Time-dependent dynamical behavior of surface tension on rotating fluids under microgravity environment

Abstract A study of the dynamical behavior of aircraft wings modeled as doubly-tapered thin-walled beams, made from advanced anisotropic composite materials, and incorporating a number of non-classical effects such as transverse shear, and warping inhibition is presented. The supplied numerical results illustrate the effects played by the taper ratio, anisotropy of constituent materials, transverse shear flexibility, and warping inhibition on free vibration and dynamic response to time-dependent external excitations. Although considered for aircraft wings, this analysis and results can be also applied to a large number of structures such as helicopter blades, robotic manipulator arms, space booms, tall cantilever chimneys, etc.

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Surface-Tension-Driven Flows in Rotating Fluids

Rotating Thermal Flows in Natural and Industrial Processes ◽

10.1002/9781118342411.ch7 ◽

2012 ◽

pp. 345-370

Keyword(s):

Surface Tension ◽

Rotating Fluids

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Chaotic Dynamics of Piezoelectric MEMS Based on Maximum Lyapunov Exponent and Smaller Alignment Index Computations

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420300256 ◽

2020 ◽

Vol 30 (09) ◽

pp. 2030025

Author(s):

M. V. Tchakui ◽

P. Woafo ◽

Ch. Skokos

Keyword(s):

Lyapunov Exponent ◽

Chaotic Dynamics ◽

Detection Method ◽

Dynamical Behavior ◽

Time Dependent ◽

Maximum Lyapunov Exponent ◽

Nonconservative System ◽

Surface Of Section ◽

Chaos Detection ◽

Piezoelectric Mems

We characterize the dynamical states of a piezoelectric micrcoelectromechanical system (MEMS) using several numerical quantifiers including the maximum Lyapunov exponent, the Poincaré Surface of Section and a chaos detection method called the Smaller Alignment Index (SALI). The analysis makes use of the MEMS Hamiltonian. We start our study by considering the case of a conservative piezoelectric MEMS model and describe the behavior of some representative phase space orbits of the system. We show that the dynamics of the piezoelectric MEMS becomes considerably more complex as the natural frequency of the system’s mechanical part decreases. This refers to the reduction of the stiffness of the piezoelectric transducer. Then, taking into account the effects of damping and time-dependent forces on the piezoelectric MEMS, we derive the corresponding nonautonomous Hamiltonian and investigate its dynamical behavior. We find that the nonconservative system exhibits a rich dynamics, which is strongly influenced by the values of the parameters that govern the piezoelectric MEMS energy gain and loss. Our results provide further evidences of the ability of the SALI to efficiently characterize the chaoticity of dynamical systems.

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