Dynamic characteristics of combined conical-cylindrical shells

The truncated conical shape having a superimposed top cylindrical cap is widely used as a containment vessel for elevated water tanks. The evaluation of the wind and seismic responses of these tanks requires the knowledge of the dynamic characteristics of the vessels. This study reports the results of the first experimental and numerical investigation conducted to assess the dynamic behaviour of combined conical vessels. Shake table testing is conducted on a small-scale combined conical shell model. The tested specimen is then simulated numerically in a three-dimensional finite element analysis. The numerical model is validated through comparison with experimental results. An extensive parametric study is then conducted using the validated numerical model in order to determine the dynamic characteristics of full-scale combined conical vessels. Equations and charts describing the natural frequencies, the mode shapes and the generalized and effective masses of the vessels are obtained from this parametric study.     

Ambient vibration test and finite element modeling of tall liquid storage tanks

This paper addresses the experimental and numerical investigations of the dynamic parameters, natural frequencies and mode shapes, of fixed roof, ground supported, steel storage tanks. Three tall liquid storage tanks with aspect ratios greater than unity are considered. The considered tanks have similar height of 12.190 m and different radius of 6.095, 8.00, and 9.144 m. The effect of the aspect ratio, along with the liquid level on dynamic parameters is discussed. Finite element models of tanks are constructed using the finite element package ANSYS. The fluid-structure interaction is governed in the models. Yet, before using numerical techniques for analyzing the tank-liquid systems, they should be validated by experimental results. For this purpose, a series of ambient vibration tests are carried out to determine the natural frequencies and, if possible, the modes of the vibration. Comparison between numerical and experimental values shows good agreement. The new feature considered in the paper is the influence of roof on the natural frequencies and the modes of vibration. It is found that the influence of roof on the natural frequency of vibration of the considered tanks is negligible, while it does restrain the tank top against radial deformations and has significant effect on the mode shapes of tank.     

Experimental and analytical evaluation of the dynamic characteristics of conical shells

Truncated conical shaped shell structures are used in various engineering applications such as components of missiles and spacecrafts and liquid containers for elevated water tanks. The purpose of this study is to evaluate the dynamic characteristics of such type of shell structures when subjected to a transverse dynamic excitation. This paper focuses on conical steel vessels as superstructure of elevated tanks. However, results of the study can be applied to other conical shell applications. The study is conducted experimentally using a shake table device and numerically using an in-house developed shell element model. In the experimental phase, the fundamental frequency and the corresponding mode shape of a small-scale aluminum conical shell model were evaluated. Results of this experiment were used to validate the numerical model by comparing the measured values to those predicted by the model. The analytical study was then extended to evaluate the dynamic characteristics of conical steel tanks covering a wide range of practical dimensions. The study included the case of open and fixed-roof tanks. The performed analyses led to the development of a number of charts that can be used to identify the natural frequency, the mode shapes and the generalized mass and stiffness of conical tanks for both the fundamental and the cos(θ)-modes of vibration. These results would be very useful in assessing the dynamic response of conical tanks when subjected to wind and earthquake loads.     

Stability of combined imperfect conical tanks under hydrostatic loading

Steel conical vessels with upper cylindrical caps are widely used as liquid containments in elevated water tanks. This type of structure for containing water is referred to as “combined conical tank”. A number of catastrophic failures of combined conical tanks occurred during the past decades in various locations around the globe. Previous studies available in the literature focused on pure conical tanks, where the vessels have no upper cylindrical caps. The current study focuses on characterizing the buckling behaviour of combined conical tanks under the effect of hydrostatic pressure. The study is conducted numerically using a three-dimensional finite element model developed in-house. The effects of geometric imperfection and residual stresses as well as the variation of the geometric and material parameters on the buckling capacity of combined conical tanks are investigated. Finally, a comparison between the buckling capacities of combined and equivalent pure conical tanks is conducted.     

