Abstract
The preferred structural elements for taller timber buildings include cross-laminated timber (CLT), the performance of which significantly depends on the adhesive bond (AB) quality that may be influenced by manufacturing or factors within the service life. Both may contribute to a delamination, which represents a serious structural damage of the CLT. The study utilised both experimental and numerical modal analyses to assess the influence of damaged AB on CLT vibrational behavior. Both approaches confirmed that the CLT stiffness and eigenfrequencies decreased with AB damage, and both found agreement on certain modal shapes. FEA showed ideal patterns also in terms of localization of the damaged AB using modal shape damage index. Meanwhile, experiments showed its limits due to natural variability of wood, CLT, and measurement setup. The obtained results show a potential for in situ grading and inspection. However, the effect of variability of material properties of CLT should be studied further.
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Detection of Defects in Glue Bonding of Cross-laminated Timber Using Experimental and Numerical Modal Analysis
Václav Sebera,* Patrik Nop 
, Jan Zlámal , David Děcký , and Marek Nociar
The preferred structural elements for taller timber buildings include cross-laminated timber (CLT), the performance of which significantly depends on the adhesive bond (AB) quality that may be influenced by manufacturing or factors within the service life. Both may contribute to a delamination, which represents a serious structural damage of the CLT. The study utilised both experimental and numerical modal analyses to assess the influence of damaged AB on CLT vibrational behavior. Both approaches confirmed that the CLT stiffness and eigenfrequencies decreased with AB damage, and both found agreement on certain modal shapes. FEA showed ideal patterns also in terms of localization of the damaged AB using modal shape damage index. Meanwhile, experiments showed its limits due to natural variability of wood, CLT, and measurement setup. The obtained results show a potential for in situ grading and inspection. However, the effect of variability of material properties of CLT should be studied further.
DOI: 10.15376/biores.21.2.4830-4853
Keywords: CLT; Adhesive bondline; Damage; Modal analysis; Spruce; Eigenfrequency; Damping; Finite element; Modal shape damage index
Contact information: Department of Wood Science and Technology, Faculty of Forestry and Wood Technology, Mendel University in Brno, Zemědělská 1665/1, Brno 61300, Czech Republic; * Corresponding author: vaclav.sebera@mendelu.cz
Graphical Abstract
INTRODUCTION
Cross-laminated timber (CLT) is a massive timber material that is primarily used to build middle-to-tall timber buildings. The production and usage of CLTs in construction has increased worldwide due to their advantages, such as environment-friendliness and shorter time for assembly at construction sites (Brandner et al. 2016). The CLT panel is an engineered wood product whose layers are held by an adhesive. Such assembly assures that the material achieves compactness and structural performance. Therefore, the adhesive bonds play a crucial role in the CLT panel’s mechanical and utility performance. The adhesive bonds may be corrupted either during the manufacture of the panel or during its service life within the structure. Therefore, a non-destructive test (NDT) procedure that is capable of uncovering damaged adhesive bonds within the CLT panel during service life or at the end of the manufacturing process is desired.
There are many NDTs one may use, but those based on ultrasound wave propagation or vibrations have an advantage because they are easy to carry out, relatively cheap, fast, and able to operate in an elastic range of deformations (Aicher and Dill-Langer 2008; Kurz and Boller 2015; Pahnabi et al. 2024). With respect to current study, one of the suitable techniques to find and locate damage (e.g. cavity, crack, decay) in a beam or panel is modal analysis (MA), which has been used to analyze damage for several decades either implemented in finite element analysis (FEA) or experimental MA (EMA) (lrretier 2002; Brown and Allemang 2007; Shi et al. 2025). The MA provides eigenfrequencies and modal shapes that are strongly influenced by the presence of damage, since it modifies the distribution of stiffness and density within the volume of the panel when compared to undamaged scenarios. The MA provides a quality damage detection, especially when a damaged scenario (either physical or numerical) is compared to a sound one in terms of modal shapes and their derivatives.
