Vibration Analysis for Monitoring of Ancient Tie-Rods

This paper presents an application of vibration analysis to the monitoring of tie-rods. An algorithm for the axial load estimation based on experimentally measured natural frequencies is introduced and its application to a case study is reported. The proposed model of a tie-rod incorporates elastic bed-type boundary conditions that represent the contact between stonework and the tie-rod. The weighed differences between experimentally and numerically determined frequencies are minimized with respect to the parameters of the model, the main being the axial load and the stiffness at the tie-rod/wall interface. Thus, the multidimensional optimization problem is solved. Results are analysed in comparison to a model with simple fixed-end boundary conditions. In addition, the analytical formulation of the problem is delivered

Vibration analysis for monitoring of ancient tie-rods.

This paper presents an application of vibration analysis to the monitoring of tie-rods. An algorithm for the axial load estimation based on experimentally measured natural frequencies is introduced and its application to a case study is reported.The proposed model of a tie-rod incorporates elastic bed-type boundary conditions that represent the contact between stonework and the tierod. The weighed differences between experimentally and numerically determined frequencies are minimized with respect to the parameters of the model, the main being the axial load and the stiffness at the tie-rod/wall interface.Thus, the multidimensional optimization problem is solved. Results are analysed in comparison to a model with simple fixed-end boundary conditions. In addition, the analytical formulation of the problem is delivered

Detection of cracks in axially loaded tie-rods by vibration analysis

Determination of the axial load acting on steel reinforcement tie-rods is of crucial importance for ensuring the effectiveness and safety of structures, especially in the case of ancient masonry buildings. Many non-destructive dynamic techniques have been proposed and successfully tested over recent decades; however, ancient tie-rods can be affected not only by excessive loads but also by cracks, flaws and localized damage due to ageing and environmental effects, resulting in hidden dangers. This work introduces an operative, simple technique for the detection of cracks in structural tie-rods based on analysis of the dynamic behaviour of the rod itself and estimation of the flexural compliance. The method, refined and validated with extensive laboratory tests, shows how the presence of a crack changes the natural frequencies, damping and compliance of the rod in a way that can be quantified and recognized in unknown situations. On the basis of these results, a novel quantitative damage index is defined for practical use

Simulations and design of a refrigerating device based on a rotating magnetocaloric disc

The possibility of utilizing a Gd disc as an active magnetic regenerator (AMR) is investigated. We have designed a demonstration device based on a rotating disc with a fixed magnetic circuit covering one quarter of its area. The device implies zero thermal load with the operation fluid flowing through. Simulations are based on discretization of the heat transfer equations for the disc and the fluid domains using the finite difference method. The magnetocaloric effect (MCE) is included in the model as an instantaneous adiabatic temperature change of each element entering the magnetic field. Regenerative effect is obtained as at each radius of the disc the magnetocaloric material (MCM) operates switching its temperature around a different average, which decreases from periphery to centre. This allows the total temperature drop of the operational fluid to be several times larger than the adiabatic temperature change

CRACK DETECTION IN TENSIONING TIE-RODS BY DYNAMIC ANALYSIS

So-called “tie-rods” are metal beams used in a wide range of civil constructions. The main purpose of these structural elements is to provide support for masonry arches and vaults in ancient buildings, like churches, cathedrals and castles, which are known to lurch and founder in course of time. Tie-rods are subjected to axial tension and, thus, help the building resist lateral loads exerted by walls and facades. Indeed, over the years, deformations of masonry walls and eventual displacements in the building may cause significant changes in the axial loads of tie-rods. In the extremes, this can lead to either of two scenarios: failure in structural integrity of tie-rods (damages and cracks), or loss of loads and subsequent performance decline – a phenomenon referred to as the “laziness” of tie-rods. Both of the scenarios are dangerous for the safety and integrity of buildings and can lead to irretrievable harm to the precious historical heritage of the human race. For this reason regular monitoring of tie-rods’ condition is of a great importance. Health monitoring of tie-rods includes two major steps. The first one is identification of axial load and the second one is damage identification. As for the first one, multiple methods have been developed to accomplish this task, even some from the present authors [1-4]. However, the knowledge of axial load is not enough to assess the condition of structural tie-rods, because it does not contain any information on possible damages inside them, as for example that one shown in Figure 1. As for the damage identification, it definitely requires a more deep inspection of beams and a more careful analysis of experimental data, especially when tie-rods are ancient and hand-made. Such experimental techniques should be as less invasive as possible and at the same time should provide sufficient data on the beam condition, in one word non-destructive