A coupled finite element genetic algorithm for optimum design of stiffened liquid-filled steel conical tanks

In the current study an optimum design technique of stiffened liquid-filled steel conical tanks subjected to global and local buckling constraints is developed using a numerical tool that couples a non-linear finite element model developed in-house and a genetic algorithm optimization technique. This numerical tool is an extended version of an earlier one, adapted for the optimum design of unstiffened conical tanks. The design variables considered in the current study are the shell thicknesses, the geometry of the steel vessel as well as the dimensions and number of stiffeners. The developed numerical tool is capable of selecting the set of design variables that leads to optimum safe design. The analysis is conducted twice; first, case of stiffeners free at their bottom edge, which represents the case of retrofitting an existing tank. In the second case the stiffeners are assumed to be anchored to the bottom slab of the tank, which represents the situation of a newly designed tank. Finally, the optimum design of the stiffened tanks is compared to the optimum design of unstiffened tanks computed in a previous study.     

Effect of variation of component dimensions and weld profiles on the free vibration response of stiffened plates

This investigation focused on the variations observed in the natural frequencies of fabricated stiffened plates, due to the inherent variations obtained in dimensions of components and in the spacing between the girders of stiffened plates; also the variations in the size of weld profiles connecting the various components were taken into account. The present analytical study was based on the earlier experimental work done by Agung Budipriyanto (2005) in his PhD thesis. Both experimental and numerical investigations were carried out for determining the free vibration responses of the stiffened plates considered above. 99.73% confidence level of the normally distributed, measured data sets, lying between μ−3σ and μ+3σ were used to generate finite element analysis (FEA) models. The FEA models were categorized as models without and with weld profiles. From all the analyses, it was observed that the variation in dimensions of components of stiffened plates and in weld profiles produced a maximum variation in natural frequencies between −5.04% to +4.59%. If differences much larger than these differences (between the virgin and the present state) are observed during the dynamic monitoring of the ship, immediately more detailed diagnostic, prognostic and remedial measures should be instituted so that the operational sequences do not lead to further incapacitating damages in the ship.     

Experimental and analytical system identification of Eynel arch type steel highway bridge

This paper describes a full scale arch type steel highway bridges, its finite element modelling and Operational Modal Analysis. Eynel Highway Bridge which has arch type structural system with a total length of 336 m and located in the Ayvacık county of Samsun, Turkey is selected as a case study. The bridge connects the villages which are separated with Suat Uğurlu Dam Lake. The three dimensional finite element model is constructed using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The ambient vibration tests on the bridge deck under natural excitation such as traffic, human walking and wind loads are conducted using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification methods are employed namely, Enhanced Frequency Domain Decomposition method in the frequency domain and Stochastic Subspace Identification method in time domain. The correlation between the finite element model and experimental results is studied. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the bridge deck. It is demonstrated that the ambient vibration measurements using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are enough to identify the most significant modes of steel highway bridges. It is seen that there are some differences between analytical and experimental natural frequencies and experimental natural frequencies are generally bigger than the others.     

Damage detection in elevated spherical containers partially filled with liquid

Damage detection through changes in the dynamic properties has received considerable attention in recent years. However, approaches in structures supporting tanks partially filled with liquid are scarce in the technical literature.In this paper, a numerical-experimental study of damage detection in coupled fluid-structure elevated spherical tank systems is presented. The main objective is to investigate the feasibility to detect structural damage in the support structure by monitoring changes in natural frequencies. The major difficulty arises due to the changes in natural frequencies when the liquid level varies. Thus, in order to gain insight into the dynamical behaviour of the spherical containers and distinguish between the frequency shift caused by container filling conditions or by structural damage, experimental free vibration tests with small vibration amplitudes on a scaled spherical tank model are performed. The dependency of the identified frequencies on the structural damage severity is studied assuming three increasing levels of damage in the support structure. The results indicate that it is possible to detect structural damage, with acceptable confidence, up to liquid filling level of 30%. Moreover, only the “associated structural frequency” reflects the structural damage with a perceptible drop. Next, a numerical model of a real spherical container that takes into account the coupling between fluid and structure is presented to demonstrate the usefulness and validity of the results.     

