shear frame and reduced to an SDOF system by means of the mode-superposition method. The system is subjected to harmonic load. Numerical searches are conducted based on the Min. Max. procedure in order to obtain efficient interconnected (I) multiple tuned mass dampers (MTMD). Comparisons are made among the uncontrolled system, the system controlled by non-interconnected (NI) MTMD, and the system controlled by (I) MTMD in frequency and time domain. Both (NI) and (I) MTMD reduce significantly frequency response peak amplitude. It is observed that the (I) MTMD produces great reductions on maximum displacement, rms displacement, steady-state peak response, and story displacements close to the reductions obtained by (NI) MTMD using review parameters. Mass maximum displacements analysis shows that the space required for (I) MTMD installation is smaller than (NI) MTMD.