The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

Hsieh, Shang-Rou; Shaw, Steven W.

doi:10.1007/bf00162233

Cited by 13 publications

(6 citation statements)

References 23 publications

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“…Analytically derived response was compared to experimental response using the non-dimensionalized, single mode equations provided by Viscomi and Ayres [19]. Equation (1) describes rod bending vibration of a rigid and constant speed crank, driving an Euler-Bernoulli beam representation of the connecting rod, It does not include the effects of joint friction, rod end masses, base vibration, motor speed fluctuations, and contributions of higher modes• However equation (1) is simple, integrates rapidly, and it and its variants have found application in nonlinear dynamics studies [16][17][18]. That equation is: -7r9 tan 95 -~ -2-/-g cos(0 + 95) + 7r95,gg + ~ c~,g 2 …”

Section: Resultsmentioning

confidence: 99%

“…Lee and Beale [16] presented response case studies that included period doubling and jump bifurcations for small, intermediate, and large crank lengths, with and without the piston mass, and with and without a gas force acting on the piston. Hsieh and Shaw [17,18], investigated the nonlinear dynamic response for continuous ranges of parameter combinations by computer simulation, and analytical studies using the method of multiple scales.…”

Section: Introductionmentioning

confidence: 99%

“…Another objective was to catalog instability phenomena and response amplitudes over a wide range of crank speeds and crank lengths. It is envisioned that this work will complement recent analytical research efforts to quantify the effects of mechanism parameters on nonlinear elastodynamic response and stability [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Experimental observations of a flexible slider crank mechanism at very high speeds

Halbig

Beale

1995

Nonlinear Dyn

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A slider crank mechanism has been constructed and operated for the purpose of investigating steady state rod bending vibration induced by a very high speed crank. Features include a combination flywheel and adjustable length crank, a thin aluminum connecting rod, and a piston sliding on steel rod slide axes. A strain gage on the rod and magnetic pickup on the crank sensed rod strain and crank speed, respectively. For this system configuration, experimental results are categorized as small, intermediate and large crank length response. Small and intermediate cranks response was amplified due to a large superharmonic component of twice the crank speed frequency and at crank speeds near 1/2 the first natural frequency of the rod. Beyond that speed, period doubling occurred over a range of speeds for intermediate length cranks. The occurrence of period doubling was experimentally sudden and audibly noticeable, and characterized by the onset of frequency components of 1/2, 3/2, 5/2, and 7/2 times the crank speed. For large crank sizes of 0.5, 1, and 2 inches an amplified response also appeared in each at a certain speed, but at speeds lower than in the small and intermediate crank cases. Larger cranks required more frequency components to describe the response than smaller cranks. Experimental responses were correlated with computer simulations of a one mode nonlinear ordinary differential equation model, and over a wide range of speeds and for a representative of a small, intermediate, and large crank length.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Experimental observations of a flexible slider crank mechanism at very high speeds

Halbig

Beale

1995

Nonlinear Dyn

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“…Hsieh and Shaw [24] analyzed the dynamic stability of a crank-shaft-slider mechanism where the shaft is considered flexible and the crank is rigid and rotates with constant speed. The results focused on the nonlinear effects which arise from the finite deformations in the rod.…”

Section: Introductionmentioning

confidence: 99%

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

et al. 2015

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The nonlinear dynamics behavior analyzed, in this paper, consists in a pendulum vertically excited on the support by a crankshaft -slider mechanism. The novelty is the obtainment and analysis of a mathematical model for the pendulum dynamics, under an excitation of a crank-slider, which is based on an extension of the mathematical model of the classical parametric pendulums. Through the modeling, it was verified that the nonlinear dynamics of the pendulum, excited by the crankshaft -slider mechanism approaches to that of harmonic excitation, when one considered the length of the shaft is sufficient larger than the radius of the crank. The nonlinear dynamic analyses focused on observation of different kinds of motion for different values of dimensionless parameters of the adopted mathematical model. These parameters, includes the frequency of excitation, the amplitude and the geometry of the crankshaft -slider mechanism. The adopted method of analyses used tools, such as, Lyapunov exponents, parameter space plots, basins of attractions, bifurcation diagrams, phase portraits, time histories and Poincaré sections. The kinds of motion include results on fixed point, oscillations, rotations, oscillations-rotations and chaotic motions.

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“…Fung [5] studied the response of the connecting rod ends as a function of time; a thorough model for a exible slider-crank mechanism, which included shear and bending effects, was developed. Hsieh and Shaw [6] studied the stability and non-linear resonance of a slidercrank mechanism with a exible connecting rod. They assumed that the connecting rod was simply supported and made of viscoelastic material; the effects of the crank-connecting rod length and mass ratios on each resonance were studied.…”

mentioning

confidence: 99%

Active damping of the elastodynamic vibrations of a flexible slider-crank mechanism using an energy approach

Karkoub

Zribi

2001

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this paper, the problem of active damping of the elastodynamic vibrations of a exible slider-crank mechanism is addressed. The slider-crank mechanism is such that the connecting rod is exible and the crank link is rigid. The slider-crank mechanism system is underactuated since the connecting rod is not directly controlled. A dynamic model for the slider-crank mechanism is derived using the Hamiltonian principle. Then, a control scheme based on an energy approach is proposed. The control scheme uses the passivity of the system to eliminate the vibrations of the exible connecting rod. Simulation results are given to illustrate the theoretical developments.

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The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

Cited by 13 publications

References 23 publications

Experimental observations of a flexible slider crank mechanism at very high speeds

Experimental observations of a flexible slider crank mechanism at very high speeds

Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism

Active damping of the elastodynamic vibrations of a flexible slider-crank mechanism using an energy approach

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