Earthquake analysis of reinorced concrete minarets using ambient vibration test results

This paper describes a Turkish style reinforced concrete minaret, its finite element model, modal testing, finite element model updating and earthquake behaviour, before and after model updating. The minaret of a mosque located in Trabzon, Turkey is selected as an application. A three‐dimensional (3D) model of the minaret and its modal analysis is performed to obtain analytical frequencies and mode shapes using ANSYS finite element program. The ambient vibration tests are conducted on the minaret under natural excitations such as wind effects and human movement. The output‐only modal parameter identification is carried out by Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods in Operational Modal Analysis software and in doing so, dynamic characteristics (natural frequencies, mode shapes and damping ratios) are determined. A 3D finite element model of the minaret is updated to minimize the differences between analytical and experimental modal properties by changing some uncertain modelling parameters such as material properties and boundary conditions. The earthquake behaviour of the minaret is investigated using 1992 Erzincan earthquake before and after finite element model updating. Maximum differences in the natural frequencies are reduced from 21% to 8%, and good agreement is found between analytical and experimental natural frequencies. In addition to this, it is realized that finite element model updating is effective on the earthquake behaviour of the minaret. Copyright © 2008 John Wiley & Sons, Ltd.     

Model-based design and experimental validation of active vibration control for a stress ribbon bridge using pneumatic muscle actuators

This paper describes the development of an active vibration control system for a light and flexible stress ribbon footbridge. The 13 m span carbon fiber reinforced plastic (CFRP) stress ribbon bridge was built in the laboratory of the Department of Civil and Structural Engineering, Berlin Institute of Technology. Its lightness and flexibility result in high vibration sensitivity. To reduce pedestrian-induced vibrations, very light pneumatic muscle actuators are placed at handrail level, introducing control forces. First, a reduced discretized analytical model is derived for the stress ribbon bridge. To verify the analytical prediction, experiments without feedback control are conducted. Based on this model, a delayed velocity feedback control strategy is designed. To handle the nonlinearities of the muscle actuator, a subsidiary force control is implemented. Then the control performance from numerical simulation is verified by experiments under free vibration. As a result, analytical analyses agree well with experimental results. It is demonstrated that handrail-introduced forces can efficiently control the first mode response.     

Effect of the model updating on the earthquake behavior of steel storage tanks

In this paper, effect of the finite element model updating on the earthquake behavior of steel storage tanks considering fluid-structure interaction is investigated. For this purpose, a cylindrical steel storage tank filled some liquid fuel oil located in Trabzon, Turkey is selected as an example. Initial finite element model of the storage tank is developed by ANSYS software and dynamic characteristics (natural frequencies, and mode shapes) are determined analytically. Ambient vibration tests are conducted on the storage tank under natural excitations to obtain dynamic characteristics (natural frequencies, mode shapes and damping ratios), experimentally. Peak Picking technique in the frequency domain is used to extract experimental dynamic characteristics. When the analytically and experimentally identified dynamic characteristics are compared to each other, some differences are found between both results. To minimize these differences, initial finite element model of the storage tank is updated according to experimental results using some uncertainties modeling parameters such as elasticity modulus. To investigate the effect of finite element model updating on the earthquake behavior of the storage tank, earthquake analyses are performed before and after model updating. In the earthquake analyses, YPT330 component of 1999 Kocaeli earthquake is selected and applied to the models in the horizontal directions. It is seen from the analyses that the displacements and the stresses after model updating are more effective than the displacements and the stresses before model updating.     

Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and unequal stiffeners spacing is investigated using analytical, experimental and finite elements (FE) methods. Ritz method is applied in analytical solution while stiffeners treated as discrete elements. The polynomial functions are used for Ritz functions and natural frequency results for simply supported stiffened cylindrical shell with equal rings spacing and constant eccentricity is compared with other's analytical and experimental results, which showed good agreement. Also, a stiffened shell with unequal rings spacing and non-uniform eccentricity with free–free boundary condition is considered using analytical, experimental and FE methods. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes and damping in each mode. In FE method, two types of modeling, including shell and beam elements and solid element are used, applying ANSYS software. The analytical and the FE results are compared with the experimental one, showing good agreements. Because of insufficient experimental modal data for non-uniformly stiffeners distribution, the results of modal testing obtained in this study could be as useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.     

Faut-il abandonner le formalisme de monod pour la modelisation des processus de depollution par voie biologique?

The use of Monod's model to express the velocity of depollution biological treatment is opposed by experimental evidence; it is impossible:

• to estimate the effects of the substrate concentration at the inlet on the substrate concentration at the outlet during a continuous fermentation;

• to obtain in certain cases positive values of the maximum growth rate during graphical determinations using the linearized form of the model;

• to estimate the variations of the saturation constant as a function of the sludge age and the biomass fraction in each tank in the contact-stabilization process.

The first two points have often been pointed out in literature and a review of the main publications on these subjects is supplied.The third point was mentioned during original research works on the contact-stabilization process, recently carried out by Saipanich and Yue. From Lawrence and McCarty's equation, it has been shown that Monod's model leads to a saturation constant K₃ which is not a true constant but depends on the sludge age and the total biomass fraction contained in the given tank.Yue proposes a new approach described by the equation: The fact that b may be superior or inferior to 1 makes it possible to explain the anomalies noted during the graphical determination of k₀.Like Contois's model, from which it is drawn, this model is compatible with a limitation of the growth by accumulating inhibiting metabolites in the culture medium. It also keeps the possibility to characterize the limitation of the culture by exhaustion of the substrate and to take into account the substrate transfer resistance surrounding the micro-organism, by considering the constant M as the sum of a saturation constant K₃ and a characteristic constant of the substrate diffusion resistance according to Powell.It is shown that this formulation generalizes the previous modeling processes by presenting Monod's, Contois's, Powell's, Elmaleh's classical models as particular cases corresponding to particular values of the constants used.This model is applied to different effluents and numerical values of the constants used are given. Objections to Monod's approach have not only appeared in the case of mixed cultures on complex substrate, but have also been raised by several authors in the case of pure cultures on simple substrate, when substrate is not dosed by specific analytical way but by a global analytical determination as BOD, COD or TOD.     

Robust control of plate vibration via active constrained layer damping

In this paper, the theoretical modeling of a plate partially treated with active constrained layer damping (ACLD) treatments and its vibration control in an H_∞ approach is discussed. Vibration of the flat plate is controlled with patches of ACLD treatments, each consisting of a viscoelastic damping layer which is sandwiched between the piezo-electric constrained layer and the host plate. The piezo-electric constrained layer acts as an actuator to actively control the shear deformation of the viscoelastic damping layer according to the vibration response of the plate excited by external disturbances. In the first part of this paper, the Mindlin–Reissner plate theory is adopted to express the shear deformation characteristics of the viscoelastic damping layer, meanwhile GHM (Golla–Hughes–McTavish) model of viscoelastic damping material and FEM (finite element model) are incorporated to describe the dynamics of the plate partially treated with ACLD treatment. In the second part, particular emphasis is placed on the vibration control of the first four modes of the treated plate using H_∞ robust control method. For this purpose, an H_∞ robust controller is designed to accommodate uncertainties of the ACLD parameters, particularly those of the viscoelastic damping core which arise from the variation of the operation temperature and frequency. Disturbances and measurement noise are rejected in the closed loop by H_∞ robust controller. In the experimental validation, external disturbances of different types are employed to excite the treated plate. The results of the experimental clearly demonstrate that the proposed modeling method is correct and the ACLD treatments are very effective in fast damping out the structural vibration as compared to the conventional passive constrained layer damping (PCLD).     

