• Smart Structures and Systems
• /
• v.19 no.6
• /
• pp.665-678
• /
• 2017

In this paper the tuned mass-damper-inerter (TMDI) is considered for passive vibration control and energy harvesting in harmonically excited structures. The TMDI couples the classical tuned mass-damper (TMD) with a grounded inerter: a two-terminal linear device resisting the relative acceleration of its terminals by a constant of proportionality termed inertance. In this manner, the TMD is endowed with additional inertia, beyond the one offered by the attached mass, without any substantial increase to the overall weight. Closed-form analytical expressions for optimal TMDI parameters, stiffness and damping, given attached mass and inertance are derived by application of Den Hartog's tuning approach to suppress the response amplitude of force and base-acceleration excited single-degree-of-freedom structures. It is analytically shown that the TMDI is more effective from a same mass/weight TMD to suppress vibrations close to the natural frequency of the uncontrolled structure, while it is more robust to detuning effects. Moreover, it is shown that the mass amplification effect of the inerter achieves significant weight reduction for a target/predefined level of vibration suppression in a performance-based oriented design approach compared to the classical TMD. Lastly, the potential of using the TMDI for energy harvesting is explored by substituting the dissipative damper with an electromagnetic motor and assuming that the inertance can vary through the use of a flywheel-based inerter device. It is analytically shown that by reducing the inertance, treated as a mass/inertia-related design parameter not considered in conventional TMD-based energy harvesters, the available power for electric generation increases for fixed attached mass/weight, electromechanical damping, and stiffness properties.

• Earthquakes and Structures
• /
• v.10 no.6
• /
• pp.1253-1272
• /
• 2016

For a nonlinear control system, there are many uncertainties, such as the structural model, controlled parameters and external loads. Although the significant progress has been achieved on the robust control of nonlinear systems through some researches on this issue, there are still some limitations, for instance, the complicated solving process, weak conservatism of system, involuted structures and high order of controllers. In this study, the computational structural mechanics and optimal control theory are adopted to address above problems. The induced norm is the eigenvalue problem in structural mechanics, i.e., the elastic stable Euler critical force or eigenfrequency of structural system. The segment mixed energy is introduced with a precise integration and an extended Wittrick-Williams (W-W) induced norm calculation method. This is then incorporated in the market-based control (MBC) theory and combined with the force analogy method (FAM) to solve the MBC robust strategy (R-MBC) of nonlinear systems. Finally, a single-degree-of-freedom (SDOF) system and a 9-stories steel frame structure are analyzed. The results are compared with those calculated by the $H{\infty}$-robust (R-$H{\infty}$) algorithm, and show the induced norm leads to the infinite control output as soon as it reaches the critical value. The R-MBC strategy has a better control effect than the R-$H{\infty}$ algorithm and has the advantage of strong strain capacity and short online computation time. Thus, it can be applied to large complex structures.

• Structural Engineering and Mechanics
• /
• v.54 no.1
• /
• pp.105-119
• /
• 2015

Structural damage detection using modal strain energy (MSE) is one of the most efficient and reliable structural health monitoring techniques. However, some of the existing MSE methods have been validated for special types of structures such as beams or steel truss bridges which demands improving the available methods. The purpose of this study is to improve an efficient modal strain energy method to detect and quantify the damage in complex structures at early stage of formation. In this paper, a modal strain energy method was mathematically developed and then numerically applied to a fixed-end beam and a three-story frame including single and multiple damage scenarios in absence and presence of up to five per cent noise. For each damage scenario, all mode shapes and natural frequencies of intact structures and the first five mode shapes of assumed damaged structures were obtained using STRAND7. The derived mode shapes of each intact and damaged structure at any damage scenario were then separately used in the improved formulation using MATLAB to detect the location and quantify the severity of damage as compared to those obtained from previous method. It was found that the improved method is more accurate, efficient and convergent than its predecessors. The outcomes of this study can be safely and inexpensively used for structural health monitoring to minimize the loss of lives and property by identifying the unforeseen structural damages.

