scholarly journals The Role of Lagrangian Strain in the Dynamic Response of a Flexible Connecting Rod

1999 ◽  
Vol 123 (4) ◽  
pp. 542-548 ◽  
Author(s):  
Jen-San Chen ◽  
Kwin-Lin Chen
Keyword(s):  
Dynamic Response ◽  
Axial Load ◽  
Slenderness Ratio ◽  
Equations Of Motion ◽  
Transverse Displacement ◽  
Linear Strain ◽  
Connecting Rod ◽  
Lagrangian Strain ◽  
Order Of Magnitude

Previous researches on the dynamic response of a flexible connecting rod can be categorized by the ways the axial load in the rod is being formulated. The axial load may be assumed to be (1) dependent only on time and can be obtained by treating the rod as rigid, (2) related to the transverse displacement by integrating the axial equilibrium equation, and (3) proportional to linear strain. This paper examines the validity of these formulations by first deriving the equations of motion assuming the axial load to be proportional to the Lagrangian strain. In order for the dimensionless displacements to be in the order of O(1), different nondimensionalization schemes have to be adopted for low and high crank speeds. The slenderness ratio of the connecting rod arises naturally as a small parameter with which the order of magnitude of each term in the equations of motion, and the implication of these simplified formulations can be examined. It is found that the formulations in previous researches give satisfactory results only when the crank speed is low. On the other hand when the crank speed is comparable to the first bending natural frequency of the connecting rod, these simplified formulations overestimate considerably the dynamic response because terms of significant order of magnitude are removed inadequately.

scholarly journals On the Nonlinear Response of a Flexible Connecting Rod

2003 ◽  
Vol 125 (4) ◽  
pp. 757-763 ◽  
Author(s):  
Jen-San Chen ◽  
Chu-Hsian Chian
Keyword(s):  
Dynamic Response ◽  
Mechanical Design ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
Connecting Rod ◽  
Lagrangian Strain ◽  
Order Of Magnitude ◽  
Asme Journal ◽  
Parametric And External Excitations

In two recent papers (Chen, J.-S., and Chen, K.-L., 2001, “The Role of Lagrangian Strain in the Dynamic Response of a Flexible Connecting Rod,” ASME Journal of Mechanical Design, 123, pp. 542–548; Chen, J.-S., and Huang, C.-L., 2001, “Dynamic Analysis of Flexible Slider-Crank Mechanisms With Nonlinear Finite Element Method,” Journal of Sound and Vibration, 246, pp. 389–402) we reported that previous researches of others on the dynamic response of a flexible connecting rod may have overestimated the deflections by ten folds when the crank rotates near the bending natural frequency of the connecting rod because terms of significant order of magnitude were ignored inadequately. While the findings in (Chen, J.-S., and Chen, K.-L., 2001, “The Role of Lagrangian Strain in the Dynamic Response of a Flexible Connecting Rod,” ASME Journal of Mechanical Design, 123, pp. 542–548; Chen, J.-S., and Huang, C.-L., 2001, “Dynamic Analysis of Flexible Slider-Crank Mechanisms With Nonlinear Finite Element Method,” Journal of Sound and Vibration, 246, pp. 389–402.) were obtained via numerical simulations, the present paper emphasizes the analytical approach with an aim to exploring the physical insights behind these numerical results. The equations of motion are first derived by applying Hamilton’s principle with all high order terms in the strain energy function being retained. After careful examination of the order of magnitude of each term, the coupled equations are simplified to a single one in terms of the transverse deflection, which turns out to be a Duffing equation under parametric and external excitations simultaneously. Closed-form approximations of the dynamic response are then derived by using multiple scale method. It is found that the combined effects of parametric and external excitations dominate the response when Ω is close to 0.5 and 1. Away from these two speed ranges, on the other hand, the response is dominated by the external excitation alone.

Dynamics of a Multibody Mechanical System With Lubricated Long Journal Bearings

2004 ◽  
Vol 127 (3) ◽  
pp. 493-498 ◽  
Author(s):  
B. J. Alshaer ◽  
H. Nagarajan ◽  
H. K. Beheshti ◽  
H. M. Lankarani ◽  
S. Shivaswamy
Keyword(s):  
Dynamic Response ◽  
Mechanical System ◽  
Journal Bearing ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Journal Bearings ◽  
Connecting Rod ◽  
Revolute Joint ◽  
Order Of Magnitude

Clearances exist in different kinds of joints in multibody mechanical systems, which could drastically affect the dynamic behavior of the system. If the joint is dry with no lubricant, impact occurs, resulting in wear and tear of the joint. In practical engineering design of machines, joints are usually designed to operate with some lubricant. Lubricated journal bearings are designed so that even when the maximum load is applied, the joint surfaces do not come into contact with each other. In this paper, a general methodology for modeling lubricated long journal bearings in multibody mechanical systems is presented. This modeling utilizes a method of solving for the forces produced by the lubricant in a dynamically loaded long journal bearing. A perfect revolute joint in a multibody mechanical system imposes kinematic constraints, while a lubricated journal bearing joint imposes force constraints. As an application, the dynamic response of a slider-crank mechanism including a lubricated journal bearing joint between the connecting rod and the slider is considered and analyzed. The dynamic response is obtained by numerically solving the constraint equations and the forces produced by the lubricant simultaneously with the differential equations of motion and a set of initial conditions numerically. The results are compared with the previous studies performed on the same mechanism as well a dry clearance joint. It is shown that in a multibody mechanical system, the journal bearing lubricant introduces damping and stiffness to the system. The earlier studies predict that the order of magnitude of the reaction moment is twice that of a perfect revolute joint. The proposed model predicts that the reaction moment is within the same order of magnitude of the perfect joint simulation case.