Experimental and analytical system identification of Eynel arch type steel highway bridge

This paper describes a full scale arch type steel highway bridges, its finite element modelling and Operational Modal Analysis. Eynel Highway Bridge which has arch type structural system with a total length of 336 m and located in the Ayvac?k county of Samsun, Turkey is selected as a case study. The bridge connects the villages which are separated with Suat U?urlu Dam Lake. The three dimensional finite element model is constructed using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The ambient vibration tests on the bridge deck under natural excitation such as traffic, human walking and wind loads are conducted using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification methods are employed namely, Enhanced Frequency Domain Decomposition method in the frequency domain and Stochastic Subspace Identification method in time domain. The correlation between the finite element model and experimental results is studied. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the bridge deck. It is demonstrated that the ambient vibration measurements using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are enough to identify the most significant modes of steel highway bridges. It is seen that there are some differences between analytical and experimental natural frequencies and experimental natural frequencies are generally bigger than the others.     

Modelling phosphorus transport in soils and groundwater with two-consecutive reactions

A model is presented for one-dimensional transport of phosphorus (P) in soils and groundwater. Convective transport, hydrodynamic dispersion and time-dependent phosphorus sorption are accounted for in the model formulation. Time-dependent sorption of soil-P is considered to follow the two consecutive reaction model of Barrow and Shaw (J. Soil Sci.30, 67–76, 1979) which has been extensively tested against experimental data and can be described by S = k · Cⁿt^m. The assumed sorption model allows parameters to be obtained by independent batch and column experiments. A numerical technique is used to solve the solute transport equation incorporating a correction to numerical dispersion to improve the numerical solution. An analytical solution for a simplified case is also presented to test the numerical technique. Parameter sensitivity analysis shows that influent concentration and the parameter k strongly affect the initial breakthrough time of solute, with m and n affecting the shape of the breakthrough curve. Preliminary investigations show that the applicability of the model to describe column experimental breakthrough curves is promising.     

Flow-induced vibration of two circular cylinders in tandem arrangement. Part 2: Suppression of vibrations

This paper presents an experimental investigation on suppression of cross-flow vibrations of two circular cylinders in tandem arrangement, conducted at the fluid mechanics laboratory of Kitami Institute of Technology, Japan. To suppress the vibrations of the cylinders, tripping wires were deployed, attached symmetrically about the leading stagnation lines of the cylinders. Five spacing ratios were examined, i.e., L/D=0.1, 0.3, 0.8, 2.0 and 3.2 (L is the gap spacing between the two cylinders; D is the diameter of cylinder), which are representative for five Regimes I (0.1≤L/D<0.2), II (0.2≤L/D<0.6), III (0.6≤L/D<2), IV (2≤L/D<2.7) and V (L/D≥2.7), respectively, as classified in Part 1 [Kim et al., 2009. Flow-induced vibrations of two circular cylinders in tandem arrangement (part 1: characteristics of vibration). Journal of Wind Engineering and Industrial Aerodynamics, submitted together for publication]. Tripping wire position θ measured from the leading stagnation lines of the cylinders was changed from 20° to 60° to determine the optimum range of θ for suppressing structural vibrations. The shear layers separated from the two cylinders were investigated based on flow visualization. The main findings are: (i) the flow-induced vibration on the two cylinders depends strongly on θ, (ii) at θ=20–30° the vibrations on both cylinders are almost completely suppressed for all regimes except V, and (iii) for θ≥40° the vibration amplitudes of both cylinders are considerably larger than those of the plain cylinders, particularly at θ=40°, where the vibration of the upstream cylinder becomes divergent.     

