The edge crush test is the most popular laboratory test in the corrugated packaging industry. It ... more The edge crush test is the most popular laboratory test in the corrugated packaging industry. It measures the edge crush resistance of a sample in the cross-fiber direction (CD), also known as the ECT index. This parameter is widely used for the specification of the board by its producers. It is also utilized in most analytical formulas describing the load capacity of the packaging. On the other hand, the ECT value can be estimated from both analytical and numerical models based on the basic parameters of each constituent paper. Knowing the compressive strength in CD (commonly known as SCT) and the elastic properties of the individual layers, the sample geometry (i.e., the period and height of the corrugated layer), as well as the boundary conditions, the ECT value can be calculated. This is very useful as new boards can be virtually analyzed before being manufactured. In this work, both detailed numerical models based on finite elements (FE) methods and very simple analytical (engi...
The standard edge crush test (ECT) allows to determine the crushing strength of the corrugated ca... more The standard edge crush test (ECT) allows to determine the crushing strength of the corrugated cardboard. Unfortunately, this test cannot be used to estimate the compressive stiffness, which is an equally important parameter. It is because, any attempt to determine this parameter using current lab equipment quickly ends in a fiasco. The biggest obstacle is obtaining a reliable measurement of displacements and strains in the corrugated cardboard sample. In this paper, we present a method that not only allows to reliably identify the stiffness in the loaded direction of orthotropy in the corrugated board sample, but also the full orthotropic material stiffness matrix. The proposed method uses two samples: (a) traditional, cut crosswise to the wave direction of the corrugated core, and (b) cut at an angle of 45 degrees. Additionally, in both cases, an optical system with digital image correlation (DIC) is used to measure the displacements and strains on the outer surface of samples. Th...
The paper pertains the use of non-invasive diagnostic methods to assess the condition of metal el... more The paper pertains the use of non-invasive diagnostic methods to assess the condition of metal elements of machinery and equipment or metal components of building structures. The conducted research concerns the analysis of acoustic signals generated during the excitation of a steel plate and the influence of discontinuities such as grooves and apertures in its structure on spectrogram of recorded acoustic emission signals. Since the presence of the opening causes a significant increase in the initial phase of the acoustic event, higher frequencies (20-55 kHz) and faster decay of the signal, so it should be noted that the frequency analysis of recorded signals, in the initial phase of the acoustic event, can be considered as an indicator of the damage presence.
When producing packaging from corrugated board, material weakening often occurs both during the d... more When producing packaging from corrugated board, material weakening often occurs both during the die-cutting process and during printing. While the analog lamination and/or printing processes that degrade material can be easily replaced with a digital approach, the die-cutting process remains overwhelmingly analog. Recently, new innovative technologies have emerged that have begun to replace or at least supplement old techniques. This paper presents the results of laboratory tests on corrugated board and packaging made using both analog and digital technologies. Cardboard samples with digital and analog creases are subject to various mechanical tests, which allows for an assessment of the impact of creases on the mechanical properties of the cardboard itself, as well as on the behavior of the packaging. It is proven that digital technology is not only more repeatable, but also weakens the structure of corrugated board to a much lesser extent than analog. An updated numerical model of...
The optimal selection of the composition of corrugated cardboard dedicated to specific packaging ... more The optimal selection of the composition of corrugated cardboard dedicated to specific packaging structures is not an easy task. The use of lighter boards saves material, but at the same time increases the risk of not meeting the guaranteed load capacity. Therefore, the answer to the question “in which layer the basis weight of the paper should be increased?” is not simple or obvious. The method proposed here makes it easy to understand which components and to what extent they affect the load-bearing capacity of packages of various dimensions. The use of numerical homogenization allows for a quick transformation of a cardboard sample, i.e., a representative volume element (RVE) into a flat plate structure with effective parameters describing the membrane and bending stiffness. On the other hand, the use of non-local sensitivity analysis makes it possible to find the relationship between the parameters of the paper and the load capacity of the packaging. The analytical procedures pre...
