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Background: The national e-prescription system in Greece is one of the most important achievements in the e-health sector. Healthcare professionals’ feedback is essential to ensure the introduced system tends to their needs and reduces their everyday workload. The number of surveys collecting the users’ views is limited, while the existing studies include only a small number of participants. Methods: In this study, healthcare professionals’ perceptions on e-prescription are explored. For this, a questionnaire was distributed online, containing closed- and open-ended questions aiming to address strengths and identify drawbacks in e-prescription. Answers were collected from primary health care physicians, specialized medical doctors and pharmacists. Results: In total, 430 answers were collected (129 from primary health care physicians, 164 responses from specialized medical doctors and 137 pharmacists). Analysis of the collected answers reveals that the views of the three groups of healthcare professionals mostly converge. The positive impact e-prescribing systems have on the overall prescribing procedure in preventing errors and providing automation is commented. Among gaps identified and proposed improvements, health care professionals note the need for access to information on adverse drug reactions, side effects, drug-to-drug interactions and allergies. Flexible interaction with Therapeutic Prescription Protocols is desired to ameliorate monitoring and decision-making, while drug dosing features, and simplified procedures for copying, repeating, canceling a prescription, are perceived as useful to incorporate. Conclusions: Collecting healthcare professionals’ feedback is important, as their views can be transcribed to system requirements, to further promote e-prescribing and improve the provided health care services by facilitating decision making through safer and more efficient e-prescription. Introduction of the identified improvements can simplify the everyday workflow of healthcare professionals. To the best of our knowledge, a survey with more than 400 answered questionnaires on the use of e-prescription systems by healthcare professionals has never been conducted in Greece before.

An efficient methodology is presented for predicting dynamic response and fatigue life of large-scale nonlinear mechanical models, subjected to random excitation. The methodology developed is based on a combination of techniques leading to a fast and accurate determination of the dynamic response with a method related to an efficient prediction of fatigue life. Specifically, the first step involves application of an appropriate coordinate transformation, causing a drastic reduction in the degrees of freedom. This opens the way to the application of another numerical method, leading to direct determination of periodic steady-state response of nonlinear systems under periodic forcing. This approach provides a solid foundation for the subsequent application of a rainflow stress cycle counting method, leading to prediction of fatigue failure. The computational accuracy and effectiveness of the methodology is illustrated by a quite involved example model, representing a city bus subjected to road excitation. Typical results are presented for both the stochastic response and the fatigue life by considering excitation arising from selected road profiles with known statistical properties. Special attention is paid to assessing the effect of the nonlinearity, by considering profiles of different quality. Moreover, a critical comparison is performed on results referring to the expected fatigue lifetime, obtained by applying methods in both the frequency and the time domain. In this way, the applicability of classical spectral methods in nonlinear models is also investigated.

An appropriate substructuring methodology is applied in order to study the dynamic response of very large scale mechanical systems. The emphasis is put on enabling a systematic study of dynamical systems with nonlinear characteristics, but the method is equally applicable to systems possessing linear properties. The accuracy and effectiveness of the methodology are illustrated by numerical results obtained for example vehicle models, having a total number of degrees of freedom lying in the order of a million or even bigger. First, the equations of motion of each component are set up by applying the finite element method. The order of the resulting models is so high that the classical substructuring methodologies become numerically ineffective or practically impossible to apply. However, the method developed overcomes these difficulties by imposing a further, multilevel substructuring of each component, based on the sparsity pattern of the stiffness matrix. In this way, the number of the equations of motion of the complete system is substantially reduced. Consequently, the numerical results presented demonstrate that besides the direct computational savings, this reduction in the dimensions enables the application of numerical codes, which capture response characteristics of dynamical systems sufficiently accurate up to a prespecified level of forcing frequencies. The study concludes by investigating biodynamic response of passenger-seat subsystem models coupled with complex mechanical models of ground vehicles resulting from deterministic or random road excitation.

