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A new concept has been introduced that the combination of rotational mode shape with two‐dimensional wavelet packet transform to detect the added mass (damage) in a glass fibre reinforced polymer composite plate structure. Wavelet packet transform is an advanced signal processing tool that can magnify the abnormality features in the signal. Rotational mode shapes are sensitive to damage in beam and plate structures. The proposed method employs an added mass, which slides to different locations to alter the local and global dynamic characteristics of the structure. Finite element analysis is carried out to obtain the first three rotational bending mode shapes, from the damaged plate structure, then used as input to two‐dimensional wavelet packet transform. The numerical results of normalised diagonal detail wavelet packet coefficients show a peak at single or multiple added mass (damage) locations of a plate structure for two different boundary conditions. This method seems to be sensitive to relatively small amount of damage to the plate structure. A simple parametric study is carried out for the damage extent quantification. In addition, investigation with noise‐contaminated signals shows its feasibility in the real applications.

In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with dierent boundary conditions is investigated. The novelty of this study consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening and stiening size-dependent behavior of the nanorods. The viscoelastic behavior is modelled using the so-called KelvinVoigt viscoelastic damping model.Three length-scale parameters are incorporated in this newly combined theory, namely, a nonlocal, a strain gradient, and a velocity gradient parameter. The governing equation of motion and its boundary conditions for the vibration analysis of nanorods are derived by employing Hamilton's principle. It is shown that the expressions of the classical stress and the stress gradient resultants are only dened for dierent values of the nonlocal and strain gradient parameters. The case where these are equal may seem to result in an inconsistency to the general equation of motion and the related non-classical boundary conditions. A rigorous investigation is conducted to prove that that the proposed solution is consistent with physics. Damped eigenvalue solutions are obtained both analytically and numerically using a Locally adaptive Dierential Quadrature Method (LaDQM). Analytical results of linear free vibration response are obtained for various length-scales and compared with LaDQM numerical results.