• Smart Structures and Systems
• /
• v.31 no.2
• /
• pp.113-130
• /
• 2023

Hybrid simulation (HS) has attracted community attention in recent years as an efficient and effective experimental technique for structural performance evaluation in size-limited laboratories. Traditional hybrid simulations usually take deterministic properties for their numerical substructures therefore could not account for inherent uncertainties within the engineering structures to provide probabilistic performance assessment. Reliable structural performance evaluation, therefore, calls for stochastic hybrid simulation (SHS) to explicitly account for substructure uncertainties. The experimental design of SHS is explored in this study to account for uncertainties within analytical substructures. Both computational simulation and laboratory experiments are conducted to evaluate the pseudo-random Sobol sequence for the experimental design of SHS. Meta-modeling through polynomial chaos expansion (PCE) is established from a computational simulation of a nonlinear single-degree-of-freedom (SDOF) structure to evaluate the influence of nonlinear behavior and ground motions uncertainties. A series of hybrid simulations are further conducted in the laboratory to validate the findings from computational analysis. It is shown that the Sobol sequence provides a good starting point for the experimental design of stochastic hybrid simulation. However, nonlinear structural behavior involving stiffness and strength degradation could significantly increase the number of hybrid simulations to acquire accurate statistical estimation for the structural response of interests. Compared with the statistical moments calculated directly from hybrid simulations in the laboratory, the meta-model through PCE gives more accurate estimation, therefore, providing a more effective way for uncertainty quantification.

• Earthquakes and Structures
• /
• v.9 no.3
• /
• pp.603-623
• /
• 2015

The scale and nature of the recent earthquakes in the world and the related earthquake disaster index coerce the concerned community to become anxious about it. Therefore, it is crucial that seismic lateral load effect will be appropriately considered in structural design. Application of seismic isolation system stands as a consistent alternative against this hazard. The objective of the study is to evaluate the structural and economic feasibility of reinforced concrete (RC) buildings with base isolation located in medium risk seismic region. Linear and nonlinear dynamic analyses as well as linear static analysis under site-specific bi-directional seismic excitation have been carried out for both fixed based (FB) and base isolated (BI) buildings in the present study. The superstructure and base of buildings are modeled in a 3D finite element model by consistent mass approach having six degrees of freedom at each node. The floor slabs are simulated as rigid diaphragms. Lead rubber bearing (LRB) and High damping rubber bearing (HDRB) are used as isolation device. Change of structural behaviors and savings in construction costing are evaluated. The study shows that for low to medium rise buildings, isolators can reduce muscular amount of base shears, base moments and floor accelerations for building at soft to medium stiff soil. Allowable higher horizontal displacement induces structural flexibility. Though incorporating isolator increases the outlay, overall structural cost may be reduced. The application of base isolation system confirms a potential to be used as a viable solution in economic building design.

• Wind and Structures
• /
• v.4 no.1
• /
• pp.1-18
• /
• 2001

The classical two-degree-of-freedom (2-d-o-f) "sectional model" is currently used to study the dynamics of suspension bridges. Taking into account the first pair of vertical and torsional modes of the bridge, it describes well global oscillations caused by wind actions on the deck and yields very useful information on the overall behaviour and the aerodynamic and aeroelastic response, but does not consider relative oscillation between main cables and deck. The possibility of taking into account these relative oscillations, that can become significant for very long span bridges, is the main purpose of the 4-d-o-f model, proposed by the Authors in previous papers and fully developed here. Longitudinal deformability of the hangers (assumed linear elastic in tension and unable to react in compression) and external loading on the cables are taken into account: thus not only global oscillations, but also relative oscillations between cables and deck can be described. When the hangers go slack, large nonlinear oscillations are possible; if the hangers remain taut, the oscillations are small and essentially linear. This paper describes the model proposed for small and large oscillations, and investigates in detail the limit condition for linear response under harmonic actions on the cables (e.g., like those that could be generated by vortex shedding). These results are sufficient to state that, with geometric and mechanical parameters in a range corresponding to realistic cases of large span suspension bridges, large relative oscillations between main cables and deck cannot be excluded, and therefore should not be neglected in the design. Forthcoming papers will investigate more general cases of loading and dynamic response of the model.