For instance, Pandey et al. (1991) utilized MA and showed that damage in a beam modifies its eigenfrequencies. In addition, the location of the damage might be derived from the modal shape itself. The presence of a knot in a wooden beam represents a sort of damage and, therefore, it can also be found using the MA from flexural waves and curvatures, as shown in Yang et al. (2002, 2003) and Song et al. (2011). Choi et al. (2007) developed a modal-based damage-detection method to analyze simulated decay pockets in a timber beam. The authors found that the first two modes were enough to capture the extent and severity of damage using the modified damage index. Roohnia et al. (2011) successfully located a drilled hole in a defect-free beam by analysis of the shift of flexural modal frequencies if the hole is located away from the beam neutral axis. Similarly to timber beams, the MA is also suitable for the analysis of CLTs or other panels built in structures. These are usually examined at multiple points (grid), which enables visualisation of the natural modes. In particular, floor systems are often analyzed by MA, for instance in terms of their optimization with respect to design variables, their composition, and performance measures such as eigenfrequencies and damping (Weckendorf et al. 2016, Ussher et al. 2017). The MA may also be applied to floor systems built in constructions using experimental shakers and a set of accelerometers. Such an MA captures, to an advantage over pure lab tests, the interaction of the floors with constructions, since the boundary conditions in situ heavily influence dynamic behavior of CLT panels such as resonance, damping, and eigenfrequencies (Jarnerö et al. 2015; Faircloth et al. 2021; Kawrza et al. 2022). To analyze the structure, such as the CLT panel, it is advantageous to couple experimental and numerical approaches because it enables a deeper understanding of its dynamic behavior (Kawrza et al. 2021).
When carrying out MA of both sound and damaged scenarios, it is often needed to find equivalent modes (mode pairing) between them, as the damage in the structure will give rise to new modes that do not exist in sound scenarios. For that purpose, there are several metrics, among which the modal assurance criterion (MAC) and its derivatives are most commonly used (Allemang 2003). The MAC, which expresses a sort of correlation among modes, may also be used to pair modes obtained from FEA and EMA, as was demonstrated for timber beams in Kouroussis et al. (2017a,b). More recently, Bondsman and Peplow (2025) reported on beams cut out of CLT that their modal performance shows high variability in resonance frequencies, modal damping, and vibration transfer function, especially for torsional modes, due to the variability of the material. When material properties of CLT are not known, an inverse methodology utilizing MA outputs may provide them when an objective function is well stated (Bondsman and Peplow (2024).
Once the modes and eigenfrequencies are paired, the damage may be localized from the postprocessing of modal shapes, for instance, using modal shape damage index (MSDI), modal strain energy, or others (Wang and Chan 2009; Samali et al. 2010; Duvnjak et al. 2016; Li et al. 2023). For plate-like structures, these indices allowed the finding of damage based on computed or measured modal displacements and strains, as was shown for concrete and sandwich panels (Meruane et al. 2017; Duvnjak et al. 2021). It is hypothesized that damage in adhesive bonding inside the CLT panels may be detectable using such indices based on data from experimental and numerical MA.
Therefore, the specific objectives of the research were: 1) to manufacture CLT panels made of spruce with and without imperfections in bonding; 2) to perform experimental modal analysis of manufactured CLTs with simple-support boundary conditions using semiautomatic system employing the laser doppler vibrometer (LDV); 3) to perform data analysis from LDV about eigen frequencies and damping; 4) to carry out the finite element modal analysis of various scenarios in bonding to obtain eigenfrequencies and modal shapes, and to find equivalent modes among designed scenarios using MAC; and 5) to localize damage in bonding between layers using MSDI.
MATERIALS AND METHODS
Material Preparation
Tested specimens consisted of four three-layered cross-laminated timber (CLT) panels made of Norway spruce (Picea abies). The layer had a thickness of 27 mm, so the total size of the panel was 800 x 800 x 81 mm³. Each CLT panel was different in terms of its adhesive bond. The following gluing scenarios were produced: A – CLT panel was glued without an imperfection in AB; B – CLT panel was glued with an imperfection of 10% of total panel in the center of the panel; C – CLT panel was glued with an imperfection of 40% of total panel area in the center of the panel; D – CLT panel was glued with an imperfection of 40% of total panel area at the side of the panel (Fig. 1).
Fig. 1. Sketch of designed CLT damage scenarios A, B, C and D with boundary conditions (BCs) distinguished with colored dashed lines (torsion is blue, BendingL is green, BendingP is red), the circle represent place where shaker was attached to CLT for particular BCs.
The boards in neither CLT panel were glued edge-wise, and the imperfection in AB was introduced only between the top and the middle layer. The polyurethane glue PUR 2010 (AKZONOBEL) was used for the production of all CLT panels with glue spread rate of 180 g/m2 and a manufacturing pressure of ~ 0.8 MPa.