This study investigates response and stability characteristics of rotordynamic systems interconnected with gear pairs and supported on oil journal bearings. The systems examined are driven by a motor providing a known torque, which is transferred to a load element through shafts and a gear box. Initially, the emphasis is placed on the gear-pair action, by assuming that the interconnecting shafts are rigid. This results in low order mechanical models with strongly non-linear characteristics, whose long-time dynamics are then effectively studied by applying appropriate numerical methodologies. In this way, useful information is obtained about the influence of the loading, the gear mesh and the journal parameters on the system dynamic behaviour, including periodic, quasi-periodic and chaotic response. Efforts are also directed towards predicting the onset of oil whirl instability and investigating its effects on the system dynamics. The focus is then shifted to more realistic models, including the flexibility of the interconnecting shafts. In this case, the order of the system is first reduced by applying a component mode synthesis method, which takes advantage of the fact that the non-linearities are located at the journal bearings and the gear mesh only. As a result, it is possible to study the dynamics of the reduced rotor-bearing model by employing the methodology that was developed for the gear-pair models.

The present work investigates the dynamics of a class of two-degree-of-freedom oscillators with cubic non-linearity in the restoring forces. These oscillators are under the action of an external load including constant and harmonic components. Initially, a perturbation analysis is applied to the equations of motion, demonstrating the effect of the asymmetry induced by the constant loading component on the classical 1:1 and 1:3 internal resonances, as well as on the possibility of the appearance of a first order 1:2 internal resonance. Next, sets of slow-flow equations governing the amplitudes and phases of vibration are derived for the special case of no internal resonance and for the most complicated case corresponding to 1:1 internal resonance. The analytical findings are then complemented by numerical results, obtained by examining the dynamics of a two-degree-of-freedom mechanical system. First, the effect of certain system parameters on the existence and stability of constant and periodic solutions of the slow-flow equations is illustrated by presenting a sequence of response diagrams. Finally, the dynamics of the system used as an example is investigated further by direct integration of the slow-flow equations. This shows the existence of a period-doubling sequence culminating into a continual interchange between quasiperiodic and chaotic response. It also demonstrates a new transition scenario from phase-locked to phase-entrained and drift response.

The present work investigates dynamics of a gear-pair system involving backlash and time-dependent mesh stiffness. In addition, the system is under the action of external excitation, caused by torsional moments and gear geometry errors. First, the equation of motion is established in a strongly non-linear form. Then, the emphasis is laid on a specific forcing frequency range, corresponding to conditions of simultaneous fundamental parametric resonance and principal external resonance. For these conditions, several types of periodic steady state response are identified and determined by employing suitable methodologies, including techniques applicable to piecewise linear systems and to oscillators with time-periodic coefficients. Moreover, these methodologies are complemented by appropriate procedures revealing the stability properties of the located periodic solutions. In the second part of the work, numerical results are presented. These results verify the validity and effectiveness of the new analytical methodology and provide information on the gear-pair dynamics. First, series of typical response diagrams are obtained, illustrating the effect of the mesh stiffness variation, the damping and the forcing parameters on the gear-pair periodic response. These response diagrams are accompanied by results obtained with direct integration of the equation of motion. In this way, it is demonstrated that for some parameter combinations, the dynamical system examined can exhibit more complicated and irregular response, including crises and intermittent chaos.

Dynamics of a class of strongly nonlinear single degree of freedom oscillators is investigated. Their common characteristic is that they possess piecewise linear damping properties, which can be expressed in a general asymmetric form. More specifically, the damping coefficient and a constant parameter appearing in the equation of motion are functions of the velocity direction. This class of oscillators is quite general and includes other important categories of mechanical systems as special cases, like systems with Coulomb friction. First, an analysis is presented for locating directly exact periodic responses of these oscillators to harmonic excitation. Due to the presence of dry friction, these responses may involve intervals where the oscillator is stuck temporarily. Then, an appropriate stability analysis is also presented together with some quite general bifurcation results. In the second part of the work, this analysis is applied to several example systems with piecewise linear damping, in order to reveal the most important aspects of their dynamics. Initially, systems with symmetric characteristics are examined, for which the periodic response is found to be symmetric or asymmetric. Then, dynamical systems with asymmetric damping characteristics are also examined. In all cases, emphasis is placed on investigating the low forcing frequency ranges, where interesting dynamics is noticed. The analytical predictions are complemented with results obtained by proper integration of the equation of motion, which among other responses reveal the existence of quasiperiodic, chaotic and unbounded motions.

