Present work establishes a new formulation to determine the dynamic characteristics of a cracked beam, where the change in second moment of area is considered. The present formulation considers the shift in the neutral axis of the cracked beam-element, which has been ignored previously. Consequently, an in-depth analysis is conducted to understand the effectiveness of this new approach. The results obtained shows a promising scope for the adoption of the updated formulation for various cross-sections and future research work.
Structural analysis is mainly concerned with predicting the behaviour of a structure when subjected to any external excitation. Dynamic analysis of simple structures can be carried out using finite element analysis on various computing platforms such as MatLab. In the case of industrial applications, dynamic analysis is mainly carried out using simulations on softwares such as Ansys. The present paper compares mathematical and simulation analysis of cracked beam and the dynamic behaviour with respect to mode shape and crack position is reported.
Mechanical stress and fracture analysis of the human lumbar intervertebral discs are important in assessing disorders related to lower back pain and ageing. Finite element modelling and simulation approaches assist in easier prediction of the disc behaviour under different load conditions. The causes of mechanical failure and morphological changes still remain partially speculative. The present study addresses the issue by developing a finite element model of an L3-L4 lumbar intervertebral disc subjected to different axial compressive loadings. The morphological deformations and stress concentration regions within the disc are analyzed and reported. A mathematical relation is established to estimate the breaking strength of an L3-L4 intervertebral disc, thus indicating the risk of disc failure based on the applied load.
Bone is a dynamic connective tissue which adjusts to load variations through continuous bone remodeling, which occurs due to the dynamic behavior of bone cells. Many researchers made attempts in obtaining the dynamic characteristics of osteoblasts and its role in bone remodeling cycle. While making an effort to understand the effects of mechanical stimuli on the osteoblast, certain ambiguity is observed in the past literatures. This paper is to demonstrate the dynamics of osteoblast cells and exhibition of different natural frequencies during its life cycle. Osteoblast is modeled as a frustum of a sphere, considering it as a continuum model. The three prominent parts of an osteoblast, i.e., membrane, cytoplasm and nucleus are considered with reported material properties. Lifespan of an active osteoblast during bone remodeling cycle is considered as 90 days and progressive osteoblast stages are analysed using Ansys. First ten natural frequencies and mode shapes are extracted for nine stages and reported. It is observed that the natural frequencies of a micron sized osteoblast are in the range of kHz. A mathematical relation for the lifespan of an active osteoblast is obtained using curve fitting for fundamental natural frequencies. The natural frequency for exciting an active osteoblast on each particular day during its lifespan can be derived from the relation. This relation can serve as a guiding tool in bioengineering for in vitro bone cell culturing. Results also throw light on the excitation frequency and natural frequency of an osteoblast for proper analysis purpose. The different modes of vibration of osteoblast is identified and reported.
In this paper, a finite element mathematical model to evaluate natural frequencies and Frequency Response Functions (FRFs) of an L-shaped cracked beam structure is established. Dynamics of L-shaped beam structure is a very challenging subject and very little information is reported in literature. L-shaped beam structure is assumed to be fixed at end of the vertical column and free at the other end of the horizontal column. Natural frequencies are evaluated using finite element method in MatLab and simulations using Ansys (Version 18.2) is carried out to validate the mathematical model. Totally 18 cases with different crack positions and three different crack depths are considered for the analysis. Results obtained by both methods are tabulated and find a very good agreement in the results. Reported results can be used as a benchmark for further study of crack propagation and fatigue failure analysis in built-up structures.
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