This paper was written in honor of Prof. Viktor Olimpanovich Kononenko from Ukraine and takes into account reports of recent progress about non-ideal vibrating systems (NIS) published in the period ...from 2004 to 2017. New and old studies of NIS, with limited power supply (small DC motors or electrodynamical shakers), are usually used in laboratory tests, and therefore, the investigation of mutual interactions of driven and driving sub-system is very important. In this paper, main properties of NIS have been reviewed, such as the Sommerfeld effect, i.e., jump phenomena and the increase in power supply that is required by an excitation source operating near resonance; the possibility of saturation phenomenon occurrence, i.e., the transference of energy from higher frequency and lower amplitude to lower frequency and higher amplitude mode; and the existence of regular (periodic motion) and irregular (chaotic motion) behaviors, depending on the value of control parameters (voltage of a DC motor). This paper is divided into two goals: on the one hand will be treated about NIS and on the other hand will be provided an overview of the main engineering applications, analyzing their physical phenomena involved and the adequate methodologies to deal with them.
It is intended, in this work, to present some research results on the optimization of an impact damper for a structural system excited by a non-ideal power source. In the model, the impact vibration ...absorber is, basically, a small free mass inside a box carved in the structure that undergoes undamped linear motions colliding against the walls of the box. Whenever the mass shocks against the walls of the box, an exchange of kinetic energy between the mass and the structure may be used to control the amplitude of the dynamic response of the structure. In this work, the structure is excited by a non-ideal power source, a DC electric motor installed on it, which may present the Sommerfeld effect. A non-ideal power source is one that interacts with the motion of the structure as opposed to an ideal source whose amplitude and frequency are fixed, independent of the displacements of the structure. Here, the dynamic response of the system is computed using step-by-step numerical integration of the equations of motion derived via a Lagrangian formulation. The optimization problem is defined considering as the objective function the maximum amplitude of the structure displacement, while the design variables are the weight of the free mass and the width of the carved box. Using the augmented Lagrangian method, several optimization problems are formulated, and, solving them, the best design to maximize the efficiency of the impact damper is obtained.
•Rayleigh method is applied to a 48-m-high and a 30-m-high masts to find its fundamental frequency.•Properties of mast structures vary along its length.•FEM-based model is performed to compare ...results obtained by Rayleigh method.•Correction factors of were found that can be applied for the close equation development.
To study the vibration of beams and columns, discretization techniques are required because such structures are continuous systems with infinite degrees of freedom. However, one can associate such systems to a system with a single degree of freedom, restricting the form to which the system will deform and describing their properties as a function of generalized coordinates. This technique is called the Rayleigh method. However, actual structures are more complex than simple beams and columns because their properties vary along their length. The objective of this work is to apply the technique recommended by Rayleigh to actual structures and find a single equation and correction factor that can be used to resolve practical problems in engineering. The structural elements selected for this study are metallic high-slenderness poles, for which the frequency of the first vibration mode were calculated analytically, as well as by finite element method-based computer modeling for comparative purposes. The results indicate that the analytical solution is 16% greater and 1% minor than the computational solution, and correction factors of 1.4 and 1.32 were found, respectively.
To retrofit reinforced concrete telecommunication towers, it is necessary to update their parameters because the structure's bearing capacity is no longer the same as at the initial moment of ...commissioning. Reinforced concrete columns are elements formed from the combination of two materials-steel and concrete-making them a composite material. For the calculation of induced stresses in sections of composite materials, homogenization techniques are required. Due to the slow deformation of the concrete, as a function of the rheological behavior of the material, some of the stresses that were absorbed by the homogenized concrete section are transferred to the reinforcement, causing an increase in the initially calculated values. To evaluate the stress in the reinforcement and the structural strain, an analytical mathematical procedure with nonlinear characteristics was employed to investigate a real, slender, reinforced concrete column, for which the critical buckling load was dynamically determined. A variation of loading considering the column exclusively under its self-weight up to the imminence of instability was applied. Then, by computing the equilibrium of forces and compatibility displacements, allied to the criteria for creep, shrinkage and strength of concrete present in the European Standard EN 1992-1-1, Eurocode 2, it was possible to verify that the induced stresses in the reinforcement steel do not produce the material yielding so that strain does not initiate the cracking process in the concrete.
A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of ...numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.