An analysis is presented on the dynamics of asymmetric self-excited oscillators with one-to-two internal resonance. The essential behavior of these oscillators is described by a two degree of freedom system, with equations of motion involving quadratic nonlinearities. In addition, the oscillators are under the action of constant external loads. When the nonlinearities are weak, the application of an appropriate perturbation approach leads to a set of slow-flow equations, governing the amplitudes and phases of approximate motions of the system. These equations are shown to possess two different solution types, generically, corresponding to static or periodic steady-state responses of the class of oscillators examined. After complementing the analytical part of the work with a method of determining the stability properties of these responses, numerical results are presented for an example mechanical system. Firstly, a series of characteristic response diagrams is obtained, illustrating the effect of the technical parameters on the steady-state response. Then results determined by the application of direct numerical integration techniques are presented. These results demonstrate the existence of other types of self-excited responses, including periodically-modulated, chaotic, and unbounded motions.

A finite element model is presented for the seismic response of liquid-filled tanks. This type of analysis is complicated for unanchored tanks, because the bases of these tanks separate from their foundations during strong ground motion. This changes the dynamic behavior of these structures considerably and may result in severe loading. The analysis starts by geometrically discretizing the shell structure using cylindrical finite elements. Then, application of Hamilton’s principle in the structural domain yields the equations of motion for the coupled fluid/structure system. The foregoing analytical procedure employs the closed-form solution for the hydrodynamic response problem, resulting in a compact system of equations of motion. Primary attention is paid to the formulation of the nonlinear base uplift problem. Effects due to shell and ground flexibility are also included.

An analysis is presented on the dynamics of a two-degree-of-freedom non-linear mechanical oscillator. The model consists of a rigid body which is supported by non-linear springs and can exhibit both vertical translation and rocking motions. Attention is focused on the response of the system under external excitation of the translation only, close to conditions of subharmonic resonance of order three. For the cases where the two linear natural frequencies of the system are almost identical, approximate periodic motions are determined by applying the method of multiple time scales. It is shown that besides linear and non-linear single-mode response, two-mode response is also possible, due to the 1:1 internal resonance. Some important aspects of the dynamics when no internal resonance is activated are also investigated. Next, the analytical findings the effect of the system parameters on the existence and stability of the predicted motions. The results reveal patterns of appearance of the periodic motions, providing valuable help in the efforts to eliminate them and achieve proper vibration isolation. Finally, direct integration of the original equations of motion shows that complex responses of the system can coexist with the analytically predicted motions, within the frequency ranges of interest.

Non-linear vibration of rotating thin circular rings under parametric excitation is analyzed. First, a geometrical discretization is performed by applying an energy principle. The resulting dynamical model involves two degrees of freedom, representing the vibration amplitudes of two in-plane flexural modes with the same circumferential wavenumber. These modes are coupled through gyroscopic and non-linear terms, while the parametric excitation originates by small periodic perturbations of the spin speed of the ring. Then, approximate solutions are determined by applying the method of multiple time scales. It is first shown thatonlycombination parametric resonance of the additive type is possible for the system examined. For this case, the existence and stability properties of the constant solutions of the averaged equations—corresponding to trivial or quasi-periodic motions of the original system—are investigated. Then, emphasis is placed on understanding the relation between the response of the slightly damped and the undamped system, as well as the transition from a rotating to a stationary state. Finally, a numerical study of the original dynamical system with small damping is performed, demonstrating the existence and coexistence of a quasi-periodic response with subharmonic, chaotic and unbounded motions.

A singular perturbation method is applied in carrying out an investigation on the connection between frequency veering and mode localization phenomena in a two-degree-of-freedom damped linear oscillator. The components of the system examined are dissimilar, and as a result the modes are localized for most of the combinations of the parameters. However, the natural frequencies become close, leading to curve veering, only for some special combinations of the parameters. A typical mathematical consequence is that regular perturbation expansions of the natural frequencies, in terms of a single parameter, break down in the vicinity of curve veering. In the present study, damping effects are included and this breakdown is shown to happen for the natural frequencies as well as the damping ratios of the system examined. This difficulty is eventually overcome by applying the method of matched asymptotic expansions. Accurate, uniformly valid expressions are derived for both the frequencies of free oscillation and the corresponding damping ratios. Copyright 1993, 1999 Academic Press

