Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

Meccanica ◽  
2010 ◽  
Vol 45 (6) ◽  
pp. 847-855 ◽  
Author(s):  
Nicolae Herişanu ◽  
Vasile Marinca
Keyword(s):  
Cantilever Beam ◽  
Large Amplitude ◽  
Analytical Approximation ◽  
Rotary Inertia ◽  
Lumped Mass ◽  
Non Linear

Large Amplitude Vibration of a Cantilever Beam with Tip Mass under Random Base Excitation

2002 ◽  
Vol 4 (4) ◽  
pp. 203-210 ◽  
Author(s):  
Guangfeng Cheng ◽  
Chuh Mei ◽  
Raymond Y. Y. Lee
Keyword(s):  
Cantilever Beam ◽  
Large Amplitude ◽  
Beam Theory ◽  
Single Mode ◽  
Rotary Inertia ◽  
System Response ◽  
Base Excitation ◽  
Random Response ◽  
Lumped Mass ◽  
Tip Mass

Nonlinear large amplitude random vibration of cantilever beam with lumped mass and rotary inertia under zero mean, stationary, Gaussian random base excitation is studied, using the inextensional beam theory. Single-mode approximation is employed to discretize the Lagrange's equation. The resulting nonlinear governing modal equation of motion is solved with application of the stochastic linearization method. Two examples, a cantilever beam with/without tip mass, are analyzed as application of the developed methodology. Effects of mass and rotary inertia variation on system response are investigated in detail. Results showed that increasing rotary inertia could reduce the random response of the beam structure and the random response of the structure is quite sensitive to the tip mass variation. The nonlinearities of the inextensional beam vibration result in a spring hardening system.

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

Asymmetric FPSO Roll Response due to the Influence of Lines Arrangement

2012 ◽  
Author(s):  
Marcos Donato Ferreira ◽  
Mauro Costa de Oliveira ◽  
Rafaella Cristina Carvalho ◽  
Sergio Hamilton Sphaier
Keyword(s):  
Integration Scheme ◽  
Impulse Response Functions ◽  
Viscous Effects ◽  
Lumped Mass ◽  
Explicit Integration ◽  
Deep Waters ◽  
Campos Basin ◽  
Motion Responses ◽  
Non Linear ◽  
Ship Hydrodynamic

In the development of the mooring design of FPSOs in spread mooring system (SMS) configuration, it was observed that the utilization of asymmetric riser arrangement in deep waters might lead to an asymmetrical roll response of the FPSO. In particular, concentrating all riser connections on the portside, it could be observed that roll and heave coupling under the influence of the riser dynamics might lead to a much lower roll response associated with waves coming from portside than from the starboard direction. Simulations were carried using an in-house time domain simulator, where the ship hydrodynamic behavior was represented through the use of impulse response functions and the lines dynamic through the use of non-linear finite element method, using an explicit integration scheme and a lumped mass approach. Non-linear viscous effects could be easily associated to the ship and line velocities. Measured motion responses of an actual FPSO in operation in Campos Basin are compared with the computations.

Parametrically Excited Electrostatic MEMS Cantilever Beam With Flexible Support

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Mark Pallay ◽  
Shahrzad Towfighian
Keyword(s):  
Cantilever Beam ◽  
Large Amplitude ◽  
Chaotic Behavior ◽  
Signal To Noise Ratio ◽  
Mass Sensors ◽  
Flexible Support ◽  
Sensing Applications ◽  
Electrostatic Mems ◽  
Fringe Fields ◽  
Steady State Amplitude

Parametric resonators that show large amplitude of vibration are highly desired for sensing applications. In this paper, a microelectromechanical system (MEMS) parametric resonator with a flexible support that uses electrostatic fringe fields to achieve resonance is introduced. The resonator shows a 50% increase in amplitude and a 50% decrease in threshold voltage compared with a fixed support cantilever model. The use of electrostatic fringe fields eliminates the risk of pull-in and allows for high amplitudes of vibration. We studied the effect of decreasing boundary stiffness on steady-state amplitude and found that below a threshold chaotic behavior can occur, which was verified by the information dimension of 0.59 and Poincaré maps. Hence, to achieve a large amplitude parametric resonator, the boundary stiffness should be decreased but should not go below a threshold when the chaotic response will appear. The resonator described in this paper uses a crab-leg spring attached to a cantilever beam to allow for both translation and rotation at the support. The presented study is useful in the design of mass sensors using parametric resonance (PR) to achieve large amplitude and signal-to-noise ratio.

Approximate Solutions to a Cantilever Beam Using Optimal Homotopy Asymptotic Method

2013 ◽  
Vol 430 ◽  
pp. 22-26 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu ◽  
Traian Marinca
Keyword(s):  
Small Parameter ◽  
Cantilever Beam ◽  
Asymptotic Method ◽  
Approximate Solutions ◽  
Lumped Mass ◽  
Engineering Problems ◽  
Approximate Frequency ◽  
Optimal Homotopy Asymptotic Method ◽  
Analytical Expressions

The response of a cantilever beam with a lumped mass attached to its free end subject to harmonical excitation at the base is investigated by means of the Optimal Homotopy Asymptotic Method (OHAM). Approximate accurate analytical expressions for the solutions and for approximate frequency are determined. This method does not require any small parameter in the equation. The obtained results prove that our method is very accurate, effective and simple for investigation of such engineering problems.

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