The moisture content (MC) of the CLT panels prior to MA was measured using a dielectric moisture meter (Orion Wagner L601) 10 times from each side of the panel, so the resulting MC of the panel is expressed as the mean value from 20 measurements (Table 1). Before measurement, the global density of the CLT panels was also calculated as the weight of the panel divided by its nominal volume (Table 1).
Table 1. Moisture Content and Global Density of the CLT Panels during Measurement (CV – coefficient of variation, in brackets)
Numerical Modal Analysis
For performing all numerical modal analyses of CLT panels, the software used was Ansys 21R2 (Ansys Inc., USA). The FE models of CLT were created based on physical CLT scenarios (A, B, C, D), and one extra was created (A+). The scenario A+ represents a CLT panel that is glued not only between layers, but also within the layer, so it represents the stiffest scenario simulated. The FE models were built using a top-down approach by quadratic solid finite elements (FE) SOLID185. In total, the FE models had about 58k of FE’s and 86k nodes (Fig. 2). The boundary conditions mimicked the experimental modal analysis setup, so all the FE models were constrained in a way that nodes at the bottom of CLTs at certain locations were simply supported (see Fig. 1). This reflected supporting the CLT panel during experimental modal analysis on elastic ropes at the location of vibrational nodes. The material properties of spruce used in all FE models were linear elastic orthotropic.
Fig. 2. a) Geometrical model of CLT with colored distinction of lamellae; b) Whole FE mesh of CLT panel and c) Detail of the FE mesh
The material properties were taken from Požgaj et al. (1993) because it was based on materials grown in the same region (Czechia and Slovakia) as in the present work. The properties were as follows: ρ = 450 kg.m-3, EL = 13.65 GPa, ER = 0.789 GPa, ET = 0.289 GPa, GLR = 0.474 GPa, GRT = 0.573 GPa, GLT = 0.289 GPa, μLR = 0.014 GPa, μRT = 0.557 GPa, μLT = 0.014 GPa, where E is the normal elastic modulus, G is the shear modulus, and μij is Poisson’s ratio, and indices L, R and T stand for wood anatomical directions longitudinal, radial and tangential, respectively.
The imperfection in glueing was made by not joining the FE nodes of adjacent layers (boards). Therefore, the reference scenarios (A and A+) had only one node at the location shared by two elements from different layers, but scenarios with imperfection had two nodes at the same location and without any interaction between them (no contact was defined). The Block-Lanzcos solver for all analyses was used, and frequencies up to 800 Hz for all panels were investigated. However, each scenario had a different number of modes computed up to 800 Hz due to imperfections. Therefore, to find equivalent natural frequencies and modal shapes compared to the reference scenario (A), the modal assurance criterion (MAC) with a threshold of 0.3 was employed. Consequently, the MAC made it possible to sort modal shapes and natural frequencies and enabled a tool to compare them also to outputs of experimental modal analysis. Once modal shapes were obtained, relative displacement fields of all scenarios from the surface of the panels were extracted. Then, from the extracted modal displacements, the modal shape damage index (MSDI) was calculated between reference scenario and scenarios with damaged AB. The MSDI was used to investigate whether the damaged glue bondline inside the CLT panel is detectable from surface modal shape data. The MSDI was calculated using Eq. 1,
(1)
where φ denotes modal displacement, indices u and d stand for undamaged and damaged scenarios, respectively. All the post finite-element calculations and statistics were performed in Matlab 2024R1 (Mathworks, USA).
Experimental Modal Analysis
The EMA approach was used to determine the plane dynamic response of the entire specimens. Each specimen was tested in three configurations, corresponding to three fundamental plane vibration modal shapes (Fig. 1). In each configuration, the specimen was supported by flexible ropes at the nodal lines. For the torsional mode configuration, the ropes crossed the specimen perpendicularly at 50% of its length, with the dynamic force applied at one corner (blue lines in Fig. 1a). For the longitudinal bending (BendingL) and the perpendicular bending (Bendingp) mode configurations, the nodal lines were located at 22.4% and 77.6% of the specimen length, with the dynamic load applied at the center (red and green lines at Fig. 1a).