An analysis is presented for determining exact steady state response for a class of strongly non-linear multiple-degree-of-freedom oscillators. These oscillators consist of a linear component, with an arbitrary number of degrees of freedom and configuration, incorporating a component with a geometric non-linearity. Their behavior is analyzed by generalizing previous work on single- and two-degree-of-freedom piecewise linear systems under harmonic excitation. First, a methodology is developed for locating harmonic and subharmonic response characterized by one abrupt change of the parameters of the non-linear element per response cycle. Then, a stability analysis is presented, which is appropriate for general piecewise linear systems. The present analysis is applicable to a variety of engineering areas. Here, its validity and effectiveness is demonstrated by applying it to two classes of problems with large practical significance and rich dynamics. Performance of vibration absorbers with elastic stops is investigated first, while in the second category of examples the oscillators exhibit 2:1 and 3:1 internal resonance. Regular and irregular motions are encountered and analyzed. The response characteristics are compared with those of systems with continuous non-linearities. Copyright 1993, 1999 Academic Press

Two simplified models are presented for determining the hydrodynamic loads developed during the seismic response of tall unanchored liquid storage tanks. In both models the general procedure starts by first solving the fluid response problem in closed form. This eliminates all but the sloshing unknowns associated with the hydrodynamic problem. In the first model, the geometrical discretization is performed by applying the assumed mode method. In the second model, the system parameters are identified by requiring the same base loads when the real system and the model are subjected to the same base motion. During the formulation process, special attention is paid to developing a simple but sufficiently accurate analytical modeling of the mechanism associated with the separation of the base plate of the tank from its foundation, which occurs during strong ground motion. Soil flexibility and liquid sloshing effects are also modeled. The accuracy of both models is verified by comparison with experimental data. In addition, this comparison shows the applicability of these models for determining the seismic loads in tall unanchored tanks.

A finite element model is presented for the seismic response of liquid-filled tanks. This type of analysis is complicated for unanchored tanks, because the bases of these tanks separate from their foundations during strong ground motion. This changes the dynamic behavior of these structures considerably and may result in severe loading. The analysis starts by geometrically discretizing the shell structure using cylindrical finite elements. Then, application of Hamilton’s principle in the structural domain yields the equations of motion for the coupled fluid/structure system. The foregoing analytical procedure employs the closed-form solution for the hydrodynamic response problem, resulting in a compact system of equations of motion. Primary attention is paid to the formulation of the nonlinear base uplift problem. Effects due to shell and ground flexibility are also included.

A methodology is first presented for analyzing long time response of periodically exited nonlinear oscillators. Namely, a systematic procedure is employed for determining periodic steady state response, including harmonic and superharmonic components. The stability analysis of the located periodic motions is also performed, utilizing results of Froquet theory. This methodology is then applied to a special class of two degree of freedom nonlinear oscillators, subjected to harmonic excitation. The numberical results presented in the second part of this study illustrate effects caused by the interaction of the modes as well as effects of the nonlinearities on the steady state response of these oscillators. In addition, sequences of bifurcations are analyzed for softening systems, leading to unbounded response of the model examined. Finally, the importance of higher harmonics on the response of systems with strongly nonlinear characteristics is investigated.

This work investigates nonlinear dynamic response of circular rings rotating with spin speed which involves small fluctuations from a constant average value. First, Hamilton's principle is applied and the equations of motion are expressed in terms of a single time coordinate, representing the amplitude of an in-plane bending mode. For nonresonant excitation or for slowly rotating rings, a complete analysis is presented by employing phase plane methodologies. For rapidly rotating rings, periodic spin speed variations give rise to terms leading to parametric excitation. In this case, the vibrations that occur under principal parametric resonance are analyzed by applying the method of multiple scales. The resulting modulation equations possess combinations of trivial and nontrivial constant steady state solutions. The existence and stability properties of these motions are first analyzed in detail. Also, analysis of the undamped slow-flow equations provides a global picture for the possible motions of the ring. In all cases, the analytical predictions are verified and complemented by numerical results. In addition to periodic response, these results reveal the existence of unbounded as well as transient chaotic response of the rotating ring.

