International Journal of Structural Stability and Dynamics

The paper delineates the procedure to assess probable failure sections through the dynamic conditions of a vertically tapered frame using the experimental modal analysis (EMA), which is validated through the finite element analysis (FEA). The modal parameters are experimentally determined by the frequency response functions (FRFs) using the accelerometer, force transducer, electro-dynamic shaker, dynamic signal analyzer (DSA) and post processed by the ME’Scope software. The ANSYS Workbench 14 was used for finding the modal parameters through the FEA. The FEA model was also tested by convergence study. The boundary conditions of the vertically tapered frame in the FEA is kept similar to the EMA. The values obtained by the two methods have been compared for their proximity.

Modal coupling is an important characteristic of most nonlinear dynamic systems. Although the existence of modal coupling can make the dynamic responses of a system quite complicated, it can be utilized to provide potential solutions to regulate nonlinear vibration. In this paper, the mechanism of modal coupling is used as a means to suppress vibration of a flexible arm undergoing joint motion. A secondary oscillatory system is attached to the flexible arm to generate appropriate modal coupling. Via this nonlinear coupling, internal resonance can be successfully induced and used to transfer vibration energy from the flexible arm to the vibration absorber. Moreover, the damping enhancement effect is studied, which is found to help suppressing vibrations. The feasibility of the idea presented herein has been demonstrated in the numerical simulations.

Tensegrity systems are composed of any given set of cables connected to a set of struts in which the cables connectivity must be able to stabilize the configuration. Self-stresses contribute to the rigidity and stability of the system. Therefore, self-stress distribution has a dominant effect on the stability behavior of these systems. In this study, the stability behavior of plane double-layer tensegrity systems considering different distributions of self-stresses is evaluated. Based on the results obtained, collapse mechanisms, load carrying capacities, stiffness of the systems and slackening of the cables are affected by self-stress distribution. Therefore, self-stress design is a key factor that plays a dominant role on the stability behavior of tensegrity systems. These results can lead to the suggestion of some guidelines on the selection of self-stress distribution for the design of tensegrity systems against instability.

In this paper, the effect of various arrangements of displacement, velocity and acceleration related weighting matrices on the performance of active control systems on nonlinear frames has been studied. Different arrangements of weighting matrices and feedback combinations of the response have been considered to design the active controllers using a single actuator for reducing the response of an eight-storey bilinear hysteretic frame under white noise excitations. The nonlinear Newmark-based instantaneous optimal control algorithm has been used, where the distributed genetic algorithm (DGA) is employed to determine the proper set of weighting matrices. For each set of feedback and weighting matrices, the active control system has been designed with the optimal weights determined. Here, the objective is to minimize the maximum control force required to reduce the maximum structural drift to a value below the desired level. The numerical results of simulation show that, for the cases studied, the use of different arrangements of weighting matrices in the proposed method for the performance index of the active control law has no significant impact on the performance of the active control system. However, the type of response feedback combination included in the control law considerably affects the performance, and the controllers designed based on velocity feedback have been found to be more effective. It was also shown that for all the weight-cases, using the full feedback of response can lead to design controllers that require minimum control force to reduce the structural response with more online measurements. The robustness of the designed controllers for different weighting matrices arrangements and feedback combinations has also been tested under a number of real earthquake excitations with the results discussed.

This paper studies the dynamic interaction between two or more adjacent foundations resting on the surface of a stratified soil. The precise integration scheme adopted ensures that the numerical results obtained are highly accurate. Only the interfaces between the foundations and the soil need to be discretized and there is no limit on the thickness or on the number of soil layers to be considered. Numerical examples are provided to verify the accuracy and computational stability of the proposed approach. A series of parametric studies have been carried out to clarify the effects of layer depth, soil damping, spacing between adjacent foundations, masses and moment inertias of supporting structures and the wave propagation velocity on the dynamic behavior of three-dimensional (3D) foundation–soil–foundation interaction (FSFI).

In this study, the free vibration analysis of edge cracked cantilever microscale beams composed of functionally graded material (FGM) is investigated based on the modified couple stress theory (MCST). The material properties of the beam are assumed to change in the height direction according to the exponential distribution. The cracked beam is modeled as a modification of the classical cracked-beam theory consisting of two sub-beams connected by a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces to the classical one when the length scale parameter is zero. The problem considered is investigated using the Euler–Bernoulli beam theory by the finite element method. The system of equations of motion is derived by Lagrange’s equations. To verify the accuracy of the present formulation and results, the frequencies obtained are compared with the results available in the literature, for which good agreement is observed. Numerical results are presented to investigate the effect of crack position, beam length, length scale parameter, crack depth, and material distribution on the natural frequencies of the edge cracked FG microbeam. Also, the difference between the classical beam theory (CBT) and MCST is investigated for the vibration characteristics of the beam of concern. It is believed that the results obtained herein serve as a useful reference for research of similar nature.