Buckling of thin-walled conical shells under uniform external pressure

Shells are for the most part the deep-seated structures in manufacturing submarines, missiles, tanks and their roofs, and fluid reservoirs; therefore it is a matter of concern to bring about some basic regulations associated with the existing codes. Above all, truncated conical shells (frusta) and shallow conical caps (SCC) subjected to external uniform pressure when discharging liquids or wind loads are discussed closely in this paper concerning and thrashing out their empirical nonlinear responses along with envisaging numerical methods in contrast. The buckling aptitude of shells is contingent upon two leading geometric ratios of “slant-length to radius” (L/R) and “radius to thickness” (R/t). In this paper, developing six frusta and four shallow cap specimens and their relevant FE models, use is made of laboratory modus operandi to enumerate buckling elastic and plastic responses and asymmetric imperfection sensitivity, whose adequacy has been reckoned through comparisons with arithmetical and numerical data correspondingly. These obtained upshots were aimed at validating and generalizing the data for unstiffened truncated cones and SCC in full scale.     

Design procedure for stiffened water-filled steel conical tanks

Since the collapse of the steel liquid-filled conical tank located in Fredericton, Canada in December 1990, a concern has been raised about the safety of existing tanks. In a previous investigation, it was shown that welding longitudinal stiffeners to the bottom part of hydrostatically loaded conical tanks would provide a significant enhancement to the buckling capacity of this type of shell structure. In the current study, an attempt is made to develop a simple procedure that can be used in designing stiffened conical tanks. The procedure is based on the theory of orthotropic shells and design formulae for unstiffened tanks previously developed by Vandepitte.The study is conducted numerically using an in-house developed shell element model to simulate both the walls of the tank and the stiffeners. The study considers stiffening existing tanks and the design of newly stiffened ones. As the application of the orthotropic theory depends on the ratio between the stiffener spacing and the shell thickness, limiting values for such a ratio have been evaluated and are presented graphically. The orthotropic design procedure is then described and applied in two examples involving a retrofitted as well as a newly designed stiffened conical tanks.     

Flow-induced vibrations of two circular cylinders in tandem arrangement. Part 1: Characteristics of vibration

This paper presents the results of an investigation on the flow-induced vibration characteristics of two circular cylinders in tandem arrangement, with L/D=0.1–3.2 and reduced velocity U_r=1.5–26, where L is the gap spacing between the cylinders and D is the cylinder diameter. The cylinder vibration was restricted to a plane normal to the incident flow. Three different experimental conditions were examined: (i) both cylinders were allowed to vibrate; (ii) the downstream cylinder only was allowed to vibrate with the upstream cylinder fixed; and (iii) the upstream cylinder only was allowed to vibrate with the downstream cylinder fixed. Five Regimes I–V were identified, depending on L/D, fluctuating lift forces and vibration characteristics of the cylinders. In Regimes I (0.1≤L/D<0.2) and IV (2≤L/D<2.7), the cylinder vibration is absent. In Regime II (0.2≤L/D<0.6), both cylinders vibrate violently for U_r>6, including a divergent vibration of the upstream cylinder. In this regime, the vibration amplitude of the downstream cylinder is strongly dependent on whether the upstream cylinder is vibrating or fixed, whereas that of the upstream cylinder is weakly dependent on the downstream cylinder. In Regime III (0.6≤L/D<2), the convergent vibrations of the two cylinders occur at and around U_r≈6.7. In this regime, the upstream cylinder vibration is completely suppressed when the downstream cylinder is fixed, but the downstream cylinder vibration is almost independent on the upstream cylinder. Regime V corresponds to L/D≥2.7, where the two cylinders are separated sufficiently far, thus each vibrating like an isolated cylinder at and around U_r≈6. In this regime, the downstream cylinder vibration is strongly dependent on the upstream cylinder, but the upstream cylinder vibration is almost insensitive to the downstream cylinder condition.