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An analytical rheological‐dynamical visco‐elastic solution of one‐dimensional longitudinal continuous vibration of bars has been developed and used to evaluate the validity of the classical analytical elastic solutions. As it is well known, the resonance occurs only in the continuous or singledegree‐of‐freedom ideal elastic system when the excitation frequency ωP is equal to the one of the natural frequency of the bar. However, owing to the visco‐elastic nature of materials and frequency dependence of the damping factor it is useful to consider separately the situations arising when the is positive (system is stable) and when it is negative. Negative damping factor means that the complementary solution of the response would not die away (system is unstable because of the factor e). Rheologic behavior of the bar can be characterized by one parameter, i.e. dynamic time of retardation TK D=1/ω, like in a single‐degree‐of‐freedom spring mass system. RDA model has the same phase angle as a simple single‐degree‐of‐freedom spring mass system with damping in the steady state vibration and from that the damping factor is obtained. This paper provides description of the dynamic magnification factor and the transmissibility of several metallic materials using RDA similitude and could be concluded that an ideally effective antivibration mount material should satisfy at least two requirements: first, it should posses a relatively large damping factor; and second, it should possess a damping factor that either remains constant or decreases only slowly with frequency.

This paper aims to simplify a new frequency-independent model to calculate vertical vibration of rigid circular foundation resting on homogenous half-space and subjected to vertical harmonic excitation is presented in this paper.

The proposed model is an oscillator of single degree of freedom, which comprises a mass, a spring and a dashpot. In addition, a fictitious mass is added to the foundation. All coefficients are frequency-independent. The spring is equal to the static stiffness. Damping coefficient and fictitious mass are first calculated at resonance frequency where the response is maximal. Then, using a curve fitting technique the general formulas of damping and fictitious mass frequency-independent are established.

The validity of the proposed method is checked by comparing the predicted response with those obtained by the half-space theory. The dynamic responses of the new simplified model are also compared with those obtained by some existing lumped-parameter models.

Using this new method, to calculate the dynamic response of foundations, the engineer only needs the geometrical and mechanical characteristics of the foundation (mass and radius) and the soil (density, shear modulus and the Poisson’s ratio) using just a simple calculator. Impedance functions will no longer be needed in this new simplified method. The methodology used for the development of the new simplified model can be applied for the resolution of other problems in dynamics of soil and foundation (superficial and embedded foundations of arbitrary shape, other modes of vibration and foundations resting on non-homogeneous soil).

A newly developed frequency-independent lumped parameter model (LPM) is the purpose of the present paper. This new model’s direct outcome ensures high efficiency and a straightforward calculation of foundations’ vertical vibrations. A rigid circular foundation shape resting on a nonhomogeneous half-space subjected to a vertical time-harmonic excitation is considered.

A simple model representing the soil–foundation system consists of a single degree of freedom (SDOF) system incorporating a lumped mass linked to a frequency-independent spring and dashpot. Besides that, an additional fictitious mass is incorporated into the SDOF system. Several numerical methods and mathematical techniques are used to identify each SDOF’s parameter: (1) the vertical component of the static and dynamic foundation impedance function is calculated. This dynamic interaction problem is solved by using a formulation combining the boundary element method and the thin layer method, which allows the simulation of any complex nonhomogeneous half-space configuration. After, one determines the static stiffness’s expression of the circular foundation resting on a nonhomogeneous half-space. (2) The system’s parameters (dashpot coefficient and fictitious mass) are calculated at the resonance frequency; and (3) using a curve fitting technique, the general formulas of the frequency-independent dashpot coefficients and additional fictitious mass are established.

Comparisons with other results from a rigorous formulation were made to verify the developed model’s accuracy; these are exceptional cases of the more general problems that can be addressed (problems like shallow or embedded foundations of arbitrary shape, other vibration modes, etc.).

In this new LPM, the impedance functions will no longer be needed. The engineer only needs a limited number of input parameters (geometrical and mechanical characteristics of the foundation and the soil). Moreover, a simple calculator is required (i.e. we do not need any sophisticated software).

This paper is concerned with a new proposal regarding the analysis of visco‐elastoplasticity and fatigue and is based on rheological‐dynamical theory. Due to the analogy between rheological model and dynamical model with viscous damping, it becomes obvious that inelastic response of members is essentially a dynamical problem. An analytical rheological‐dynamical viscoelasto‐ plastic solution of one‐dimensional longitudinal continuous vibration under loading and solution for the stress relaxation as unloading have been developed and used to obtain the fatigue limit of thin long bars. Rheologic behavior of the bar can be characterized by one parameter, like in a single‐degree‐of‐freedom spring mass system. In all inelastic strains time rate effects are always present to some degree. Whether or not their exclusion has a significant influence on the prediction of the material fatigue behavior depends upon several factors like: maximum absolute stress in the cycle, coefficient of asymmetry of cycle, creep coefficient, slope of the strain hardening portion of the stress‐strain curve, relative frequency and uniaxial yield stress. This paper provides description of dynamic magnification factor, relaxation of stress, stress concentration and the fatigue limit of thin long symmetrical bars.

The purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.

The problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.

The modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.

The paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

In this study, a railway superstructure is modeled with a new approach called locally continuous supporting, and its behavior under the effect of moving load is analyzed by using analytical and numerical techniques. The purpose of the study is to demonstrate the success of the new modeling technique.

In the railway superstructure, the support zones are not modeled with discrete spring-damping elements. Instead of this, it is considered to be a continuous viscoelastic structure in the local areas. To model this approach, the governing partial differential equations are derived by Hamilton’s principle and spatially discretized by the Galerkin’s method, and the time integration of the resulting ordinary differential equation system is carried out by the Newmark–Beta method.

