ANALYSIS OF THE NATURAL VIBRATION FREQUENCY TEST METHOD TO OBTAIN THE MODULUS OF ELASTICITY OF WOOD STRUCTURAL COMPONENTS

There are several techniques to characterize the elastic modulus of wood and those currently using the natural frequencies of vibration stand out as they are non-destructive techniques, producing results that can be repeated and compared over time. This study reports on the effectiveness of the testing methods based on the natural frequencies of vibration versus static bending to obtain the elastic properties of reforested structural wood components usually employed in civil construction. The following components were evaluated: 24 beams of Eucalyptus sp. with nominal dimensions (40 x 60 x 2.000 mm) and 14 beams of Pinus oocarpa with nominal dimensions (45 x 90 x 2.300 mm) both without treatment; 30 boards with nominal dimensions (40 x 240 x 2.010 mm) and 30 boards with nominal dimensions (40 x 240 x 3.050 mm), both of Pinus oocarpa and with chromate copper arsenate (CCA) preservative treatment. The results obtained in thiswork show good correlation when compared to the results obtained by the static bending mechanical method, especially when applying the natural frequency of longitudinal vibration. The use of longitudinal frequency was reliable and practical, therefore recommended for determining the modulus of elasticity of wood structural elements. It was also found that no specific support is needed for the specimens using the longitudinal frequency, as well as no previous calibrations, reducing the execution time and enabling to test many samples.

DETERMINATION OF THE E/G RATIO OF WOOD LOGS USING TRANSVERSE VIBRATION

The Bernoulli's model for vibration of beams is often used to make predictions of bending modulus of elasticity when using dynamic tests. However this model ignores the rotary inertia and shear. Such effects can be added to the solution of Bernoulli's equation by means of the correction proposed by Goens (1931) or by Timoshenko (1953). But to apply these corrections it is necessary to know the E/G ratio of the material. The objective of this paper is the determination of the E/G ratio of wood logs by adjusting the analytical solution of the Timoshenko beam model to the dynamic testing data of 20 Eucalyptus citriodora logs. The dynamic testing was performed with the logs in free-free suspension. To find the stiffness properties of the logs, the residue minimization was carried out using the Genetic Algorithm (GA). From the result analysis one can reasonably assume E/G = 20 for wood logs.

Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 Elsevier B.V. All rights reserved.

Parametric Analysis of Effective Material Properties of Thickness-Shear Piezoelectric Macro-Fibre Composites

A previous study on the characterization of effective material properties of a d(15) thickness-shear piezoelectric Macro-Fibre Composite (MFC) made of seven layers (Kapton, Acrylic, Electrode, Piezoceramic Fibre and Epoxy Composite, Electrode, Acrylic, Kapton) using a finite element homogenization method has shown that the packaging reduces significantly the shear stiffness of the piezoceramic material and, thus, leads to significantly smaller effective electromechanical coupling coefficient k(15) and piezoelectric stress constant e(15) when compared to the piezoceramic fibre properties. Therefore, the main objective of this work is to perform a parametric analysis in which the effect of the variations of fibre volume fraction, Epoxy elastic modulus, electrode thickness and active layer thickness on the MFC effective material properties is evaluated. Results indicate that an effective d(15) MFC should use relatively thick fibres having relatively high shear modulus and relatively stiff epoxy filler. On the other hand, the electrode thickness does not affect significantly the MFC performance.

New Improved Version of J 1 ...J 4 Interferometry Method and its Application to Nanometric Vibration Measurements

Piezoelectric ceramics, such as PZT, can generate subnanometric displacements, bu t in order to generate multi- micrometric displacements, they should be either driven by high electric voltages (hundreds of volts ), or operate at a mechanical resonant frequency (in narrow band), or have large dimensions (tens of centimeters). A piezoelectric flextensional actuator (PFA) is a device with small dimensions that can be driven by reduced voltages and can operate in the nano- and micro scales. Interferometric techniques are very adequate for the characterization of these devices, because there is no mechanical contact in the measurement process, and it has high sensitivity, bandwidth and dynamic range. A low cost open-loop homodyne Michelson interferometer is utilized in this work to experimentally detect the nanovi brations of PFAs, based on the spectral analysis of the interfero metric signal. By employing the well known J 1 ...J 4 phase demodulation method, a new and improved version is proposed, which presents the following characteristics: is direct, self-consistent, is immune to fading, and does not present phase ambiguity problems. The proposed method has resolution that is similar to the modified J 1 ...J 4 method (0.18 rad); however, differently from the former, its dynamic range is 20% larger, does not demand Bessel functions algebraic sign correction algorithms and there are no singularities when the static phase shift between the interferometer arms is equal to an integer multiple of  /2 rad. Electronic noise and random phase drifts due to ambient perturbations are taken into account in the analysis of the method. The PFA nanopositioner characterization was based on the analysis of linearity betw een the applied voltage and the resulting displacement, on the displacement frequency response and determination of main resonance frequencies.