In this paper, the axial compression buckling problem of castellated columns about the major axis when exposed to a fire is investigated. An analytical formula for calculating the critical buckling load of castellated columns is derived, which considers not only the shear deformation effect of web openings but also the non-uniform cross-section temperature distribution due to non-symmetric fire exposure. The results show that for the same average temperature, the critical buckling load of a castellated column with non-uniform temperature distribution is smaller than that of a castellated column with uniform temperature distribution. The web shear effect caused due to web openings can significantly reduce the critical buckling load of the castellated column, particularly for the columns with shorter lengths or wider flanges. However, the change of the shear effect on the critical load with different temperature distributions is very small and can be generally ignored.

The forced-free responses of nonuniform beams under moving point loads are analyzed in this paper. Simple approximate analytical formulae for the forced responses of undamped nonuniform beams, derived using the fundamental mode by the Rayleigh–Ritz (R–R) method, are presented. The responses of both simply supported and clamped–clamped beams are analyzed. The responses are also determined by the finite element method (FEM) in which nonuniform elements are used for fast convergence. It is found that the present method yields results that are very close to those obtained by the FEM. As this method does not require time integration, it is faster and computationally more efficient. Though the single-mode analysis of forced vibration of uniform beams under moving loads has been done by several researchers, its application to nonuniform beams has not been reported.

Presented herein is a new computational strategy to eliminate the thermal effect in measured responses. The internal forces of a structure and its thermal load components are estimated alternately at each time step based on a recursive least-squares algorithm. The noise effect in the measured data and the estimated force in previous steps are removed with the Kalman filter. This approach directly models the thermal effects on the dynamic responses without the temperature information. This approach adopts force identification technique which has been researched extensively in the last two decades. The effectiveness of the proposed approach is validated via numerical studies with a bridge structure with or without noise in the measured data. The thermal load in the structural components can be estimated accurately with the proposed strategy with less than 8% error when there is 10% noise in the measured responses of the structure.

A fast, reliable and optimized numerical procedure of the hydrodynamic response analysis of a slender-body structure is presented. With this method, the dynamic response and reliability of a six-leg jack-up-type wind turbine installation vessel under various environmental conditions is analyzed. The modified Morison equation is used to calculate the wave and wind-driven current excitation forces on the slender-body members. The Det Norske Veritas (DNV) rule-based formula is used to calculate the wind loads acting on the superstructure of the jack-up leg. From the modal analysis, the natural period and standardized displacement of the structure are determined. The Newmark-beta time-integration method is used to solve the equation of motion generating the time-varying dynamic responses of the structure. A parametric study is carried out for various current velocities and wind speeds. In addition, a reliability analysis is conducted to predict the effects of uncertainty of the wave period and wave height on the safety of structural design, using the reliability index to indicate the reliability of the dynamic response on the critical structural members.

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of a hermetic capsule comprising a cylinder closed with hemi-ellipsoidal caps at both ends. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components $u_r$, $u_{\theta }$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in $\theta$ and in time, and the Legendre polynomials in the r and z directions instead of ordinary ones. Potential (strain) and kinetic energies of the hermetic capsule are formulated, and the Ritz method is used to solve the eigenvalue problem, thereby yielding upper bound values of the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Typical convergence studies are carried out for the first five frequencies. The frequencies from the present 3D method are in good agreement with those obtained from other 3D approach and 2D shell theories proposed by previous researchers.

In this paper, the influence of foundation stiffness on the seismic behavior of shear wall-frame systems was investigated. First, a basic differential equation was established to account for the interaction between the foundation and superstructure. By solving the equation, the influence of foundation stiffness on the lateral stiffness, inter-story drift, and internal force distribution of the superstructure at the elastic stage was elucidated. Subsequently, the concept and method for determining the range of foundation stiffness suitable for shear wall-frame systems were proposed. By taking a 12-story shear wall-frame structure built on a shallow foundation as an example, a parametric study was performed for various frame-to-wall relative stiffness ratios and foundation stiffnesses. The effect of shallow foundation stiffness on the base shear distribution and energy dissipation of the superstructure was clarified, with results compared with those of the fixed-base model. The analysis results indicated that the degeneration of foundation stiffness due to earthquake damages will result in significant redistribution of internal forces, namely, the internal forces of the walls decrease, while those of the frames increase. In particular, the shear-force and bending moment of the bottom frame columns rise drastically, which may greatly reduce the safety margin and should be considered in practical design.