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The damping of spruce wood is analysed at different moisture content levels for the first three vibration modes of tangentially and radially vibrating samples. Two methods were used to determine the damping. The first was the vibration envelope fitting as an improved version of the well-known logarithmic decrement, and the second was the newer and recently increasingly used wavelet transform. Both methods showed that the damping of spruce wood first decreases and then increases with moisture content, with the damping in the first vibration mode being about 9% higher in the radial direction than in the tangential direction. In the second and third vibration modes, the damping in the tangential direction was higher than in the radial direction by about 10% and 8.8%, respectively. The measured damping factors from the envelope fitting had, on average, 15.9% higher values than those from the wavelet transform. It can be concluded from the results that the wavelet transform is more accurate for determining the damping factor, as it enables the decoupling of multi-degree of freedom systems if mode coupling is present. [ABSTRACT FROM AUTHOR]

The trend of production machines with higher operation speeds brought the issues of vibration amplitude and acoustic emissions to the surface. To solve this problem, a standard approach requiring mass and/or stiffness increase, and utilizing high-damping polymer composite materials, e.g. by adding them to the empty spaces of the original structures is employed. The presented polymer composite application is for rotor bearing casing in which the polymer particle composite is added into the mechanical system by filling the empty space between the rotor bearing casing and the housing body. Before this application, an analysis of four polymer composite samples with different compositions was made. Then the logarithmic decrements were measured by two experimental methods and one composite was selected. The application showed acoustic emission maximum amplitude reduction of 67% and 33% when excitation amplitudes are low (up to 5 g) and large (above 10 g), respectively. In the case of the FFT spectrum of acoustic emissions, the reduction was 85% and 51%. [ABSTRACT FROM AUTHOR]

In recent decades, the most impactful effects of thermal gradients on the shear modulus of compacted soils have been increasingly well documented. The thermal repercussions on the corresponding damping ratios, however, have not been as thoroughly investigated. In this work, a series of thermo-controlled resonant column tests was conducted on statically compacted samples of three distinct types of cohesive-frictional soils, namely low plasticity clay, non-plastic silt, and clayey sand, to assess the effect of elevated soil temperatures on their respective small-strain damping ratios. Damping ratio for each soil type and test condition was determined via both the frequency response curves (bandwidth method) and the underdamped free-vibration cycles (logarithmic decrement) in order to perform a comparative analysis of damping assessment methods. The corresponding stress–strain hysteresis loops were also evaluated for further qualitative insights into any possible thermal sensitivities of their material damping in the field. Results show a mostly detrimental effect of increasing soil temperature on the small-strain stiffness of cohesive-frictional soils, with their damping ratio remaining virtually unchanged (clays) or experiencing a gradual increase (silts and sands) with increasing soil temperature. [ABSTRACT FROM AUTHOR]

The trend of production machines with higher operation speeds brought the issues of vibration amplitude and acoustic emissions to the surface. To solve this problem, a standard approach requiring mass and/or stiffness increase, and utilizing high-damping polymer composite materials, e.g. by adding them to the empty spaces of the original structures is employed. The presented polymer composite application is for rotor bearing casing in which the polymer particle composite is added into the mechanical system by filling the empty space between the rotor bearing casing and the housing body. Before this application, an analysis of four polymer composite samples with different compositions was made. Then the logarithmic decrements were measured by two experimental methods and one composite was selected. The application showed acoustic emission maximum amplitude reduction of 67% and 33% when excitation amplitudes are low (up to 5 g) and large (above 10 g), respectively. In the case of the FFT spectrum of acoustic emissions, the reduction was 85% and 51%.

The damping of spruce wood is analysed at different moisture content levels for the first three vibration modes of tangentially and radially vibrating samples. Two methods were used to determine the damping. The first was the vibration envelope fitting as an improved version of the well-known logarithmic decrement, and the second was the newer and recently increasingly used wavelet transform. Both methods showed that the damping of spruce wood first decreases and then increases with moisture content, with the damping in the first vibration mode being about 9% higher in the radial direction than in the tangential direction. In the second and third vibration modes, the damping in the tangential direction was higher than in the radial direction by about 10% and 8.8%, respectively. The measured damping factors from the envelope fitting had, on average, 15.9% higher values than those from the wavelet transform. It can be concluded from the results that the wavelet transform is more accurate for determining the damping factor, as it enables the decoupling of multi-degree of freedom systems if mode coupling is present.

