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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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Three-dimensional trajectory tracking of a hybrid autonomous underwater vehicle in the presence of underwater current

TL;DR: A six degrees-of-freedom nonlinear kinematic and dynamic model of a Hybrid Autonomous Underwater Vehicle (H-AUV) is derived for the two modes of locomotion, propelled and gliding modes to ensure minimal trajectory tracking error and energy consumption.
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Recursive and symbolic calculation of the elastodynamic model of flexible parallel robots

TL;DR: The generalized Newton–Euler model is used and combined with the principle of virtual powers to minimize the number of operators and intermediate variables to compute the elastodynamic model of a prototype of a planar parallel robot developed at IRCCyN: the DualEMPS.
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Active vibration control of smart hull structure using piezoelectric composite actuators

TL;DR: In this article, the active vibration control performance of the smart hull structure with macro-fiber composite (MFC) is evaluated and a linear quadratic Gaussian (LQG) control algorithm is designed in order to effectively and actively control the imposed vibration.
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Experimental analysis of the dynamic, mechanical behaviour of a chicken egg

TL;DR: In this paper, the dynamic, mechanical behaviour of a chicken egg is assessed and modal analysis tests revealed several spherical modes in the 2-7 kHz frequency band. But the authors did not identify the mode shapes, resonant frequencies and corresponding damping ratios of these modes.
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Analysis and numerical modelling of eddy current damper for vibration problems

TL;DR: In this article, a new inverse method to numerically determine the dynamic properties of the contactless eddy current damper is proposed, based on a lineal viscous force.