nobxeny eiriol hazett
Catherin Bergan
This document describes an experiment to determine the modulus of rigidity of a wire using an oscillating method. Key details include:- The experiment measures the time period of oscillations of a solid cylindrical rod suspended by a wire when a mass is attached. - The modulus of rigidity is calculated using a formula involving the mass, length, and radius of the rod, length and radius of the wire, and time period of oscillations. - Procedural steps include measuring the diameter, length, and mass of components and recording the time for 10 oscillations to calculate the time period. - Based on the observations recorded, the calculated modulus of rigidity of the wire is 1.48 1014 dynRead less
The aim of this paper was to predict the static bending modulus of elasticity (MOES) and modulus of rupture (MOR) of Scots pine (Pinus sylvestris L.) wood using three nondestructive techniques. The mean values of the dynamic modulus of elasticity based on flexural vibration (MOEF), longitudinal vibration (MOELV), and indirect ultrasonic (MOEUS) were 13.8, 22.3, and 30.9 % higher than the static modulus of elasticity (MOE S ), respectively. The reduction of this difference, taking into account the shear deflection effect in the output values for static bending modulus of elasticity, was also discussed in this study. The three dynamic moduli of elasticity correlated well with the static MOE S and MOR; correlation coefficients ranged between 0.68 and 0.96. The correlation coefficients between the dynamic moduli and MOE S were higher than those between the dynamic moduli and MOR. The highest correlation between the dynamic moduli and static bending properties was obtained by the flexural vibration technique in comparison with longitudinal vibration and indirect ultrasonic techniques. Results showed that there was no obvious relationship between the density and the acoustic wave velocity that was obtained from the longitudinal vibration and ultrasonic techniques.
The aim of this paper was to predict the static bending modulus of elasticity (MOES) and modulus of rupture (MOR) of Scots pine (Pinus sylvestris L.) wood using three nondestructive techniques. The mean values of the dynamic modulus of elasticity based on flexural vibration (MOEF), longitudinal vibration (MOELV), and indirect ultrasonic (MOEUS) were 13.8, 22.3, and 30.9 % higher than the static modulus of elasticity (MOES), respectively. The reduction of this difference, taking into account the shear deflection effect in the output values for static bending modulus of elasticity, was also discussed in this study. The three dynamic moduli of elasticity correlated well with the static MOES and MOR; correlation coefficients ranged between 0.68 and 0.96. The correlation coefficients between the dynamic moduli and MOES were higher than those between the dynamic moduli and MOR. The highest correlation between the dynamic moduli and static bending properties was obtained by the flexural vibration technique in comparison with longitudinal vibration and indirect ultrasonic techniques. Results showed that there was no obvious relationship between the density and the acoustic wave velocity that was obtained from the longitudinal vibration and ultrasonic techniques.
Nondestructive materials evaluation (NDE) is the approach of evaluating physical and mechanical characteristics of the material without changing its end-use performance (Ross et al.1998). The instruments used for nondestructive evaluation can be applied widely at different processing levels, starting from wood-based composites to standing trees (Lin et al. 2006). Usually NDE is carried out using three methods, ultrasonic, stress waves, or resonant frequency vibrations (Ilic 2001a). The acoustics study commonly used in the area of wood and wood-based materials is solid acoustics in the audible (20 Hz to 20 kHz) and ultrasound (> 20 kHz) frequency ranges (Smith 2001).
The ultrasonic moduli of elasticity determination depend on the ultrasonic wave speed and density. The ultrasonic velocities range from 1000 to 2000 m.s-1 perpendicular to the grain direction and from 5000 to 6000 m.s-1 parallel to the grain direction of solid wood; the radial velocity is approximately 50% higher than the tangential velocity (Beall 2002).
The common mode shapes of a vibrating beam are longitudinal, flexural, and torsional vibrations. They are the dynamic equivalents of static tension, bending, and torsion (Bucur 2006). The classical destructive bending evaluation of modulus of elasticity is time- and money-consuming when applied to standing trees. This may lead to reduced opportunities for determining the optimal use of the produced wood from standing trees (Ilic 2003).