A curve-fitting technique using a minimum error criterion was presented for identifying higher damping ratios near the critical damping ratio in single-degree-of-freedom systems. Free vibration decay tests were performed on a linear spring–mass–damper system with constant initial conditions using a modified commercial vibration apparatus. A vibration mass was supported with an extremely low-friction air-bearing guide. Mass displacement was measured using a laser displacement sensor. The magnitude of the viscous damping forces was varied and controlled using an electromagnetic damper installed in the apparatus. Higher damping ratios (ζ > 0.8) were accurately identified using the curve-fitting technique, while lower and medium damping ratios 0 < ζ < 0.7 were estimated using the conventional logarithmic decrement method from the measured free vibration decay curves. [ABSTRACT FROM AUTHOR]

Problem of predicting the residual service life of airplanes and helicopters is highly relevant for flight safety. In this paper, on the basis of the conducted research on the change of mechanical characteristics during materials fatigue accumulation, it is proposed to control the service life by changing the dissipative characteristics. In case of fatigue damage, the accumulative logarithmic decrement of oscillation damping δ increases to the limit maximum value δm, which corresponds to the critical length of the main fatigue crack, which leads to failure. The limit value δm can be set depending on the amount of energy spent on the development of the main fatigue crack, taking into account the dangerous part of the consumed energy. With the accumulation of fatigue damage, the growth of logarithmic decrement occurs at the expense of energy expenditure for the growth of fatigue cracks and internal friction. This is taken into account by the coefficient α, which allows to allocate a dangerous part of the energy that goes into the development of a main fatigue crack. The problem of durability prediction consists of two stages. At first, it is needed to determine δm for the critical crack length. Then, based on the two values of logarithmic decrement at the corresponding load cycles, the number of cycles to failure – to the critical length of the crack – is predicted by the Peris formula

There are numerous non-destructive methods in welded joints investigation, but the most promising, especially in applications with steady monitoring of the structure, is the vibrodiagnostic approach. In the course of the research work, the responses were obtained and detected by accelerometers, providing valuable diagnostic information, which later was mathematically processed in the field of time or frequency. The mathematical processing aimed to distinguish significant characteristics embedded in the processes typical of the investigated joints and allow an assessment of how they were made. For this purpose, two methods were proposed, based on determining the logarithmic decrement as a function of time. Due to the complicated course of the impact responses, the method of calculating the logarithmic decrement has been suggested, involving the approximation of responses with various functions. According to the research, the analysis of changes in the logarithmic decrement as a function of time applied to welded plates was proposed, as it enables the initial assessment of joint quality. [ABSTRACT FROM AUTHOR]

The process of obtaining aerated (filled with air bubbles) polymer coatings has been developed and investigated by the method of flame spraying with an assessment of their ability to damp vibrations. A technology for the controlled formation of aerated polymer coatings has been developed while using the capabilities of the ОИМ (OIM) 050 polymer thermal atomizer design which consists in providing a concurrent air flow between the flame torch and the jet of powder material. The experiments have been carried out with such thermoplastic polymers as polyethylene terephthalate, high pressure polyethylene, ultra high molecular weight polyethylene, polyamide. It has been found that the aeration coefficient grows almost in direct proportion with an increase in the amount of air in the concurrent flow for all investigated polymer coatings. It is noted that the aeration process is influenced by the rheological properties of liquid polymers, or rather, the value of the polymer melt flow rate. The limiting values of air in the concurrent flow have been determined, which make it possible not to reduce the adhesion of polymer coatings to steel substrates by less than 6 MPa and not to decrease their hardness by more than 25–30 %. Studies of the damping properties of samples with polymer coatings have been carried out on a stand, the kinematic diagram of which is based on loading the free end of a cantilever sample, abrupt removal of the load and registration of free damped oscillations by an induction-type contactless sensor connected to a computer. It is shown that the use of aeration when forming noise-absorbing coatings on steel samples can increase their logarithmic damping decrement by 18–26 %.

