Experimental results were obtained for the natural frequencies and the mode shapes of graphite-epoxy and boron-epoxy composite materials having fiber orientations of 0°, 15° , 30° and 90° with respect to cantilever beam axes. Certain elastic constants were experimentally determined and used in a programmed numerical solution in which rotary inertia, trans verse shear, and coupled bending-torsion effects were included. The experi mental results for the 15° and 30° beams gave a clear indication of the interaction between bending and twisting and good agreement was obtained with the numerical results.

The Vibration of Cantilever Beams of Fiber Reinforced Material

An experimental methodology is presented for the simutaneous determination of the section flexural modulus and the section shear modulus of thin-walled fiber reinforced polyester and vinylester pultruded beams. A pilot test program, involving four different fiber reinforced plastic (FRP) beams, is described and results are discussed. A slenderness ratio is introduced to characterize the shape of the thin-walled beam, and recommended values of this ratio are suggested for design purposes. With available values of the section moduli the designer has the option of using the Timoshenko beam theory instead of the Euler-Bernoulli beam theory.

Flexural and shear moduli of full-section fiber reinforced plastic (FRP) pultruded beams

Three techniques for measuring fracture healing are presented. These techniques are: (1) use of strain gauge measurements of the forces in an external fixator to determine fracture stiffness, (2) measurement of the vibration modes of a fractured long bone compared to the unfractured contralateral and (3) comparison of the ultrasound velocity across the fracture site with that for the normal unfractured bone. Examples of clinical results obtained using these techniques are presented, and the advantages and disadvantages of each technique are discussed.

Biomechanical measurement of fracture healing.

The vibration of beams of fibre reinforced material

This paper presents a feasibility study on using Lamb waves to detect and locate through-width delamination in fiber-reinforced plastic beams. An active diagnostic system is proposed for clamped-free specimens. It consists of a piezoelectric patch and an accelerometer both mounted near the support. Such a system can locate damage in an absolute sense, that is, a priori knowledge on the response from pristine specimens is not required. The fundamental anti-symmetric Lamb wave mode is chosen as the diagnostic wave. It is generated by applying a voltage in the form of sinusoidal bursts to the piezoelectric patch. The proposed system was applied to locate delaminations in some fabricated Kevlar/epoxy beam specimens. With an appropriate actuating frequency, distortions of waveforms due to boundary reflections can be reduced. Based on their arrival times and the known propagating speed of Lamb waves, the delaminations can be located. The errors associated with the predicted damage positions range from 4.5% to 8.5%.

Delamination detection in smart composite beams using Lamb waves

The resonant frequencies of unidirectional graphite epoxy com posite beams were found to deviate markedly from classical beam theory predictions at higher modes of vibration. Timoshenko beam theory was used to account quantitatively for the dependence of ex perimental resonant frequencies on mode of vibration, length/thickness ratio, and the ratio of Young's modulus/shear modulus of the com posite beam. By using reasonable values for the longitudinal-trans verse shear moduli, the longitudinal Young's modulus of anisotropic composite beams under vibration agreed well with values determined by static tests and became independent of mode of vibration and L/t. The vibrating beam test method was employed for the deter mination of E11, E22, and G12.

T.J. Dudek

Papers

Young's and Shear Moduli of Unidirectional Composites by a Resonant Beam Method