An analytical investigation is carried out on the free vibration of a two degree of freedom weakly nonlinear oscillator. Namely, the method of multiple time scales is first applied in deriving modulation equations for a van der Pol oscillator coupled with a Duffing oscillator. For the case of non-resonant oscillations, these equations are in standard normal form of a codimension two (Hopf-Hopf) bifurcation, which permits a complete analysis to be performed. Three different types of asymptotic states-corresponding to trivial, periodic and quasiperiodic motions of the original system-are obtained and their stability is analyzed. Transitions between these different solutions are also identified and analyzed in terms of two appropriate parameters. Then, effects of a coupling, a detuning, a nonlinear stiffness and a damping parameter are investigated numerically in a systematic manner. The results are interpreted in terms of classical engineering terminology and are related to some relatively new findings in the area of nonlinear dynamical systems.

The forced response of a class of weakly non-linear oscillators with self-excited characteristics is investigated. The non-linearity is symmetric, the external forcing is harmonic and the essential dynamics are described by a two-degree-of-freedom oscillator, whose linear natural frequencies satisfy conditions of 1:3 internal resonance. Firstly, sets of equations governing the slow time variation of the amplitudes and phases of approximate solutions of the equations of motion are obtained by applying an asymptotic analytical method. For primary resonance of the first mode, only mixed-mode response is possible, since the second mode is always activated through the non-linearities. On the other hand, when conditions of primary resonance of the second mode are met, single-mode response is also possible. In both cases, a methodology is developed which reduces the determination of constant solutions of the slow-flow equations to the solution of two coupled polynomial equations. The stability analysis of these solutions is also provided. Next, numerical results are presented for an example practical system, in the form of response diagrams. These results show the effect of some system parameters on the existence and interaction of various branches of constant solutions. Then, more numerical results are presented, obtained by direct integration of the slow-flow equations in forcing frequency ranges where these equations possess no stable constant solution. The results demonstrate the existence of periodic and chaotic solutions of these equations.

The dynamics of two-degree-of-freedom oscillators including Rayleigh and Duffing type non-linearities is investigated. The method of multiple scales is first applied and a set of averaged equations is derived for cases of primary external resonance. These equations admit two types of constant solutions. The first type involves the directly excited mode only, while for some parameter combinations the non-linear damping terms excite the second mode also, even when no internal resonance is present. Stability and bifurcation analyses are then presented. Emphasis is placed on deriving explicit conditions on the system parameters that will lead to forms of the evolution equations which can be studied in detail, by utilizing results from the area of dynamical systems. To illustrate the effectiveness and accuracy of the analysis, numerical results are presented for a dynamic model of a specific practical system: namely, a three-parameter study is first carried over in order to reveal basic response features of a metal cutting system. Codimension one, two and three bifurcations are determined and their effect on the interaction and transition between the response modes is investigated. A representative sample of response diagrams and results from direct integration are also presented, providing an overall picture of the dynamics.

The stability analysis for periodic motions of a class of harmonically excited single degree of freedom oscillators with piecewise linear characteristics is presented. The common characteristic of these oscillators is that they posses viscous and constant damping properties, which depend on their velocity direction. The presence of constant damping terms in the equation of motion introduces acceleration discontinuities and makes possible the appearance of finite time intervals within the periodic solution where the oscillator is stuck at the same position. Harmonic and subharmonic motions with an arbitrary number of solution pieces are examined. The analysis takes advantage of the fact that the exact solution form for any solution piece included between two consecutive zero velocity values is known. It is based on the derivation of a matrix relation which determines how an arbitrary but small perturbation at the beginning of a periodic solution propagates to the end of a response period. Then, results obtained by bifurcation analysis of the periodic solutions are also presented. At the end, some of the analytical predictions are confirmed by considering an example mechanical model.

investigation is carried out for a class of piecewise linear oscillators with asymmetric characteristics. The damping and restoring forces are general trilinear functions of the system velocity and displacement, respectively, while the excitation is harmonic in time. First, an analysis is presented which determines harmonic and subharmonic steady-state response. Then, a special formulation is employed in examining the stability of located periodic motions. Finally, numerical results are presented for several representative sets of the system parameters. Effects of asymmetries in the response due to unequal gaps as well as unequal stiffness and damping coefficients are analyzed in detail. Asymmetric response of a system with symmetric technical characteristics is also investigated. The behavior of the systems examined resembles response of similar nonlinear systems with continuous characteristics, like the response of the Duffing and van der Pol oscillators. Complicated nonperiodic response is also encountered and analyzed.