Dynamics of a Multibody Mechanical System With Lubricated Long Journal Bearings

2001 ◽  
Author(s):  
B. J. Alshaer ◽  
H. M. Lankarani ◽  
S. Shivaswamy
Keyword(s):  
Dynamic Response ◽  
Mechanical System ◽  
Journal Bearing ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Journal Bearings ◽  
Connecting Rod ◽  
Revolute Joint ◽  
Order Of Magnitude

Abstract Clearances exist in different kinds of joints in multibody mechanical systems, which could drastically affect the dynamic behavior of the system. If the joint is dry with no lubricant, impact occurs, resulting in wear and tear of the joint. In practical engineering design of machines, joints are usually designed to operate with some lubricant. Lubricated journal bearings are designed so that even when the maximum load is applied, the joint surfaces do not come into contact with each other. In this paper, a general methodology for modeling lubricated long journal bearings in multibody mechanical systems is presented. This modeling utilizes a new method of solving for the forces produced by the lubricant in a dynamically loaded long journal bearing. A perfect revolute joint in a multibody mechanical system imposes kinematic constraints, while a lubricated journal bearing joint imposes force constraints. As an application, the dynamic response of a crank-slider mechanism including a lubricated journal bearing joint between the connecting rod and the slider is considered and analyzed. The dynamic response is obtained by numerically solving the constraint equations and the forces produced by the lubricant simultaneously with the differential equations of motion and a set of initial conditions numerically. The results are compared with the previous studies performed on the same mechanism as well a dry clearance joint. It is shown that in a multibody mechanical system, the journal bearing lubricant introduces damping and stiffness to the system. The earlier studies previous predict that the order of magnitude of the reaction moment is twice that of a perfect revolute joint. The proposed model predicts that the reaction moment is within the same order of magnitude of the perfect joint simulation case.

THE ROLE OF SUSPENSION STRUCTURE IN THE DYNAMIC RESPONSE OF ELECTRORHEOLOGICAL SUSPENSIONS

1994 ◽  
Vol 08 (20n21) ◽  
pp. 2789-2809 ◽  
Author(s):  
M. PARTHASARATHY ◽  
K. H. AHN ◽  
B. M. BELONGIA ◽  
D. J. KLINGENBERG
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Superposition Principle ◽  
Experimental Investigations ◽  
Linear Deformation ◽  
Rheological Response ◽  
Oscillatory Response ◽  
Electrorheological Suspensions ◽  
Suspension Structure

The dynamic response of electrorheological (ER) suspensions has received little attention relative to the effort devoted to the study of the steady shear response. We report on simulation and experimental investigations of the dynamic oscillatory response of ER suspensions, in particular focusing on the relationship between suspension structure and the rheological response. We consider the response of monodisperse and polydisperse suspensions under linear deformation, as well as the response in the nonlinear regime. Dimensional analysis of the equations of motion predict that the linear rheological response obeys a time-field strength superposition principle, which is confirmed by experiment. The response is found to exhibit a sharp dispersion that is only broadened slightly by polydispersity. Nonlinear deformation is found to significantly broaden the observed dispersion.

scholarly journals Effects of Crank Length on the Dynamics Behavior of a Flexible Connecting Rod

2000 ◽  
Vol 123 (3) ◽  
pp. 318-323 ◽  
Author(s):  
Jen-San Chen ◽  
Chu-Hsian Chian
Keyword(s):  
Rotation Speed ◽  
Equations Of Motion ◽  
Mapping Technique ◽  
Global Dynamics ◽  
Connecting Rod ◽  
Lagrangian Strain ◽  
Strain Formulation ◽  
Dynamics Response ◽  
Nonlinear Equations Of Motion ◽  
Crank Length

Global dynamics behavior of a damped flexible connecting rod is considered in this paper with emphasis on the effects of the rigid crank length. Nonlinear equations of motion in terms of axial and transverse deflections are derived based on Lagrangian strain formulation. When the crank length is small compared to the connecting rod, it is found that only one periodic solution exists in the speed range up to 1.5 times the first bending natural frequency of the connecting rod. As the crank length increases, however, multiple solutions may exist and the associated domains of attraction can be identified by cell-to-cell mapping technique. Moreover, the steady state response may become chaotic, which renders precise prediction of the dynamics response meaningless. The onset rotation speed of chaotic vibration decreases when the crank length increases. This result shows that previous research utilizing simplified or linearized models can predict the dynamics response of the flexible connecting rod only when both the crank length and the rotation speed are small.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Dynamics Simulation and Analysis of Transition Stage of Tilt-Rotor Aircraft

2016 ◽  
Vol 842 ◽  
pp. 251-258 ◽  
Author(s):  
Muhammad Rafi Hadytama ◽  
Rianto A. Sasongko
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Flight Dynamics ◽  
Dynamics Simulation ◽  
Tilt Rotor ◽  
Vertical Takeoff And Landing ◽  
Improved Stability ◽  
Simulation Results ