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The paper is devoted to the analysis of the influence of ambient temperature on the linear free and non-linear harmonic vibrations of laminate plates with viscoelastic layers. The Zener fractional material model is adopted. The plate kinematics is described using the refined zig-zag theory. The formulation of vibrations of the plate is based on the physical law with the separation of deviatoric and volumetric deformation. The temperature influence is included using the frequency-temperature superposition principle. The shift factor applied to modify the damping properties of the viscoelastic material is computed using the Willams-Landel-Ferry formula. The paper contains the results of several analyses of laminate plates with various viscoelastic materials for which the material data were available in the literature. In particular, the analyses focus on determination of the properties characteristic for the plates with Zener fractional model under the influence of the ambient temperature. • Frequency-temperature superposition for temperature influence on plates vibrations • Refined zig-zag theory applied to define the plate kinematics • Fractional Zener material with separated volumetric and deviatoric deformation • Numerous analyses of various viscoelastic materials • Explanation of non-monotonous character of temperature effects on damping [ABSTRACT FROM AUTHOR]

Background: This study empirically evaluates the influence of medical information on patient trust at the physician level, the medical profession, hospitals, and with the payer. Restoring patient trust in a medical setting in Poland appears to be significantly affected due to the COVID-19 pandemic. Patient trust improves results from medical treatment, raises perception of healthcare performance, and smoothens the overall functionality of healthcare systems.Methods: In order to study trust volatility, patients took part in a three-stage experiment designed via: (1) measured level of trust, (2) randomly dividing participants into two groups-control (i.e., re-examination of level of trust) and experimental (i.e., being exposed to a piece of certain manipulative information), and (3) checking whether observational changes were permanent.Results: Results indicate that in the experimental group the increase of trust was noticed in the payer (27.7%, p < 0.001), hospitals (10.9%, p = 0.011), and physicians (decrease of 9.2%, p = 0.036).Conclusion: The study indicated that in Poland medical information is likely to influence patient trust in healthcare while interpersonal and social trust levels may be related to increases of trust in hospitals and in the payer versus decreases in physicians. [ABSTRACT FROM AUTHOR]

Passive damping systems are energy dissipating devices that are used in building constructions to reduce excessive vibration caused by wind or earthquakes. Recently, the use of inerters, devices using the inertia of the rotating mass, as a passive damping system has become more and more popular. Inerter, regardless of the construction, generates a resistance force that is proportional to the relative acceleration at the terminal ends of the device. The purpose of this study is to evaluate the effectiveness of the viscoelastic (VE) dampers in combination with the inerter. For the derived equations of motion of structures with VE dampers and inerters, the Laplace transformation is applied, which leads to a nonlinear eigenproblem. The solution to the eigenproblem is obtained using the continuation method, also known as the homotopy or as the path following method. It was found that for some cases of inerter connection with ve damper, there are some additional solutions in relation to the degrees of freedom of the structure. Furthermore, the dynamic characteristics of the structure associated with the above-mentioned additional eigenvalue are strongly dependent on the equivalent inerter mass. Damping efficiency is tested by determining changes in the system's dynamic characteristics: natural frequencies, non-dimensional damping ratios and displacement transfer functions. The presented approach allows determining the appropriate parameters of the inerter and VE damper and their appropriate location on the structures that correspond to the most effective damping. The obtained numerical results confirm the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Planar frame structures made of a viscoelastic material are considered in the paper. The technically very important structures made of a homogenous material are contemplated. A family of rheological models (classic and fractional) are used to describe the mechanical properties of the viscoelastic material. In particular, the dynamic characteristics of the structures are of interest. A numerically very efficient method is proposed to determine such characteristics. The method requires the solution to the linear eigenvalue problem for corresponding elastic structures and the solution to a nonlinear, algebraic equation. The presented method is much more efficient than other methods where, very often, the continuation method is used to solve the nonlinear eigenvalue problem. The influence of temperature changes on dynamic characteristics is analyzed using the frequency–temperature principle. The results of several parametric analyses are presented and discussed. For the first time, the influence of temperature on the dynamic characteristics of beams has been studied in detail. [ABSTRACT FROM AUTHOR]

• Harmonic vibrations of VE laminate plates with exponential complex-conjugate solution form and harmonic balance method. • The use of refined zig-zag theory for the description of layered plate kinematics. • Application of fractional Zener material model with separation of volumetric and deviatoric strain. The paper is devoted to the theoretical formulation of the harmonic vibrations problem for laminate plates in the von Kàrmàn geometrically non-linear regime. The plate layers are modelled as viscoelastic using the fractional Zener material with the linear elastic material being a special case. The model of the material is formulated with the separation of the volumetric and deviatoric strain. The laminate plate kinematics is described using the refined zig-zag theory. The vibrations of the plate are formulated using the alternative exponential form with complex-conjugate amplitudes. The harmonic balance method and the time-averaging are applied to derive the amplitude equation of the problem in hand. The efficiency and correctness of the formulation is verified in the continuation paper Part 2 – numerical analysis. [ABSTRACT FROM AUTHOR]

• FE solution of harmonic vibrations for VE layered plates with exponential complex-conjugate form and refined zig-zag theory. • Effective application of the continuation method to solve the discretised amplitude equation. • Numerous analyses of the influence of various plate and formulation parameters on the resonance behaviour of laminate plates. The paper is devoted to the numerical analysis of the harmonic vibrations of laminate plates with viscoelastic layers in the von Kàrmàn geometrically non-linear regime. The amplitude equation derived in the prequel paper Part 1 – theoretical background is discretized using the 8-noded bi-quadratic plate finite elements. The response curves are obtained using the continuation method to solve the discretised amplitude equation treated as the equation with the frequency of vibrations as a parameter. The proposed method of solution is verified by comparing the results with those from available literature. Furthermore, several numerical analyses are performed, including testing of FE mesh density, plate aspect ratio, various VE materials, support conditions and layers layout as well as the possibility of simplification of the complex-valued zig-zag function used in the description of plate kinematics. Several results of practical importance are found and discussed in the conclusions. [ABSTRACT FROM AUTHOR]

A method for analyzing the influence of temperature on the dynamic characteristics of structures with viscoelastic dampers is proposed in this paper. Dampers which are described by so-called fractional rheological models are considered. The temperature-frequency superposition principle is used to describe the influence of temperature on the dynamic characteristics. The concept of continuous dependence of damping on an artificially introduced parameter is adopted for solving, in an approximate way, the nonlinear eigenvalue problem from which dynamic characteristics are determined. The correctness and effectiveness of the method was verified by means of two examples. [ABSTRACT FROM AUTHOR]

This study concerns the structural systems in which additional damping was introduced by means of viscoelastic (VE) dampers modeled with the fractional derivative models. The fractional derivative models have an ability to correctly describe the behavior of VE materials in a wide range of frequency, using a small number of model parameters. However, the governing equation of motion includes fractional derivatives together with ordinary ones. In the proposed approach, after applying the Laplace transform and the inverse transform to the equations of motion, the solution obtained for the system with fractional dampers is equivalent to the modal solution used in the case of proportional damping. In order to validate the proposed approach, the maximum response of the structural system equipped with dampers is determined in the time domain. Thus, the equations of motion with fractional derivatives derived for the considered system are numerically integrated. Moreover, the paper extends the response spectrum concept to structures equipped with fractional viscoelastic dampers. [ABSTRACT FROM AUTHOR]

The paper is devoted to non-linear vibrations of plates, made of the Zener viscoelastic material modelled with the Caputo fractional derivative, and in particular to their response to harmonic excitation. The plate geometric non-linearity is of the von Kármán type. In the formulation shear effects and rotary inertia are considered, too. The problem is solved in the frequency domain. A one-harmonic form of the solution for plate displacements corresponding to the plate formulation is assumed. The amplitude equation is obtained from the time averaged principle of virtual work. The time averaging precedes the use of the harmonic balance method. In the space discretization the finite element method is used involving 8-noded rectangular plate elements with selective-reduced integration. Several numerical examples are analyzed and the response curves are found using a path-following method. The purpose of these analyses is to identify material features of the adopted model of viscoelasticity with the fractional derivative. [ABSTRACT FROM AUTHOR]

The problem of non-linear, steady state vibration of beams, harmonically excited by harmonic forces is investigated in the paper. The viscoelastic material of the beams is described using the Zener rheological model with fractional derivatives. The constitutive equation, which contains derivatives of both stress and strain, significantly complicates the solution to the problem. The von Karman theory is applied to take into account geometric nonlinearities. Amplitude equations are obtained using the finite element method together with the harmonic balance method, and solved using the continuation method. The tangent matrix of the amplitude equations is determined in an explicit form. The stability of the steady-state solution is also examined. A parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam's responses. [ABSTRACT FROM AUTHOR]

The influence of uncertain design parameters on dynamic characteristics and the frequency response function is considered in this paper. A structure with dampers modeled as a shear frame is analyzed. The dampers properties of dampers are described by fractional derivatives. The design parameters of the considered structure change only in a specified range and the interval analysis is taken into account in calculating the lower and upper bounds of dynamic characteristics. Several methods are used to obtain the limit values of objective functions: the vertex method and the method of approximation using the first- and the second-order Taylor series expansion. The vertex method is adopted as a comparative method. Two examples are presented in order to illustrate the considered methods. In the case of large uncertainties, the obtained results differ from those obtained by means of the vertex method. Therefore, a new method using the second-order Taylor series expansion is proposed. The method consists of a sequence of changes of only one parameter and requires much fewer combinations when the number of uncertain design parameters is high. [ABSTRACT FROM AUTHOR]

The problem of geometrically non-linear steady state vibrations of beams excited by harmonic forces is considered in this paper. The beams are made of a viscoelastic material defined by the classic Zener rheological model - the simplest model that takes into account all the basic properties of real viscoelastic materials. The constitutive stress-strain relationship for this type of material is given as a differential equation containing derivatives of both stress and strain. This significantly complicates the solution to the problem. The von Karman theory is applied to describe the effects of geometric nonlinearities of beam deformations. The equations of motions are derived using the finite element methodology. A polynomial approximation of bending moments is used. The order of basis functions is set so as to obtain a coherent approximation of moments and displacements. In the steady-state solution of equations of motion, only one harmonic is taken into account. The matrix equations of amplitudes are derived using the harmonic balance method and the continuation method is applied for solving them. The tangent matrix of equations of amplitudes is determined in an explicit form. The stability of steady-state solution is also examined. The resonance curves for beams supported in a different way are shown and the results of calculation are briefly discussed. [ABSTRACT FROM AUTHOR]

In paper the design sensitivity analysis of dynamic characteristics of structures with viscoelastic (VE) dampers is considered. The dampers are modeled using the classical rheological model and the rheological model with fractional derivatives. The design sensitivity is analyzed by using direct differentiation method and adjoint variables method. The formulae enabling the calculation of sensitivity of the first and the second order with respect to chosen design parameters have been derived. Sensitivity analysis of eigenvalues, eigenvectors and dynamic characteristics such as natural frequencies and non-dimensional damping ratios are presented. The correctness of the presented formulae is illustrated in examples. [ABSTRACT FROM AUTHOR]

This paper concerns the dynamic analysis of composite beams containing elastic and viscoelastic (VE) layers. A method for determination of the dynamic characteristics of multilayered beams with VE layers (i.e., natural frequencies, non-dimensional damping ratios and modes of vibration) is presented. The Euler-Bernoulli beam theory and the Timoshenko theory are used to describe the elastic and VE layers, respectively. To describe the mechanical properties of a VE layer, the four-parameter rheological model with fractional derivative is applied. A number of particular rheological models are particular cases of this general model. The virtual work principle and the finite element method together with the Laplace transform are used to derive the equation of motion in the frequency domain. The dynamic characteristics of a beam with VE layers are obtained as the solution to a properly defined nonlinear eigenvalue problem. The continuation method is adopted for solving the nonlinear eigenproblem. Several conclusions concerning the accuracy of the method and variability of results are presented on the basis of numerical studies. [ABSTRACT FROM AUTHOR]

• Pioneer application of refined zig-zag theory in dynamic analysis of laminate plates. • Separate fractional Zener material description for volumetric and deviatoric strains. • Derivation of efficient finite element formulation leading to the non-linear eigen-value problem. The refined zig-zag theory is used to solve the dynamic problems for composite sandwich plates made from the elastic and the viscoelastic (VE) layers. The linear constitutive relations are used to model physical properties of the VE layers separately for volumetric and deviatoric strains. The fractional Zener model is used in the formulation of VE material. The Laplace transformation and the finite element method are used to derive the discretized nonlinear eigenvalue problem. The required dynamic characteristics of the plates – the frequency and the damping ratio, fundamental in design of structural elements in many fields of engineering, can be obtained using the procedure described in the companion paper Litewka P. Lewandowski R, Wielentejczyk P. Free vibrations of laminate plates with viscoelastic layers using the refined zig-zag theory – Part 2. Numerical analysis. [ABSTRACT FROM AUTHOR]

• Efficient solution procedure for non-linear eigen-value problem based on homotopy and quasi-Newton methods. • Numerical verification of the proposed formulation and testing of various solution variants. • Extensive analyses of results sensitivity to the model parameters. In this paper the numerical procedure to solve the non-linear eigen-value problem describing the free vibrations of the laminate plates with viscoelastic (VE) layers is presented. The derivation of that main equation based on the refined zig-zag theory and using fractional Zener material model to describe VE material is presented in the companion paper Lewandowski R, Litewka P. Wielentejczyk P. Free vibrations of laminate plates with viscoelastic layers using the refined zig-zag theory – Part 1. Theoretical background. The solution obtained using the continuation method provides the required dynamic characteristics of the plates – the frequency and the damping ratio. In the iterative part of each continuation step either the full Newton or the quasi-Newton iterative procedure are used. Several numerical examples are solved to verify accuracy, efficiency and versatility of the proposed formulation. Numerous parametric studies are carried out to determine the influence of various solution variants and combinations of material parameters onto the results describing the damping properties of laminate plates. [ABSTRACT FROM AUTHOR]

