A note on the periodic and chaotic responses of an SDOF system with piecewise linear stiffness subjected to combined harmonic- and flow-induced excitations

2008 ◽  
Vol 311 (1-2) ◽  
pp. 567-578 ◽  
Author(s):  
Wang Lin ◽  
Ni Qiao
Keyword(s):  
Piecewise Linear ◽  
Sdof System ◽  
Piecewise Linear Stiffness

scholarly journals Vibrations of a Beam Moving Over Supports with Clearance

1994 ◽  
Vol 1 (6) ◽  
pp. 549-557
Author(s):  
H.P. Lee
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Euler Beam ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Euler Beam Theory ◽  
The Stability ◽  
Effect Of Support ◽  
Piecewise Linear Stiffness

The transverse vibration of a beam moving over two supports with clearance is analyzed using Euler beam theory. The equations of motion are formulated based on a Lagrangian approach and the assumed mode method. The supports with clearance are modeled as frictionless supports with piecewise-linear stiffness. A feature of the present formulation is that its complexity does not increase with increased number of supports. Results of numerical simulations are presented for various prescribed motions of the beam. The effect of support clearance on the stability of the beam is investigated.

Rotations of Pendulum When Its Pivot Oscillates Chaotically

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Sze-Hong Teh ◽  
Ko-Choong Woo ◽  
Hazem Demrdash
Keyword(s):  
Control Method ◽  
Piecewise Linear ◽  
Control Input ◽  
Velocity Control ◽  
Chaotic Oscillations ◽  
Vertical Excitation ◽  
Stiffness Characteristic ◽  
Adjustable Mechanism ◽  
Piecewise Linear Stiffness ◽  
Excitation Conditions

This paper investigates the possibility of energy generation via pendulum rotations when the source of vertical excitation is chaotic in nature. The investigations are conducted using an additional height-adjustable mechanism housing a secondary spring to optimize a configuration of experimental pendulum setup. Chaotic oscillations of the pendulum pivot are made possible at certain excitation conditions due to a piecewise-linear stiffness characteristic introduced by the modification. A velocity control method is applied to maintain the rotational motion of the pendulum as it interacts with the vertical oscillator. The control input is affected by a motor, and a generator is used to quantify the energy extraction. The experimental results imply the feasibility of employing a pendulum device in a chaotic vibratory environment for energy harvesting purpose.

Nonlinear Vibrations of Piecewise-Linear Systems by Incremental Harmonic Balance Method

1992 ◽  
Vol 59 (1) ◽  
pp. 153-160 ◽  
Author(s):  
S. L. Lau ◽  
W.-S. Zhang
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Vibrations ◽  
Piecewise Linear ◽  
Practical Interest ◽  
Harmonic Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
Stiffness Characteristics ◽  
Ihb Method ◽  
Piecewise Linear Stiffness

The incremental harmonic balance (IHB) method is extended to analyze the periodic vibrations of systems with a general form of piecewise-linear stiffness characteristics. An explicit formulation has been worked out. This development is of significance as many structural and mechanical systems of practical interest possess a piecewise-linear stiffness. Typical examples show that the IHB method is very effective for analyzing this kind of systems under steady-state vibrations.

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