Modulus of elasticity (MOE) is a property that describes the material stiffness. A high value of wood MOE indicates that the wood has a high resistance to deformation (Liang and Fu 2007). Several studies have considered the relationships between the dynamic and static modulus of the elasticity of wood; some of these are reported by Liu et al. (2006), who investigated the dynamic modulus of wood using the transverse and longitudinal vibration techniques. They showed a significant linear correlation between the static MOE and the dynamic MOEobtained from both techniques. Sales et al. (2011) ascertained the accuracy of the ultrasonic and transverse vibration techniques for evaluating the static bending modulus of elasticity. The authors indicated that the values of the coefficient of determination for the ultrasonic technique and for transverse vibration were significant and that both techniques were valid tools for the nondestructive evaluation of the MOE of structural timber pieces. However, few reports have considered the comparison of resonance frequency and ultrasonic techniques for predicting the modulus of rupture of Scots pine wood. The acoustic wave velocity transmission through timber can be affected by several factors, such as moisture content, temperature, grain orientation, density, decay, and geometry (Beall 2002).
The main objective of this study was to investigate the dynamic modulus of elasticity of Scots pine wood by flexural vibration, longitudinal vibration, and indirect ultrasonic techniques, and to evaluate the degree of the association between the dynamic MOE obtained by the three different techniques with the static MOE and MOR.
The experiments were carried out using 40 specimens of Scots pine (Pinus sylvestris L.). The dimensions of each specimen were 20 mm x 60 mm in the cross section and 500 mm in length. The dynamic modulus of elasticity was determined for each specimen using ultrasonic and resonance vibration techniques. After the nondestructive evaluation, the specimens were tested in a static bending test.
The specimens were supported by rubber threads, and the flexural and longitudinal vibrations were induced by impacting the specimen with a hammer, as shown in Fig. 1, for each test. An ultra-linear measurement condenser microphone Behringer (type ECM8000) and afire-wire external soundcard (Edirol FA-101 with 24- bit/192 kHz sampling frequency) were used for recording the signal.
where MOELV is the dynamic modulus of elasticity based on longitudinal vibration, MOEF is the flexural dynamic modulus of elasticity, is the frequency of longitudinal vibration, is the fundamental frequency of the free-free flexural vibration in the first mode, is the specimen length, is the wood density, is the radius of gyration of the cross section, and (4.73) is a constant corresponding to the first mode of free-free flexural vibration.
Measurements of the ultrasonic velocities were made with a Portable Ultrasonic Nondestructive Digital Indicating Tester (PUNDIT). The device, equipped with two 150 kHz piezo-electric transducers (transmitting and receiving transducer), generates an ultrasonic impulse by electronic excitation of the transducer. There are three test set-ups that can be used to measure the ultrasonic velocity using PUNDIT; they are the direct, indirect, and semi-direct measurements (Fig. 2). The measurements were conducted in this study with only the indirect (surface) method. In order to estimate the exact length of the transmission path, a series of measurements with the transducers at different distances were performed.
where is the ultrasonic wave velocity (m.s-1), L is the specimen length (m), and t is the transit time (s). The dynamic modulus of elasticity based on indirect ultrasonic was determined through the one dimensional wave equation as follows (Bucur 2006),
The test was performed using the apparatus used in flexural vibration; the microphone was placed above the end at one corner of the sample and the torsional vibration was established by hitting the other end at the corner as described in (Nakao and Okano 1987). The shear modulus value was calculated from the following equation (Cho 2007),
where G is the shear modulus, is thetorsional vibration frequency at thefirst mode, n is the mode number, is the wood density, is the polar moment of inertia, and = 0.141bh3(b and h are the cross-sectional dimensions).
The wood density at 12% moisture content was determined from the weight and volume of the specimens. The values of the static bending modulus of elasticity were recalculated as described in Teranishiet al. (2008), by taking into account the value of the shear deflection in the center-load bending test according to Equation 6,
It was observed that the average ultrasonic velocity (VUS) was higher than those obtained from longitudinal vibration (VLV). Several researchers have reported that the longitudinal wave velocity by ultrasonic techniques was higher than the longitudinal vibration techniques (Baar et al. 2012; Bucur 2006). Machado et al. (2009), in a study on three wood species, reported that the indirect ultrasonic method of testing had lower values than that using the direct method. However, a strong relationship existed between both, with an R2 value of 0.90.Thus, the difference between the ultrasonic and longitudinal vibration wave velocity will increase when using the direct method. In addition, the direct method cannot be applied to wood members in-service, because the ends of the wood would be unavailable (Machado and Palma 2011).
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