scholarly journals NONLINEAR FREE VIBRATION IN CONSERVATIVE FIELD : The Periodic Solution Problems of Nonlinear Equations of Motion-Part 3

1979 ◽  
Vol 278 (0) ◽  
pp. 9-14
Author(s):  
YOUICHI MINAKAWA
Keyword(s):  
Periodic Solution ◽  
Free Vibration ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Nonlinear Free Vibration ◽  
Nonlinear Equations Of Motion

Free Vibration of Flexible Cables

2015 ◽  
Author(s):  
Andrea Arena
Keyword(s):  
Free Vibration ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Torsional Stiffness ◽  
Axial Stiffness ◽  
Geometric Nonlinearities ◽  
Nonlinear Equations Of Motion ◽  
Extensible Cables ◽  
Flexible Cables ◽  
Elastic Cables

The free undamped vibrations of cables undergoing stretching, bending and twisting are investigated. To this end, a geometrically exact model of elastic cables accounting for bending and torsional stiffness is employed. The cable kinematics retain the full geometric nonlinearities. Starting from a prestressed catenary configuration, the nonlinear equations of motion are linearized about the initial equilibrium. In particular, two initial equilibrium states (shallow and taut) are considered while varying the cable elastic axial stiffness. The influence of the bending flexibility on the cable frequencies is assessed by direct comparisons with the frequencies predicted by classical cable theories of purely extensible cables.

Nonlinear Free Vibration Analysis of a Fluid-Conveying Microtube

2014 ◽  
Author(s):  
Shamim Mashrouteh ◽  
Mehran Sadri ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Variational Iteration Method ◽  
Solution Technique ◽  
Nonlinear Free Vibration ◽  
Nonlinear Equations Of Motion ◽  
Analytical Expressions

Nonlinear free vibration of a microstructure has been analyzed in this study. A fluid-conveying microtube is mathematically modeled using non-classical beam theory. Partial differential equation of the model is considered in non-dimensional form. Simply-supported boundaries are taken into account and assuming three vibrating modes, an analytical method is employed to obtain the nonlinear equations of motion. Variational iteration method has been utilized as an analytical solution technique. In order to obtain the nonlinear natural frequencies of the system, analytical expressions are found based on this method. A parametric study is also carried out to investigate the effect of different parameters on the vibration characteristics of the microstructure.

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