This study focused on improving the design of slender structures with reinforced concrete (RC) telecommunication towers as the main application. Analytical procedure based on Rayleigh's method to ...compute the first natural vibration frequency and the critical buckling load was development. All the nonlinearities present in the system were considered, in addition to the soil-structure interaction and the variation of the geometric properties along the length of the structure. The geometric nonlinearity and imperfections of the tower structure were computed as functions of the axial load using a geometric stiffness matrix. Further, the material nonlinearity was accounted for by reducing the flexural stiffness. As concrete structures exhibit viscoelasticity, creep was calculated using the Eurocode 2 model. The soil-structure interaction was modeled as a set of distributed springs. To validate the proposed method, the first frequency and critical buckling load were compared with those yielded by FEM simulations. The frequency results were in good agreement with those of the FEM simulations, indicating that the proposed method is sufficiently accurate for use in engineering design applications and easy to implement. On the other hand, the buckling load results obtained using the proposed method and FEM differed significantly, motivating further investigation.
The studies on the so-called smart materials have grown in the last years due to the diverse possibilities that these materials can provide. These types of materials have the ability to respond to an ...external excitation, altering its physical form, and being able to be considered as actuators. Among these materials are the Shape Memory Alloys (SMA), several metal alloys that are able to memorize a shape and recover it after a deformation through an increase of its thermal energy. In this paper, an actuator consisting of an SMA wire is used to attenuate the vibration and Sommerfeld effect of a non-ideal type oscillator. The temperature control of the actuator was carried out through the application of an electric current in the wire. Results are presented for different currents, with the objective of investigating the temperature variation for vibration control applications. The results showed that it is possible to apply SMA actuators to the attenuation of the Sommerfeld Effect as well as in the reduction of the total vibration of the system.
The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crank-shaft-slider mechanism. The novelty is the obtainment and analysis of a ...mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crank-shaft-slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crank-shaft-slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations–rotations and chaotic motions.
In this paper, we examine the nonlinear control method based on the saturation phenomenon and of systems coupled with quadratic nonlinear ties applied to a shear-building portal plane frame ...foundation that supports an unbalanced direct current with limited power supply (non-ideal system). We analyze the equations of motion by using the method of averaging and numerical simulation. The interaction of the non-ideal structure with the saturation controller may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. Special attention is focused on passage through resonance when the non-ideal excitation frequency is near the portal frame natural frequency and when the non-ideal system frequency is approximately twice the controller frequency (two-to-one internal resonance).
The aim of this paper is to describe the seismic hazard performance on the site of Rules Dam, in Granada province (southern Spain), and the seismic influence on this body’s dam, as well as on its ...critical elements, the reservoir and the interaction fluid-structure. The seismic hazard defines the Deterministic Seismic Hazard Assessment (DSHA) and the Probabilistic Seismic Hazard Assessment (PSHA), which are important to calculate the Safety Evaluation Earthquake (SEE) and the Operating Basis Earthquake (OBE), respectively. This recent seismogenic zone provides important data to do the analysis, such as regional geologic setting, seismic history and seismology. In the Spanish code the Peak Ground Acceleration (PGA) for this area is 0.17 g, however in the current analysis the greatest soil acceleration registered is 0.35 g, which is about twice the value. Three accelerograms (controlling earthquakes), by using the Engineering Strong-Motion database, have been chosen to identify the seism’s main characteristics. The dam analysis using different software needs to be done to calculate the vibration periods, the hydrodynamic pressure and the maximal vertical stresses. Time-history analyses have been made to analyze the consequences of a dam failure and to estimate minor damage acceptance. The analyses show that the stresses exceed the tensile maximum allowed creating plastic hinges. There are other factors which can affect the dam’s behavior such as the vertical component of the earthquake and the silt in the reservoir bottom. The concrete arch gravity dam needs to be modeled in two- and three-dimensions, in accordance to classic theoretical method and current codes, considering its big dimensions (length of the crest: 620 m; radius: 500 m; area of the reservoir whit a operating level: 308 Ha). A dam is an extremely strategic work which needs to be carefully designed to avoid environmental damage to water reservoirs and nearby facilities and for human security. Given that the recent sources of hazard in Spain are from 2015, it would be advisable to reassess the seismic hazard particularly related to existing dams of category A (Spanish code) in areas of high seismicity.
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