This work concerns the concept and verification of the experimental possibility of using a wavele... more This work concerns the concept and verification of the experimental possibility of using a wavelet transform to assess a steel structure’s condition. In the research, a developed measuring stand was used. Mechanical waves in the metal plate were excited by the impact. These waves were recorded with an electroacoustic transducer and registered in the form of electrical signals. Both the signals generated by the actuator of the plate and the signals reaching the transducer were recorded. The registered data were decomposed into wavelet coefficients. Laboratory tests have shown the possibility of applying this type of test to identify damage in steel structural elements—the relationship between the details of the wavelet transform and the type of damage was demonstrated.
Detection, localization and estimation of details of concentrated defects hidden in structural el... more Detection, localization and estimation of details of concentrated defects hidden in structural elements as an important part of structural health monitoring is considered here. In this work the effectiveness of discrete wavelet transform combined with inverse analysis is also discussed. The efficiency of the method is studied particularly when applied to eigenmodes of a cantilever steel beam expressed in amplitudes of vertical displacements, velocities, accelerations or strains. The structural response signal measured in discrete points is transformed using wavelet decomposition which clearly improve identifiability of damaged structure. Authors use a parametrized finite element model which mimic the real structure and by changing control parameters embedded in the numerical model minimize the discrepancy between the wavelet representation of both ’real’ and numerically computed measurable quantities. For the discrepancy function minimization (within least-square framework) the dete...
The paper presents the problem of damage detection in thin plates while considering the influence... more The paper presents the problem of damage detection in thin plates while considering the influence of static and dynamic characteristics, especially with regard to the modes of vibration as well as the excitation by static loads. The problem of Kirchhoff plate bending is described and solved by the Boundary Element Method (BEM). Rectangular plates supported on boundary or plates supported on boundary and resting on the internal columns are examined. A defect is introduced by the additional edges forming a crack in the plate domain. The analyses of static and dynamic structural responses are carried out with the use of Discrete Wavelet Transform (DWT). Signal decomposition according to the Mallat pyramid algorithm is applied. To obtain a more adequate input function subjected to DWT the white noise disturbing the signal is considered together with the structural response. In the dynamic experiments the plate undergoes vibrations similar to natural modes. The measured variables are sta...
This paper is concerned with defect detection in plate structures while considering the influence... more This paper is concerned with defect detection in plate structures while considering the influence of external loads. The examined structures are based on Kirchhoff plate structures. Rectangular plate structures are considered. Plate bending is described using the boundary element method. The boundary and boundary-domain integral equations are formulated in a modified, simplified approach without the need of using a value known from the classical theory of Kirchhoff plate bending. Constant-type boundary elements in a non-singular approach are introduced. The plates are loaded with a single static concentrated force or dynamic moving force. External loading is applied at selected points along the direction parallel to one dimension of the plate. Defects are introduced by additional edges forming slots or holes in relations to the basic plate domain. Deflections and curvatures are taken into account as structural responses. Analysis of structural responses is conducted using the signal...
Journal of Theoretical and Applied Mechanics, 2018
The paper is concerned with damage detection in plates while using the Discrete Wavelet Transform... more The paper is concerned with damage detection in plates while using the Discrete Wavelet Transform (DWT). Rectangular plate structures resting on a Winkler or elastic half-space type foundation, with free boundaries are examined. Plate bending is described and solved by the Boundary Element Method in a direct approach. Defects are introduced by additional edges forming slots in relation to the basic plate domain. Numerical investigation is conducted basing on signal analysis of the structural static response and by taking advantage of multi-resolution analysis (MRA) of the signal function which can be represented in a multi-scale manner. The obtained signal is decomposed with the use of Daubechies or Coiflet wavelet families. The white noise generator is used to model measurement inaccuracy which is an inevitable element of a real experiment. The efficiency of DWT of the contaminated signal in damage detection is studied.
The problem of non-destructive damage detection pla ys an important role in monitoring of the eng... more The problem of non-destructive damage detection pla ys an important role in monitoring of the engineering structures. This issue has been the sub ject of studies undertaken by many scientists who proposed some approaches based on e. g. evolutionary algorithms [1], load optimization [7], information of natural frequencie s [2], heat transfer [11], inverse analysis [3, 4] and artificial neural networks [8, 10]. Another, relatively modern tool, which can be effectively used for damage detection is wavelet tr ansformation (WT) [9] also in its discrete form (DWT) [5, 6].