The dynamic load was applied using a dynamic shaker GW-V20 (DataPhysics Instruments GmbH, Filderstadt, Germany) connected via epoxy-bonded nuts placed at the antinodes of the fundamental modal shapes (Fig 1). The excitation signal was a looped logarithmic sine sweep in the frequency range of 50 to 5000 Hz. Specimen vibrations were measured using a PDV-100 laser vibrometer (Polytec GmbH, Waldbronn, Germany) over a 51 × 51 – point grid, with spacing between individual points set to 2% of the specimen’s side length. Measured signals were recorded using a Steinberg UR22MKII external sound card (Steinberg Media Technologies GmbH, Hamburg, Germany) at a sampling frequency of 44.1 kHz. The synchronisation of excitation, data acquisition, and the control of stepper motors moving the vibrometer in two axes along the assembled frame was ensured using a Raspberry Pi 4B system (Raspberry Pi Holdings Ltd., Cambridge, UK) (Fig. 3). For all scenarios with imperfections, measurements were taken from the layer where the imperfections were located. To improve the laser vibrometer signal-to-noise ratio, a reflective aluminium adhesive foil was added to the measured specimen surface.
Fig. 3. The setup used for experimental modal analysis. The red arrows indicate the movement of vibrometer at the testing frame.
Experimental Data Analysis
All tasks related to signal processing and data evaluation were carried out in the MATLAB environment (MathWorks, Natick, USA). A Fast Fourier Transform (FFT) was performed on the signal from each measured point. The frequency spectrum of the entire specimen was created as the mean of the spectra of all measured points. To identify the modal shapes corresponding to the frequency peaks in the spectrum, the amplitudes of individual points at resonance frequencies were visualised. The dynamic shear elastic modulus (Gdyn) was determined using the frequency of the torsional modal shape according to Eq. 2,
(2)
where l is the length of the specimen (m), m is the mass of the specimen (kg), n is the order of the torsional mode (n=1), b is the width of the specimen (m), t is the thickness of the specimen (m), and R is a correction factor expressed by Eq. 3.
(3)
The MOED was calculated from the bending mode frequency (fB) using Eq. 4,
(4)
where β is a constant corresponding to the mode order (β = 4.73 for n = 1), and i is the radius of gyration, calculated using Eq. 5.
(5)
The damping ratio (ζ) of each observed modal shape was estimated using the half-power method. At the amplitude level of 1/√2 of the frequency peak (f), the corresponding lower (fₗ) and upper (fᵤ) frequencies were determined. The value of ζ was calculated using Eq. 6.
(6)
RESULTS AND DISCUSSION
Numerical Analysis
The numerical MAs were carried out for all the scenarios up to 800 Hz and for all three configurations. Their outputs are first plotted as frequency vs. mode number paths (Fig. 4). The figure shows modes before mode matching, so it does not show frequencies at equivalent modes. However, these paths are a good illustration of the fact that the damage in adhesive bonds (AB) introduced new eigenfrequencies (modes) that did not occur for sound and reference scenarios (A or A+). These frequency-mode paths start to differ for damaged scenarios from the reference one at certain bifurcation points. The greater the extent of the AB damage, the earlier this point appears in the diagram. Further, the damage in AB decreases the eigenfrequencies due to the reduction of stiffness caused by the missing adhesive. The defectless scenarios A and A+ show very parallel paths, and because A is less stiff, its eigenfrequency paths are slightly below the paths for scenario A+.
Fig. 4. Frequency vs. mode number paths obtained from numerical MA for three configurations: a) BendingL, b) BendingP, and c) Torsion
Scenario B started to differ from A and A+ at all BCs around 600 Hz; meanwhile, severe damages in AB (scenario C primarily) started bifurcating much earlier, or they had a unique path (scenario D). The damage in AB at the side (scenario D) represented the least stiff scenario and had the lowest eigenfrequencies. This means that if debonding of lamellae occurred at the side, the impact to the vibrational and structural performance of CLT was higher than when it occurred in the middle of the CLT, for instance, due to errors in manufacture. From Fig. 4, it is visible that for damaged scenarios, there were many new modes with very similar eigenfrequencies that did not exist for sound scenarios. These conjugated frequencies appeared as horizontal-like ranges in Fig. 4 and represented modes of vibration of loose lamellae. Their vibrations lay in a plane of the CLT panel, and examples of such conjugated eigenfrequencies may be seen in Fig. 5a, 5b and 5c.
Fig. 5. a), b) and c) represent conjugated new modes that occur due to damage in AB (scenario C; d) and e) represent modes of scenario A (8th mode) and C (18st mode) in torsion configuration paired on a basis of MAC = 0.60.