An averaging methodology is employed in studying dynamics of a two-degree-of-freedom nonlinear oscillator. The main system is modeled as a van der Pol oscillator under harmonic forcing. The objective is to reduce its amplitude of oscillation near resonance, by attaching to it a damped vibration absorber with a Duffing spring. It is first shown that substantial reduction in the response amplitude can be achieved in this way. However, for some combinations of the parameters, the low-amplitude periodic motion of the system in the original resonance regime becomes unstable through a Hopf bifurcation of the averaged equations. Direct numerical integration shows that this gives rise to amplitude modulated or chaotic response of the oscillator, with much higher vibration amplitudes than the unstable periodic response, which coexists with these complex motions. Finally, it is shown that the present analysis can be employed in selecting the parameters in ways that exploit the significant practical advantages arising from the presence of the absorber, by predicting and avoiding these instabilities.

An explanation is provided for the earthquake-induced damage observed at the top of liquid storage tanks. An analysis is developed and the results are compared with experimental work. The basic steps of the analysis, which is developed for the general dynamic response of fluid-filled tanks under horizontal ground excitation, are first presented. In this analysis, the structural displacements are expanded in appropriate series forms which involve both rigid body and flexible components. The latter components are expressed as linear combinations of terms, each of which is a product of a function with assumed spatial dependence and an unknown time-dependent function. These time functions are then determined from the solution of the fluid/structure system equations, which are set up by employing Hamilton’s principle. In the present work, results are obtained and compared with model tests carried out at Caltech, during which buckling was observed at the top of the tank under a known base excitation history. Computing analytically the corresponding pressure distribution and using the BOSOR computer code for the buckling computations, a value for the amplitude of the ground acceleration which results in buckling at the top of the tank is calculated. Good correlation with the test work is obtained.

An analysis is presented for a class of two degree of freedom weakly nonlinear oscillators, with symmetric restoring force. Conditions of one-to-three internal resonance and subharmonic external resonance of the lower vibration mode are assumed to be satisfied simultaneously. As a consequence, the second vibration mode may also be under the action of external primary resonance. Initially, a set of slow-flow equations is derived, governing the amplitudes and phases of approximate long time response of these oscillators, by applying an asymptotic analytical method. Determination of several possible types of steady-state motions is then reduced to solution of sets of algebraic equations. For all these solution types, appropriate stability analysis is also performed. In the second part of the study, this analysis is applied to an example mechanical system. First, a systematic search is performed, revealing effects of system parameters on the existence and stability properties of periodic motions. Frequency-response diagrams are presented and attention is focused on understanding the evolution and interaction of the various solution branches as the external forcing and nonlinearity parameters are varied. Finally, numerical integration of the equations of motion demonstrates that the system exhibits quasiperiodic or chaotic response for some parameter combinations.

Free vibration of a two degree of freedom weakly nonlinear oscillator is investigated. The type of nonlinearity considered is symmetric, it involves displacement as well as velocity terms and gives rise to self-excited oscillations in many engineering applications. After presenting the equations of motion in a general form, a perturbation methodology is applied for the case of 1:3 internal resonance. This yields a set of four slow-flow nonlinear equations, governing the amplitudes and phases of approximate motions of the system. It is then shown that these equations possess three distinct types of solutions, corresponding to trivial, single-mode and mixed-mode response of the system. The stability analysis of all these solutions is also performed. Next, numerical results are presented by applying this analysis to a specific practical example. Response diagrams are obtained for various combinations of the system parameters, in an effort to provide a complete picture of the dynamics and understand the transition from conditions of 1:3 internal resonance to non-resonant response. Emphasis is placed on identifying the effect of the linear damping, the frequency detuning and the stiffness nonlinearity parameters. Finally, the predictions of the approximate analysis are confirmed and extended further by direct integration of the averaged equations. This reveals the existence of other regular and irregular motions and illustrates the transition from phase-locked to drift response, which takes place through a Hopf bifurcation and a homoclinic explosion of the averaged equations.