The edge crush test is the most popular laboratory test in the corrugated packaging industry. It ... more The edge crush test is the most popular laboratory test in the corrugated packaging industry. It measures the edge crush resistance of a sample in the cross-fiber direction (CD), also known as the ECT index. This parameter is widely used for the specification of the board by its producers. It is also utilized in most analytical formulas describing the load capacity of the packaging. On the other hand, the ECT value can be estimated from both analytical and numerical models based on the basic parameters of each constituent paper. Knowing the compressive strength in CD (commonly known as SCT) and the elastic properties of the individual layers, the sample geometry (i.e., the period and height of the corrugated layer), as well as the boundary conditions, the ECT value can be calculated. This is very useful as new boards can be virtually analyzed before being manufactured. In this work, both detailed numerical models based on finite elements (FE) methods and very simple analytical (engi...
The standard edge crush test (ECT) allows to determine the crushing strength of the corrugated ca... more The standard edge crush test (ECT) allows to determine the crushing strength of the corrugated cardboard. Unfortunately, this test cannot be used to estimate the compressive stiffness, which is an equally important parameter. It is because, any attempt to determine this parameter using current lab equipment quickly ends in a fiasco. The biggest obstacle is obtaining a reliable measurement of displacements and strains in the corrugated cardboard sample. In this paper, we present a method that not only allows to reliably identify the stiffness in the loaded direction of orthotropy in the corrugated board sample, but also the full orthotropic material stiffness matrix. The proposed method uses two samples: (a) traditional, cut crosswise to the wave direction of the corrugated core, and (b) cut at an angle of 45 degrees. Additionally, in both cases, an optical system with digital image correlation (DIC) is used to measure the displacements and strains on the outer surface of samples. Th...
The paper pertains the use of non-invasive diagnostic methods to assess the condition of metal el... more The paper pertains the use of non-invasive diagnostic methods to assess the condition of metal elements of machinery and equipment or metal components of building structures. The conducted research concerns the analysis of acoustic signals generated during the excitation of a steel plate and the influence of discontinuities such as grooves and apertures in its structure on spectrogram of recorded acoustic emission signals. Since the presence of the opening causes a significant increase in the initial phase of the acoustic event, higher frequencies (20-55 kHz) and faster decay of the signal, so it should be noted that the frequency analysis of recorded signals, in the initial phase of the acoustic event, can be considered as an indicator of the damage presence.
When producing packaging from corrugated board, material weakening often occurs both during the d... more When producing packaging from corrugated board, material weakening often occurs both during the die-cutting process and during printing. While the analog lamination and/or printing processes that degrade material can be easily replaced with a digital approach, the die-cutting process remains overwhelmingly analog. Recently, new innovative technologies have emerged that have begun to replace or at least supplement old techniques. This paper presents the results of laboratory tests on corrugated board and packaging made using both analog and digital technologies. Cardboard samples with digital and analog creases are subject to various mechanical tests, which allows for an assessment of the impact of creases on the mechanical properties of the cardboard itself, as well as on the behavior of the packaging. It is proven that digital technology is not only more repeatable, but also weakens the structure of corrugated board to a much lesser extent than analog. An updated numerical model of...
The optimal selection of the composition of corrugated cardboard dedicated to specific packaging ... more The optimal selection of the composition of corrugated cardboard dedicated to specific packaging structures is not an easy task. The use of lighter boards saves material, but at the same time increases the risk of not meeting the guaranteed load capacity. Therefore, the answer to the question “in which layer the basis weight of the paper should be increased?” is not simple or obvious. The method proposed here makes it easy to understand which components and to what extent they affect the load-bearing capacity of packages of various dimensions. The use of numerical homogenization allows for a quick transformation of a cardboard sample, i.e., a representative volume element (RVE) into a flat plate structure with effective parameters describing the membrane and bending stiffness. On the other hand, the use of non-local sensitivity analysis makes it possible to find the relationship between the parameters of the paper and the load capacity of the packaging. The analytical procedures pre...
