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Formulas for natural frequency and mode shape

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The article was published on 1979-01-01 and is currently open access. It has received 2002 citations till now. The article focuses on the topics: Natural frequency & Normal mode.

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Elastic beam finite element with a transverse elasto-plastic crack

TL;DR: In this article, a cracked beam finite element has been formulated based on elasto-plastic fracture mechanics and the finite element method, and the model can be applied to static, dynamic and stability analysis of cracked beam-like structures.
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Observations on non‐linear dynamic characteristics of suspension bridges

TL;DR: In this article, the authors examine the two principal nonlinearities of inclined and vertical hanger suspension bridges and show that the effect of cable sag only becomes significant when deflections approach the extent of cable elasticity.
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New non-linear modelling for vibration analysis of a straight pipe conveying fluid

TL;DR: In this paper, a non-linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends, using the Euler-Bernoulli beam theory and the nonlinear Lagrange strain theory from the extended Hamilton's principle.
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The Artificial Bee Colony algorithm in layer optimization for the maximum fundamental frequency of symmetrical laminated composite plates

TL;DR: In this paper, the applicability of the Artificial Bee Colony (ABC) algorithm to the layer optimization was investigated, and the optimal stacking sequences were determined for two layer numbers, twenty boundary conditions and two plate length/width ratios.
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A finite difference model For cMUT devices

TL;DR: A finite difference method was implemented to simulate capacitive micromachined ultrasonic transducers (cMUTs) and compared to models described in the literature such as finite element methods, finding that one master curve described the clamped capacitance.