Stability of Non-Linear Vibrations of Doubly Curved Shallow Shells

Large amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular boundary, simply supported at the four edges and subjected to harmonicexcitation normal to the surface in the spectral neighbourhood of the fundamental mode are subject of investigation in this paper. The first part of the study was presented by the authors in [M. Amabili et al. Nonlinear Vibrations of Doubly Curved Shallow Shells. Herald of Kazan Technological University, 2015, 18(6), 158-163, in Russian]. Two different non-linear strain-displacement relationships, from the Donnell’s and Novozhilov’s shell theories, are used to calculate the elastic strain energy. In-plane inertia and geometricimperfections are taken into account. The solution is obtained by Lagrangian approach. The non-linear equations of motion are studied by using (i) a code based on arclengthcontinuation method that allows bifurcation analysis and (ii) direct time integration. Numerical results are compared to those available in the literature and convergence of the solution is shown. Interaction of modes having integer ratio between their natural frequencies, giving rise to internal resonances, is discussed. Shell stability under dynamic load is also investigated by using continuation method, bifurcation diagram from direct time integration and calculation of the Lyapunov exponents and Lyapunov dimension. Interesting phenomena such as (i) snap-through instability, (ii) subharmonic response, (iii) period doubling bifurcations and (iv) chaotic behavior have been observed

Устойчивость нелинейных колебаний пологих оболочек двоякой кривизны

Large amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular boundary, simply supported at the four edges and subjected to harmonicexcitation normal to the surface in the spectral neighbourhood of the fundamental mode are subject of investigation in this paper. The first part of the study was presented by the authors in [M. Amabili et al. Nonlinear Vibrations of Doubly Curved Shallow Shells. Herald of Kazan Technological University, 2015, 18(6), 158-163, in Russian]. Two different non-linear strain-displacement relationships, from the Donnell’s and Novozhilov’s shell theories, are used to calculate the elastic strain energy. In-plane inertia and geometricimperfections are taken into account. The solution is obtained by Lagrangian approach. The non-linear equations of motion are studied by using (i) a code based on arclengthcontinuation method that allows bifurcation analysis and (ii) direct time integration. Numerical results are compared to those available in the literature and convergence of the solution is shown. Interaction of modes having integer ratio between their natural frequencies, giving rise to internal resonances, is discussed. Shell stability under dynamic load is also investigated by using continuation method, bifurcation diagram from direct time integration and calculation of the Lyapunov exponents and Lyapunov dimension. Interesting phenomena such as (i) snap-through instability, (ii) subharmonic response, (iii) period doubling bifurcations and (iv) chaotic behavior have been observed.В статье рассматриваются высокоамплитудные (геометрически нелинейные) колебания пологих оболочек двоякой кривизны c прямоугольными границами, свободно опертых по всем четырем краям и подвергающихся нормальному к поверхности гармоническому воздействию в спектральной окрестности основной формы. Первая часть проведенных исследований была представлена в работе [М. Амабили и др. Нелинейные колебания пологих оболочек двоякой кривизны // Вестник КГТУ, 2015. - Т. 18, № 6. - С. 158-163] авторов. Для расчета энергии упругой деформации были использованы два различных нелинейных соотношения между деформацией и перемещением: из теории Доннелла и теории Новожилова. Учитывались также геометрические несовершенства формы оболочкии и влияние инерции в плоскости. Построены приближенные уравнения динамики в форме уравнений Лагранжа второго рода. Предполагается, что потенциальная энергия сил упругости разлагается в ряд, в котором ограничиваются членами третьего порядка. Для исследования устойчивости невозмущенного движения используется метод функций Ляпунова и метод характеристичных чисел. Полагая функцию Ляпунова квадратичной формой с постоянными коэффициентами, определяются условия, при которых решение, соответствующее невозмущенному движению системы при гармоническом воздействии, является устойчивым. Определяется оценка наибольшего характеристичного числа Ляпунова. Приводятся результаты численных экспериментов, полученных для системы с гармоническим возбуждением. Рассматривается случай сферической оболочки, исследуется эффект влияния различной кривизны, проводится бифуркационный анализ