An analysis developed for the response of liquid storage tanks under horizontal base excitation is employed and numerical results are obtained for unanchored tanks. These results are compared and found to be in good agreement with experimental data. Base uplift is shown to cause a dramatic reduction in the effective beam-type stiffness of a tank, which in turn reduces the tank response frequency and changes the developed hydrodynamic loads significantly. Based on these results, an explanation is provided for some great qualitative and quantitative differences in the behavior of a tank, resulting from its base fixity condition alone.

A set of equations is derived describing the dynamic response of cylindrical liquid storage tanks under horizontal ground excitation. The structure consists of a flexible cylindrical tank with a roof and a bottom plate and rests on a flexible ground through a rigid foundation. Portion of the base of the tank may separate from and lift off the foundation during ground motion. The solution of the hydrodynamic problem is first found in closed form. Then, Hamilton’s principle is applied and the equations governing the behavior of the coupled fluid/structure/ground system are derived. During this procedure, the base uplifting is modeled by an appropriate rotational nonlinear spring placed between the base of the tank and the foundation.

Two simplified models are presented for determining the hydrodynamic loads developed during the seismic response of tall unanchored liquid storage tanks. In both models the general procedure starts by first solving the fluid response problem in closed form. This eliminates all but the sloshing unknowns associated with the hydrodynamic problem. In the first model, the geometrical discretization is performed by applying the assumed mode method. In the second model, the system parameters are identified by requiring the same base loads when the real system and the model are subjected to the same base motion. During the formulation process, special attention is paid to developing a simple but sufficiently accurate analytical modeling of the mechanism associated with the separation of the base plate of the tank from its foundation, which occurs during strong ground motion. Soil flexibility and liquid sloshing effects are also modeled. The accuracy of both models is verified by comparison with experimental data. In addition, this comparison shows the applicability of these models for determining the seismic loads in tall unanchored tanks.

In this study, a review is presented on previous work referring to analytical modeling of mechanical systems having components that come in contact during their motion in ways that involve impact and/or friction. This study is focused mostly on dynamical systems that can be represented by a finite number of degrees-of-freedom. First, models consisting of oscillators are considered and the contact action is represented by a combination of discrete spring and damper elements or rigid constraints. These models may also involve clearances and effects from friction forces. Then, systems involving rigid or discretized deformable components are examined. Depending on the approach chosen, a contact event is modeled in either an algebraic or a differential manner. In the former, the concept of a restitution coefficient plays a dominant role. In the latter, the Darboux–Keller method is applied, which also requires a restitution coefficient but considers the dynamics during the contact phase by using the normal impulse component as an independent variable, in place of time. The same category of systems is also examined next, separately, by considering techniques of nonsmooth mechanics, which are more convenient to apply in several cases, like in modeling multiple contact events. Finally, some special recent techniques developed for Filippov systems and for systems involving impact and friction are presented. This study concludes by identifying and suggesting possible topics for future research.

A systematic theoretical approach is presented, revealing dynamics of a class of multibody systems. Specifically, the motion is restricted by a set of bilateral constraints, acting simultaneously with a unilateral constraint, representing a frictional impact. The analysis is carried out within the framework of Analytical Dynamics and uses some concepts of differential geometry, which provides a foundation for applying Newton's second law. This permits a successful and illuminating description of the dynamics. Starting from the unilateral constraint, a boundary is defined, providing a subspace of allowable motions within the original configuration manifold. Then, the emphasis is focused on a thin boundary layer. In addition to the usual restrictions imposed on the tangent space, the bilateral constraints cause a correction of the direction where the main impulse occurs. When friction effects are negligible, the dominant action occurs along this direction and is described by a single nonlinear ordinary differential equation (ODE), independent of the number of the original generalized coordinates. The presence of friction increases this to a system of three ODEs, capturing the essential dynamics in an appropriate subspace, arising by bringing the image of the friction cone from the physical to the configuration space. Moreover, it is shown that the classical Darboux–Keller approach corresponds to a special case of the new method. Finally, the theoretical results are complemented by a selected set of numerical results for three examples.