Perturbations for vibration of nano-beams of local/nonlocal mixture

Here we extend the perturbation approach, previously presented in the literature for Eringen’s two-phase local/nonlocal mixture model, to free vibration of purely flexible beams. In particular, we expand the eigenvalues and the eigenvectors into power series of the fraction coefficient of the non-local material response up to 2nd order. We show that the family of 0th order bending couples satisfy the natural and essential boundary conditions of the 1st order; hence, the 1st order solution can conveniently be constructed using the eigenspace of the 0th order with no necessity of additional conditions. We obtain the condition of solvability that provides the incremental eigenvalue in closed form. We further demonstrate that the 1st order increment of the eigenvalue is always negative, providing the well-known softening effect of long-range interactions among the material points of a continuum modelled with Eringen’s theory. We examine a simply supported beam as a benchmark problem and present the incremental eigenvalues in closed form. © 2023, Association of American Publishers. All rights reserved.2-s2.0-8515266294

The minimum variance distortionless response beamformer for damage identification using modal curvatures

This study presents a damage identification procedure in beams based on the use of beamforming algorithms, which are mostly utilized in inverse problems of source identification and image reconstruction. We choose the modal curvatures as observed quantities and compare the performance of the Bartlett beamformer, minimum variance distortionless response (MVDR) processor, and of a conventional objective function based on the modal curvatures. By means of a set of experiments, we show that the MVDR processor can overcome some of the difficulties encountered with other estimators, especially in cases of slight damage, or damage located between two sensors. © 2023, Association of American Publishers. All rights reserved.2-s2.0-8515265642

Vibration of Pre-Loaded Shallow Circular Arches

We study dynamics of pre-stressed pinned shallow slender circular arches by one-dimensional field equations, simplified and solved by perturbation. The static response to a uniform load and small imperfections is found: the transverse displacement depends in closed form on the load. The first two frequencies of small vibration about the deformed shape, plus possible bifurcations in terms of the initial geometry and the pre-load are found

Approximate closed-form solutions for vibration of nano-beams of local/non-local mixture

This paper presents an approach to natural vibration of nano-beams by a linear elastic constitutive law based on a mixture of local and non-local contributions, the latter based on Eringen's model. A perturbation in terms of an evolution parameter lets incremental field equations be derived; another perturbation in terms of the non-local volume fraction yields the variation of the natural angular frequencies and modes with the 'small' amount of non-locality. The latter perturbation does not need to comply with the so-called constitutive boundary conditions, the physical interpretation of which is still debated. The possibility to find closed-form solutions is highlighted following a thorough discussion on the compatibility conditions needed to solve the steps of the perturbation hierarchy; some paradigmatic examples are presented and duly commented.WOS:0008890320000012-s2.0-85142699132Science Citation Index ExpandedQ3ArticleUluslararası işbirliği ile yapılan - EVET2022YÖK - 2022-23Aralı

Vibration of locally cracked pre-loaded parabolic arches

We study linear dynamics of an initially parabolic arch deformed by a uniform ‘dead’ load. The arch is seen as a fully deformable one-dimensional continuum with rigid cross-sections, one of which suffers from a small local crack at its boundary. The crack is simulated by springs, the stiffnesses of which are evaluated via stress intensity factors. By two first-order perturbations we investigate a non-trivial equilibrium adjacent to the reference configuration and small vibration superposed on it. The modulation of the initial load on the natural angular frequencies and its consequences on damage detection is described and commented. It turns out that neglecting the initial load, recalling for actual ‘dead’ structural actions, can be misleading in damage identification, while its inclusion leads to better results.WOS:000827043900004Scopus - Affiliation ID: 60105072Science Citation Index ExpandedQ1ArticleUluslararası işbirliği ile yapılan - EVETTemmuz2022YÖK - 2021-22Eki

Buckling and Post‐Buckling of Parabolic Arches with Local Damage

We investigate buckling and post-buckling of parabolic arches with crack-like damages. The latter may be simplified models of either the failure of connections of large structures and actual cracks in relatively small-size applications. We model the arch as a one-dimensional curved beam and study its fundamental and bifurcated path under reasonable kinematic and constitutive assumptions.The crack is modeled by the spring analogy and the SIFs, following the literature and previous works by the authors