The eigenfrequencies that represent the vibrations of loose lamellae make the situation of comparing particular scenarios between each other more difficult. For that reason, MAC was used to find equivalent modes amongst different scenarios at a certain configuration. For successful mode pairing, MAC values should be as high as possible to assure high-quality matching. It is generally recommended to have MAC higher than 0.7. However, in this case, the damage in AB was so severe for scenarios C and D that the modal shapes were changed substantially. Therefore, the minimal MAC was set to be 0.3, and then paired modes with low MAC values (0.3 to 0.5) were investigated carefully, and also visually. The MAC value above 0.5 did not guarantee correct matching. This was apparent from Figs. 5d and 5e, which show matched modes (8th in A scenario and 18th in C scenario) with MAC = 0.60. The outputs of mode matching using MAC for the first 15 modes are shown in Tables 2, 3 and 4 for BendingL, BendingP, and Torsion, respectively. Tables 2, 3 and 4 contain sequences of data for each scenario as: mode number, eigenfrequency (in Hz), relative frequency difference (in %) and MAC (unitless), so it enables to learn to what extent the damage in AB alters the vibration modes.
From the Tables 2, 3 and 4, the following observations may be drawn: (i) for equivalent modes, the eigenfrequency decreased as the damage in AB increased, although there were a few exceptions given by matching with low MAC; (ii) the minimal MAC value within 15th studied modes decreased as damage in AB increased (the same was observed for mean MAC); (iii) the correlation coefficients (R) between MAC and relative difference of frequency with respect to scenario A decreased with increase of damage and they ranged from -0.87 to 0.14, which implies that MAC may be one of the indicators of damage; however, non-negligible uncertainties should be kept in mind; (iv) mean relative difference of paired eigenfrequencies (mRD) with respect to scenario A increased with increase of damage of AB for studied 15 modes; (v) the reference scenario A with respect to scenario A+ actually behaved as a defect in gluing with similar mRD as found between A and C for instance; this implies that the effect of gluing boards by sides resulted in substantial change in eigenfrequencies, especially for first 7 modes; (vi) for bending configurations, damage in D was so severe that a few modes did not occur at all.
Table 2. FEM-computed Eigenfrequencies for the First 15 Equivalent Modes with Respect to Reference Scenario A in BendingL Configuration
The modal shapes (summed modal displacement vector) of the first 15 modes shown in Tables 2, 3 and 4 are attached as supplemental materials S1, S2 and S3, respectively, and they are also aligned with respect to scenario A. Looking at the S1, S2, and S3, one may make following conclusions: a vast majority of modal shapes of damaged scenarios B, C and D were matched with modal shapes of A (A+ also), although there were a few cases where even visually the modal shape looked different. For instance: (ii) in configuration bendingL (see S1), it was mode no. 6 and 9 of scenarios C and D; (ii) in configuration bendingP, it was mode no. 3, 5, 6, 12, and 15 of scenarios C and D (see S2), and (iii) in configuration torsion, it was mode no. 8 and 14 (see S3). At this stage, the first 15 modes were evaluated, no matter whether they had significant modal displacement perpendicular to CLT, which is important for the experimental part because this component was measured.
Table 3. FEM-computed Eigenfrequencies for the First 15 Equivalent Modes with Respect to Reference Scenario A in BendingP Configuration
Experimental Analysis
The EMA provided several outputs. First, using equations 1 to 5 made it possible to obtain fundamental material properties such as dynamic moduli of CLTs in given scenarios. The frequencies used for the calculation of dynamic moduli were selected according to the associated measurement configuration (torsional for torsion, etc.), and the results are shown in Table 5. From the table, one may see that properties differed substantially amongst scenarios: (i) the value of Gdyn was lower for scenario B by 1.3%, for C by 23.9% and for D by 29.9%; (ii) MOEDL was higher for B by 4.9%, for C it was higher by 1.9%, and for D it was lower by 21.7%; (iii) MOEDT was lower for B by 7.5%, for C by 31.6%, and for D by 48.0%. Theoretically speaking, all stiffnesses of the CLTs tended to decrease as the damage in AB increased, which was clearly apparent for Gdyn and MOEDT. The opposite tendencies shown in Table 5 for MOEDL may be attributed to the variability of wood stiffness and mass within lamellae and within the CLT panels, and, lastly, to measurement inaccuracies (discussed further).
Table 4. FEM-computed Eigenfrequencies for the First 15 Equivalent Modes with Respect to Reference Scenario A in Torsion Configuration