In this paper, we present an extensive experimental study on the dynamic mechanical properties of composites with polymer matrices, as well as a quantification of the parameters that influence these properties. Polymer-composite matrices make it possible to form any reinforcement arrangement of fibres, particles, and layers, which makes it possible to form composite materials with certain dominant mechanical properties according to the internal arrangement for the application. In this study, we focused on the dynamic properties (i.e., damping parameters, such as the loss factor (tan d), logarithmic decrement (λ), storage modulus (E′), and loss modulus (E″)) of composites with polymer matrices, including parameters such as the fibre material, fabric weaving, fibre orientation, temperature, frequency, particle size, volume of short fibres, and epoxy resin type. If other articles focus on one type of composite and 1–2 parameters, then the benefit of this article lies in our analysis of 8 mentioned parameters in the experimental analysis of 27 different types of composites with polymer matrices. The tested fibre materials were glass, aramid, and carbon; the tested woven fabrics were twill, plain, unidirectional, and satin; the temperature range was from −50 to +230 °C; the frequency was 1 Hz and 10 Hz; the particle size was 0.1–16 mm; the volume percentages of the short fibres were 3, 6, and 12 vol.% of the hybrid polymer composites and the type of polymer matrix. We used the free-damped-vibration method with vibration dynamic signal analysis and the forced-damped vibration of dynamic mechanical thermal analysis for testing. We ranked the parameters that influence the dynamic vibration properties according to the effects. Among sets of results provided in the paper, considering the storage modulus, loss modulus, and loss factor, the best results of the fibre composites were for aramid-fibre-reinforced polymers, regardless of the weave type, with an advantage for unidirectional fabric. The best results of the particle composites were for those with fine filler sizes that incorporated the short fibres. [ABSTRACT FROM AUTHOR]

Based on a generalization of the available data and the existing calculation norms for heat exchange equipment, a consistent method for calculating the vibrational characteristics of the tube bank that determines its working capacity is proposed: the maximum amplitudes of tube vibrations, the stresses at the tube joints in a tube plate, and the stresses in welds. One of the conditions for the tube bank capacity is the absence of hydroelastic instability, which can occur if the flow velocity reaches critical values. A hydroelastic instability curve is shown, which provides, taking into account certain parameters of the bank design, the possible critical flow velocity. Calculations are carried out for a specific design of the water cooler, and conclusions are drawn of its working capacity at a given fluid flow rate. [ABSTRACT FROM AUTHOR]

In this paper, we present an extensive experimental study on the dynamic mechanical properties of composites with polymer matrices, as well as a quantification of the parameters that influence these properties. Polymer-composite matrices make it possible to form any reinforcement arrangement of fibres, particles, and layers, which makes it possible to form composite materials with certain dominant mechanical properties according to the internal arrangement for the application. In this study, we focused on the dynamic properties (i.e., damping parameters, such as the loss factor (tan d), logarithmic decrement (λ), storage modulus (E′), and loss modulus (E″)) of composites with polymer matrices, including parameters such as the fibre material, fabric weaving, fibre orientation, temperature, frequency, particle size, volume of short fibres, and epoxy resin type. If other articles focus on one type of composite and 1–2 parameters, then the benefit of this article lies in our analysis of 8 mentioned parameters in the experimental analysis of 27 different types of composites with polymer matrices. The tested fibre materials were glass, aramid, and carbon; the tested woven fabrics were twill, plain, unidirectional, and satin; the temperature range was from −50 to +230 °C; the frequency was 1 Hz and 10 Hz; the particle size was 0.1–16 mm; the volume percentages of the short fibres were 3, 6, and 12 vol.% of the hybrid polymer composites and the type of polymer matrix. We used the free-damped-vibration method with vibration dynamic signal analysis and the forced-damped vibration of dynamic mechanical thermal analysis for testing. We ranked the parameters that influence the dynamic vibration properties according to the effects. Among sets of results provided in the paper, considering the storage modulus, loss modulus, and loss factor, the best results of the fibre composites were for aramid-fibre-reinforced polymers, regardless of the weave type, with an advantage for unidirectional fabric. The best results of the particle composites were for those with fine filler sizes that incorporated the short fibres.

For a resonant spruce wood (Picea sp.) the acoustic parameters (resonant/ modal frequency (f) and logarithmic decrement (δ)), were determined before and after thermal modification at 160 °C. The material studied came from the Romanian Carpathian mountains and was classified by luthiers as good and very good resonant wood. Thermal modification did not result in significant changes in the number of modes, but differences in the modal frequencies for individual modes were noted. Thermal modification also decreased the logarithmic decrement in the highest quality material. [ABSTRACT FROM AUTHOR]

The correct evaluation of damping from experimental measurements is important for subsequent analyses, be it in the field of structural dynamics, earthquake engineering, vibration control, structural health monitoring, etc. In this work, we demonstrate how an accurate evaluation of modal damping is possible by using a minimal amount of acceleration sensors and exciting the structure using a simple hammer. However, the transient signals thus recovered must be carefully processed so as to extract as much accuracy from these measurements as possible. The particular experiment used here involved a metallic bridge span, which was simply supported and used for testing moving loads. Both Frequency Domain Decomposition and Principal Component Analysis were employed and subsequently compared, with the latter method showing a clear separation of modes. Thus, an accurate estimation of modal damping values from the free vibration regime is possible using the logarithmic decrement method. • Experimental evaluation of modal damping ratios. • Use of both Frequency Domain Decomposition and Principal Component Analysis and comparison. • Use of the generalized acceleration coordinates for the logarithmic decrement method. • Identification and use of the free vibration regime. • Accurate and inexpensive experimental evaluation of modal damping. [ABSTRACT FROM AUTHOR]

