International Journal of Structural Stability and Dynamics

This paper begins by presenting a Generalized Beam Theory (GBT) formulation for analyzing the vibration behavior of loaded composite thin-walled members, which accounts for the effects of (i) cross-section in-plane deformation, (ii) shear deformation, (iii) geometric and material coupling, (iv) primary, secondary and non-linear warping, and (v) rotary inertia. This formulation is then used to investigate the local and global vibration behavior of lipped channel columns and beams displaying cross-ply orthotropy, focusing on issues dealing with the variation of the fundamental frequency and vibration mode nature with the member length and applied stress level. For validation purposes, some GBT-based results are also compared with values obtained by means of 4-node shell finite element analyses using ABAQUS. Some relevant conclusions are drawn concerning the dependence of the member vibration mode shape (wave number) on the compression/bending level (applied-to-critical ratio).

The dynamic stability of an axially accelerating viscoelastic beam with two fixed supports is investigated. The Kelvin model is used for the constitutive law of the beam. A small simple harmonic is allowed to fluctuate about the constant mean speed applied to the beam, and the governing equation is truncated using the Galerkin method based on the eigenfunctions of the stationary beam. The averaged equations are derived for the cases of subharmonic and combination resonance. Finally, numerical examples are presented to demonstrate the effects of the viscosity coefficient, the mean axial speed and the beam bending stiffness on the stability boundaries.

A direct numerical approach for solving the instability problem of multi-degree-of-freedom dynamic systems with general period-parameter excitation is developed based on the Floquet theory, Fourier series and generalized eigenvalue analysis. The developed direct numerical approach to the instability is applied to an inclined stay cable with sag under periodic two-support-motion excitation. The partially differential equation for the parametrically excited vibration of the cable is derived by using the transformation of displacements and converted into ordinary differential equations according to the Galerkin method. The unstable regions for parametrically excited vibration of the damped cable system with multi-degree-of-freedom are obtained to illustrate its overall instability. The effects of each mode vibration and parameters of the cable on the unstable regions are analyzed. The developed direct numerical approach to the parametrically excited instability is applicable to more general periodic parameter-excited systems.

The multiple dual tuned mass dampers, referred to as the MDTMD, consisting of several units of dual tuned mass dampers (DTMD) are proposed for the first time herein, aimed at the effectiveness and robustness of the system for suppressing the undesirable vibrations of structures under the ground acceleration. The total number of dampers can be arbitrary and their natural frequencies are uniformly distributed. Ten typical types of the MDTMD can be devised by varying the system parameters. Employing the criteria chosen for optimum searching, parametric studies were carried out to evaluate the performance of the MDTMD of Type I-1 for its convenience in manufacturing, in which the larger mass blocks (LMBs) are assumed to have identical stiffness, but unequal masses, and the smaller mass blocks (SMBs) have identical stiffness and damping coefficient, but unequal masses and damping ratios. By adopting the maximum dynamic magnification factor (DMF) for each LMB and SMB used in estimating the stroke, an evaluation is also made for the stroke of the MDTMD. The numerical results indicate that the MDTMD (I-1) can provide better effectiveness and higher robustness in comparison with the dual tuned mass dampers (DTMD) and other MTMD systems of similar complexities. However, the stroke of the MDTMD is greater than that of the DTMD and the stroke of each SMB in the MDTMD is larger than that of the mass blocks (MBs) in the arbitrary integer and odd number based MTMD.

This paper investigates the effectiveness of elastomeric and sliding types of isolation systems for the seismic response control of cable-stayed bridges. A simplified two-dimensional lumped-mass finite-element model of the Quincy Bay-view Bridge at Illinois was developed for the investigation. The seismic isolation of cable-stayed bridges is achieved using three different isolators, namely, high damping rubber bearings (HDRB), lead rubber bearings (LRB) and friction pendulum system (FPS). Time history analysis is performed for the bridge with four different earthquake ground motions applied in the longitudinal direction using Newmark's method with linear variation of acceleration over the time interval. The seismic response of the isolated cable-stayed bridge is compared with that of the bridge with no isolation system. The results show that the isolation systems are effective for reducing the absolute acceleration of the deck and the base shear response of the tower. Further, a parametric study is performed by varying the damping ratio, yield strength and friction coefficient of HDRB, LRB and FPS to investigate the influence of these parameters on the seismic response of the bridge. From such a study, optimal values can be found for the isolators for reducing the bridge responses.

Oil and gas production from deep-water offshore fields represent a major structural engineering challenge for the industry. The tension leg platform (TLP) is a well-established concept for deep-water oil exploration. It is necessary to design an offshore TLP such that it can respond to moderate environmental loads without damage, and is capable of resisting severe environmental loads without seriously endangering the occupants. Seismic analysis of triangular TLP under moderate regular waves is investigated. The analysis considers nonlinearities due to the change in tether tension and nonlinear hydrodynamic drag forces. The coupled response of TLP under moderate regular sea waves due to change in initial pretension in the tethers caused by seismic forces (vertical direction) is then investigated. Seismic forces are imposed at the bottom of each tether as axial forces. The tether tension becomes unbalanced when the hull is under offset position. The vertical component of seismic force is an important item to take into consideration, because it is directly superposed to pretension of tethers. The change in initial pretension due to the vertical component of the earthquake affects the response of the triangular TLP in degrees-of-freedom experiencing such forces. The tether tension varies nonlinearly when the platform is subjected to seismic forces caused by the El Centro earthquake and artificially generated earthquake using Kanai–Tajimi's power spectrum. The response due to earthquakes varies with the intensity of the input ground motion. The seismic response of the triangular TLP exhibits nonlinear behavior in the presence of waves and it is non-proportionately influenced by the wave period and the wave height.

The free vibration response of shear-flexible moderately-thick orthotropic cylindrical shell panels, with fixed edges, is investigated using an analytical approach. The governing partial differential equations are developed based on Sander's kinematics and are solved using generalized Navier's with a boundary continuous double Fourier series expansion. The frequencies and mode shapes from the analytical solution for various parametric ratios, including degree of orthotropy (stiffness ratio), radius-to-segment ratio and segment-to-thickness ratio are compared with the finite element solutions that are based on an eight-node 48 degrees of freedom shell element. The rate of convergence of the analytical solution method with respect to the number of Fourier series terms, for various parametric ratios, is presented. The results of the analytical solution are very comparable to that of the finite element solution. It is clear that the presented analytical solution can be used as a benchmark to calibrate and validate numerical and finite element solutions that usually involve approximation to shell theories.

Two interesting problems are considered for enriching the curriculum of the Strength of Materials course, in the light of recently developed functionally graded materials (FGMs), characterized with the smooth variation of the elastic modulus. These are problems associated with buckling of columns with variable flexural rigidity along the axis of the column. A simple semi-inverse method is proposed for determining closed-form solutions of axially inhomogeneous columns. In order for the presentation to be given in one package, the conventional problems are also recapitulated along with the novel ones. The main approach adopted here is the use of the second-order differential equation, instead of the fourth-order one, obtained by integrating twice and having a physical meaning, since it could be derived based on moment equilibrium. This is essentially the same idea as utilized in the textbook by Timoshenko and Gere;¹ the difference is that this paper develops a semi-inverse formulation.