Both the proposed model and the solution technique are verified against conventional one-dimensional and three-dimensional finite element models for a specific case, and a very good agreement between the results is observed. The effects of geometric, structural, and loading parameters such as rail-pad length, rail-pad stiffness, rail-pad damping ratio, the gap between rail pads and vehicle speed on the dynamic response of railway superstructure are investigated in detail.

There are mainly two approaches to the modeling of rail pads. The first approach considers them as a single spring-damper connected in parallel located at the centroid of the rail pad. The second one divides the rail pad into several parts, with each of part represented by an equivalent spring-damper system. To obtain realistic results with minimum CPU time for the dynamic response of railway superstructure, the rail pads are modeled as continuous linearly viscoelastic local supports. The mechanical model of viscoelastic material is considered as a spring and damper connected in parallel.

The purpose of this study a fast procedure for the structural analysis of gas turbine blades in aircraft engines. In this connection, investigations on the behavior of gas turbine blades concentrate on the analysis and evaluation of starting dynamics and fatigue strength. Besides, the influence of structural mistuning on the vibration characteristics of the single blade is analyzed and discussed.

A basic computation cycle is generated from a flight profile to describe the operating history of the gas turbine blade properly. Within an approximation approach for high-frequency vibrations, maximum vibration amplitudes are computed by superposition of stationary frequency responses by means of weighting functions. In addition, a two-way coupling approach determines the influence of structural mistuning on the vibration of a single blade. Fatigue strength of gas turbine blades is analyzed with a semi-analytical approach. The progressive damage analysis is based on MINER’s damage accumulation assuming a quasi-stable behavior of the structure.

The application to a gas turbine blade shows the computational capabilities of the approach presented. Structural characteristics are obtained by robust and stable computations using a detailed finite element model considering different load conditions. A high quality of results is realized while reducing the numerical costs significantly.

The method used for analyzing the starting dynamics is based on the assumption of a quasi-static state. For structures with a sufficiently high stiffness, such as the gas turbine blades in the present work, this procedure is justified. The fatigue damage approach relies on the existence of a quasi-stable cyclic stress condition, which in general occurs for isotropic materials, as is the case for gas turbine blades.

Owing to the use of efficient analysis methods, a fast evaluation of the gas turbine blade within a stochastic analysis is feasible.

The fast numerical methods and the use of the full finite element model enable performing a structural analysis of any blade structure with a high quality of results.

To propose novel predictor‐corrector time‐integration algorithms for pseudo‐dynamic testing.

The novel predictor‐corrector time‐integration algorithms are based on both the implicit and the explicit version of the generalized‐α method. In the non‐linear unforced case second‐order accuracy, stability in energy, energy decay in the high‐frequency range as well as asymptotic annihilation are distinctive properties of the generalized‐α scheme; while in the non‐linear forced case they are the limited error near the resonance in terms of frequency location and intensity of the resonant peak. The implicit generalized‐α algorithm has been implemented in a predictor‐one corrector form giving rise to the implicit IPC‐ρ_∞ method, able to avoid iterative corrections which are expensive from an experimental standpoint and load oscillations of numerical origin. Moreover, the scheme embodies a secant stiffness formula able to approximate closely the actual stiffness of a structure. Also an explicit algorithm has been implemented, the EPC‐ρ_b method, endowed with user‐controlled dissipation properties. The resulting schemes have been tested experimentally both on a two‐ and on a six‐degrees‐of‐freedom system, exploiting substructuring techniques.

The analytical findings and the tests have indicated that the proposed numerical strategies enhance the performance of the pseudo‐dynamic test (PDT) method even in an environment characterized by considerable experimental errors. Moreover, the schemes have been tested numerically on strongly non‐linear multiple‐degrees‐of‐freedom systems reproduced with the Bouc‐Wen hysteretic model, showing that the proposed algorithms reap the benefits of the parent generalized‐α methods.

Further developments envisaged for this study are the application of the IPC‐ρ_∞ method and of EPC‐ρ_b scheme to partitioned procedures for high‐speed pseudo‐dynamic testing with substructuring.

The implicit IPC‐ρ_∞ and the explicit EPC‐ρ_b methods allow a user to have defined dissipation which reduces the effects of experimental error in the PDT without needing onerous iterations.

The paper proposes novel time‐integration algorithms for pseudo‐dynamic testing. Thanks to a predictor‐corrector form of the generalized‐α method, the proposed schemes maintain a high computational efficiency and accuracy.

Based on the Jones (1971) model, we construct two dynamic models of international trade in which the rate of time preference is either constant or time-varying. The main purpose is to study whether and under what conditions the results derived in the Jones model still hold in the dynamic framework. It is shown that the results of dynamic models may be similar or different to those obtained in the static model. For example, it is possible that, in both static and dynamic models, an increase in the commodity price raises this commodity's output and the return to the specific factor in this sector. However, the effects on the wage rate may be different due to the factor accumulation impact in the dynamic framework.

Usual definitions of damping in oscillatory modes are reviewed, a new definition is proposed and it is suggested that the latter offers certain advantages to both the theoretical and the practical worker in this field. An Appendix contains response formulae for three fundamental types of disturbance. These can be used for the derivation of the various expressions characterizing dynamic properties of any mode that is equivalent to a damped system of one degree of freedom. A collection of formulae, numerical tables and graphs permit a quick comparison to be made between the different definitions of damping.