This work derives an analytical expression for the optimal number of periods between samples when estimating damping using the logarithmic decrement method. This expression, obtained from an uncertainty analysis of the method's principal equation, is shown to be a function of only one system parameter: the damping ratio. This suggests that for linear systems with viscous damping there is a unique, damping-dependent period choice corresponding to minimum uncertainty in the estimated damping ratio. This result led to the discovery of a constant optimal amplitude ratio offering a straightforward guideline that can be applied by the experimenter to obtain damping ratio estimates with minimum uncertainty. The derived expressions are applied to a series of numerical and experimental systems to confirm their validity. [ABSTRACT FROM AUTHOR]

This paper investigates the estimation of foundation damping in a monopile supported offshore wind turbine. The soil-structure interaction is modelled using the commercial geotechnical Finite Element (FE) software, Plaxis 3D. This allows for a more rigorous consideration of the soil response and its effect on the overall dynamic behaviour of the system. A free vibration test is simulated by applying and removing a constant horizontal static load at the top of the tower. The structure starts free vibration when the load is removed. The free decay displacement response is measured at the point of loading. The well-known logarithmic decrement method is used for the estimation of overall damping from the free decay response. The damping is estimated at different time steps along the signal to provide an instantaneous damping. It is shown that the damping varies with the amplitude of the decaying displacement response. [ABSTRACT FROM AUTHOR]

In this work, we present a novel Hilbert-twin method to compute an envelope and the logarithmic decrement, δ, from exponentially damped time-invariant harmonic strain signals embedded in noise. The results obtained from five computing methods: (1) the parametric OMI (Optimization in Multiple Intervals) method, two interpolated discrete Fourier transform-based (IpDFT) methods: (2) the Yoshida-Magalas (YM) method and (3) the classic Yoshida (Y) method, (4) the novel Hilbert-twin (H-twin) method based on the Hilbert transform, and (5) the conventional Hilbert transform (HT) method are analyzed and compared. The fundamental feature of the Hilbert-twin method is the efficient elimination of intrinsic asymmetrical oscillations of the envelope, aHT (t), obtained from the discrete Hilbert transform of analyzed signals. Excellent performance in estimation of the logarithmic decrement from the Hilbert-twin method is comparable to that of the OMI and YM for the low- and high-damping levels. The Hilbert-twin method proved to be robust and effective in computing the logarithmic decrement and the resonant frequency of exponentially damped free decaying signals embedded in experimental noise. The Hilbert-twin method is also appropriate to detect nonlinearities in mechanical loss measurements of metals and alloys.

The parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) and a novel Hilbert-twin (H-twin) methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in internal friction values. It is unequivocally demonstrated that the Hilbert-twin method, which yields a ‘true envelope’ for exponentially damped harmonic oscillations is superior to conventional Hilbert transform method. The ‘true envelope’ of free decaying strain signals calculated from the Hilbert-twin method yields excellent estimation of the logarithmic decrement in metals, alloys, and solids.

This paper proposes a method for laboratory experiments, which allows controlling the technical state of high pressure hoses of hydraulic drives on the basis of the derived dependences of logarithmic decrement on operating time. Based on the developed method, the test bench for the study of the elastic properties of the hydraulic drive elements was designed. During the experiments, we obtained the dependences for high pressure hoses with different lengths and diameters. The obtained results have shown the sensitivity and sufficiency of the parameter “logarithmic decrement” for controlling the efficiency of the high-pressure hoses. The developed method can be used to determine the residual lifetime of HPHs during maintenance or repair of the machinery. [ABSTRACT FROM AUTHOR]

The paper considers the processing technique for amplitude-frequency response of turning and boring CNC machine units. The technique developed by V.A. Kudinov is proposed as the basic one. The essence of the technique is that the use of the experimental or calculated frequency characteristics makes it possible to determine the values of the constants characterizing natural frequency of vibration, decrement factor, unit stiffness, or weight of the technological system elements. The logarithmic decrement is calculated from the resonance peak breadth by applying the formula of the vibration theory for the system with one-degree-of-freedom vibrations. The force of impulse action on the system units is determined by experiment based on measurements by accelerometer built in an impact hammer. The theoretical amplitude-response curve is plotted for the vibration displacement of the units and the logarithmic decrement is calculated in MathCAD. [ABSTRACT FROM AUTHOR]