• Structural Engineering and Mechanics
• /
• v.38 no.1
• /
• pp.39-63
• /
• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• Wind and Structures
• /
• v.16 no.1
• /
• pp.93-115
• /
• 2013

This paper describes a study of the influence of a dynamically flexible building structure on pressures inside and net pressures on the roof of low-rise buildings with a dominant opening. It is shown that dynamic interaction between the flexible roof and the internal pressure results in a coupled system that is similar to a two-degree-of-freedom mechanical system consisting of two mass-spring-damper systems with excitation forces acting on both the masses. Two resonant modes are present, the natural frequencies of which can readily be obtained from the model. As observed with quasi-static building flexibility, the effect of increased dynamic flexibility is to reduce the first natural frequency as well as the corresponding peak value of the admittance, the latter being the result of increased damping effects. Consequently, it is found that the internal and net roof pressure fluctuations (RMS coefficients) are also reduced with dynamic flexibility. This model has been validated from experiments conducted using a cylindrical model with a leeward end flexible diaphragm, whereby good match between predicted and measured natural frequencies, and trends in peak admittances and RMS responses with flexibility, were obtained. Furthermore, since significant differences exist between internal and net roof pressure responses obtained from the dynamic flexibility model and those obtained from the quasi-static flexibility model, it is concluded that the quasi-static flexibility assumption may not be applicable to dynamically flexible buildings. Additionally, since sensitivity analyses reveal that the responses are sensitive to both the opening loss coefficient and the roof damping ratio, careful estimates should therefore be made to these parameters first, if predictions from such models are to have significance to real buildings.

• Geomechanics and Engineering
• /
• v.36 no.2
• /
• pp.183-204
• /
• 2024

In current investigation, a novel beam finite element model is formulated to analyze the buckling and free vibration responses of functionally graded porous beams resting on Winkler-Pasternak elastic foundations. The novelty lies in the formulation of a simplified finite element model with only three degrees of freedom per node, integrating both C⁰ and C¹ continuity requirements according to Lagrange and Hermite interpolations, respectively, in isoparametric coordinate while emphasizing the impact of z-coordinate-dependent porosity on vibration and buckling responses. The proposed model has been validated and demonstrating high accuracy when compared to previously published solutions. A detailed parametric examination is performed, highlighting the influence of porosity distribution, foundation parameters, slenderness ratio, and boundary conditions. Unlike existing numerical techniques, the proposed element achieves a high rate of convergence with reduced computational complexity. Additionally, the model's adaptability to various mechanical problems and structural geometries is showcased through the numerical evaluation of elastic foundations, with results in strong agreement with the theoretical formulation. In light of the findings, porosity significantly affects the mechanical integrity of FGP beams on elastic foundations, with the advanced beam element offering a stable, efficient model for future research and this in-depth investigation enriches porous structure simulations in a field with limited current research, necessitating additional exploration and investigation.

• Structural Engineering and Mechanics
• /
• v.59 no.3
• /
• pp.503-526
• /
• 2016

In-plane and out-of-plane free vibration analysis of Timoshenko curved beams is addressed based on the isogeometric method, and an effective scheme to avoid numerical locking in both of the two patterns is proposed in this paper. The isogeometric computational model takes into account the effects of shear deformation, rotary inertia and axis extensibility of curved beams, and is applicable for uniform circular beams, and more complicated variable curvature and cross-section beams as illustrated by numerical examples. Meanwhile, it is shown that, the $C^{p-1}$-continuous NURBS elements remarkably have higher accuracy than the finite elements with the same number of degrees of freedom. Nevertheless, for in-plane or out-of-plane vibration analysis of Timoshenko curved beams, the NURBS-based isogeometric method also exhibits locking effect to some extent. To eliminate numerical locking, the selective reduced one-point integration and $\bar{B}$ projection element based on stiffness ratio is devised to achieve locking free analysis for in-plane and out-of-plane models, respectively. The suggested integral schemes for moderately slender models obtain accurate results in both dominated and non-dominated regions of locking effect. Moreover, this strategy is effective for beam structures with different slenderness. Finally, the influence factors of structural parameters of curved beams on their natural frequency are scrutinized.