This work concerns the concept and verification of the experimental possibility of using a wavele... more This work concerns the concept and verification of the experimental possibility of using a wavelet transform to assess a steel structure’s condition. In the research, a developed measuring stand was used. Mechanical waves in the metal plate were excited by the impact. These waves were recorded with an electroacoustic transducer and registered in the form of electrical signals. Both the signals generated by the actuator of the plate and the signals reaching the transducer were recorded. The registered data were decomposed into wavelet coefficients. Laboratory tests have shown the possibility of applying this type of test to identify damage in steel structural elements—the relationship between the details of the wavelet transform and the type of damage was demonstrated.
Detection, localization and estimation of details of concentrated defects hidden in structural el... more Detection, localization and estimation of details of concentrated defects hidden in structural elements as an important part of structural health monitoring is considered here. In this work the effectiveness of discrete wavelet transform combined with inverse analysis is also discussed. The efficiency of the method is studied particularly when applied to eigenmodes of a cantilever steel beam expressed in amplitudes of vertical displacements, velocities, accelerations or strains. The structural response signal measured in discrete points is transformed using wavelet decomposition which clearly improve identifiability of damaged structure. Authors use a parametrized finite element model which mimic the real structure and by changing control parameters embedded in the numerical model minimize the discrepancy between the wavelet representation of both ’real’ and numerically computed measurable quantities. For the discrepancy function minimization (within least-square framework) the dete...
The paper presents the problem of damage detection in thin plates while considering the influence... more The paper presents the problem of damage detection in thin plates while considering the influence of static and dynamic characteristics, especially with regard to the modes of vibration as well as the excitation by static loads. The problem of Kirchhoff plate bending is described and solved by the Boundary Element Method (BEM). Rectangular plates supported on boundary or plates supported on boundary and resting on the internal columns are examined. A defect is introduced by the additional edges forming a crack in the plate domain. The analyses of static and dynamic structural responses are carried out with the use of Discrete Wavelet Transform (DWT). Signal decomposition according to the Mallat pyramid algorithm is applied. To obtain a more adequate input function subjected to DWT the white noise disturbing the signal is considered together with the structural response. In the dynamic experiments the plate undergoes vibrations similar to natural modes. The measured variables are sta...
This paper is concerned with defect detection in plate structures while considering the influence... more This paper is concerned with defect detection in plate structures while considering the influence of external loads. The examined structures are based on Kirchhoff plate structures. Rectangular plate structures are considered. Plate bending is described using the boundary element method. The boundary and boundary-domain integral equations are formulated in a modified, simplified approach without the need of using a value known from the classical theory of Kirchhoff plate bending. Constant-type boundary elements in a non-singular approach are introduced. The plates are loaded with a single static concentrated force or dynamic moving force. External loading is applied at selected points along the direction parallel to one dimension of the plate. Defects are introduced by additional edges forming slots or holes in relations to the basic plate domain. Deflections and curvatures are taken into account as structural responses. Analysis of structural responses is conducted using the signal...
Journal of Theoretical and Applied Mechanics, 2018
The paper is concerned with damage detection in plates while using the Discrete Wavelet Transform... more The paper is concerned with damage detection in plates while using the Discrete Wavelet Transform (DWT). Rectangular plate structures resting on a Winkler or elastic half-space type foundation, with free boundaries are examined. Plate bending is described and solved by the Boundary Element Method in a direct approach. Defects are introduced by additional edges forming slots in relation to the basic plate domain. Numerical investigation is conducted basing on signal analysis of the structural static response and by taking advantage of multi-resolution analysis (MRA) of the signal function which can be represented in a multi-scale manner. The obtained signal is decomposed with the use of Daubechies or Coiflet wavelet families. The white noise generator is used to model measurement inaccuracy which is an inevitable element of a real experiment. The efficiency of DWT of the contaminated signal in damage detection is studied.
The problem of non-destructive damage detection pla ys an important role in monitoring of the eng... more The problem of non-destructive damage detection pla ys an important role in monitoring of the engineering structures. This issue has been the sub ject of studies undertaken by many scientists who proposed some approaches based on e. g. evolutionary algorithms [1], load optimization [7], information of natural frequencie s [2], heat transfer [11], inverse analysis [3, 4] and artificial neural networks [8, 10]. Another, relatively modern tool, which can be effectively used for damage detection is wavelet tr ansformation (WT) [9] also in its discrete form (DWT) [5, 6].
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