• The subspace iteration method is used to solve nonlinear eigenvalue problem. • The continuation method is used to solve the nonlinear Hermitian eigenproblem. • The method presented allows determination of only a part of eigenvalues. • The method was tested for structures with viscoelastic elements. • The models of VE elements are described with the help of fractional derivatives. The paper presents an extension of the subspace iteration method for application in systems with viscoelastic damping elements, which are described by both classical and fractional models. The presented method enables determination of only a certain number of eigenvalues and associated eigenvectors. This is very useful, especially when the considered problem has many degrees of freedom, in which case it would be very time-consuming or even impossible to determine all the eigenvalues. At the same time, from the engineering point of view, it is not necessary to know all the eigenvalues. In this paper, the subspace iteration method is used for the first time to solve the nonlinear eigenproblems which appear in the dynamic analysis of systems with viscoelastic damping elements. The proposed solution consists of assuming the number of eigenvalues to be determined, taking the initial point of iteration and then solving the nonlinear reduced eigenproblem with Hermitian matrices in each iterative loop. The solution to the reduced eigenproblem is obtained using the continuation method, and it is an additional novelty in the paper. The correctness and effectiveness of the proposed approach are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

• The refined zig-zag theory is used to solve the dynamic problem for composite beams with viscoelastic layers. • The fractional Zener model is used in analysis. • The dynamic characteristics of multi-layered viscoelastic beams are of interest. • The hierarchical FEM and the Laplace transform are used to derive the nonlinear eigenvalue problem. • The continuation method is adopted to solve the nonlinear eigenvalue problem. In the present paper the displacement based refined zig-zag theory is used, for the first time, to solve dynamic problems of composite and sandwich beams made of both elastic and VE layers. The linear constitutive relations are used to model physical properties of the VE layers. The rheological models can be in the classical or fractional versions, but the main focus is on the fractional Zener model. The dynamic characteristics of considered beams are evaluated. The hierarchical finite element and the Laplace transformation are used to derive the nonlinear eigenvalue problem and its solutions yield the required dynamic characteristics of beams. The continuation method is adopted to solve this problem numerically. Accuracy, effectiveness and efficiency of the proposed method are verified in several examples. The results of the presented calculations are summarized with some conclusions. [ABSTRACT FROM AUTHOR]

• The governing equations of the VE Mindlin plates in the Laplace domain are derived • The simple procedure for dynamic characteristics of VE Mindlin plates is proposed. • The simple method to include the temperature influence is included. • Parametric studies of the dynamic characteristics are carried out. This paper is devoted to geometrically linear free vibrations of viscoelastic (VE) Mindlin plates. The governing equations are derived in the Laplace domain. A simple way to take into account the influence of temperature on the damping properties is included using the frequency-temperature superposition principle. The novel approach to the solution of the non-linear problem of free vibrations of VE plates significantly simplifies the procedure reducing it to a linear eigen-value problem and a simple algebraic non-linear equation with one unknown. Several numerical examples involving varying physical parameters of the model are solved and the results are discussed. [ABSTRACT FROM AUTHOR]

Introduction: The prevalence of lateral curvatures of the spine ranges from 0.3% to 15.3% in the general population. The aim of the study was to develop and compare three different screening tests for idiopathic scoliosis (IS) with respect to their effectiveness and costs.Material and Methods: The Delphi method was used to assess the efficacy of each screening algorithm in detecting IS in the population. An economic analysis was also performed.Results: Diagnostic Algorithm 1 for IS comprised a screening examination performed by nurses and a general practitioner (GP) with verification by specialists. The unit cost of carrying out diagnostic work-up for IS in Algorithm 1 was €94 per child. The second algorithm involved the use of the moiré computer method, followed by verification by a specialist. The lower unit cost of €86 per child of diagnostic work-up according to Algorithm 2 was due to fewer stages compared to Algorithm 1. The highest effectiveness with the highest costs were found for the third algorithm, with only one stage, a specialist's consultation (cost €153 per child).Conclusions: The number of stages in an algorithm does not correlate positively with its efficacy or cost. The recommended scheme is Algorithm 3, where children are examined by rehabilitation specialists or a physiotherapist using a scoliometer and an inclinometer. The use of the apparently most expensive scheme (Algorithm 3) should result in lowering the costs of treatment of established idiopathic scoliosis and, in the long term, prove to be the most cost-effective solution for the health care system. [ABSTRACT FROM AUTHOR]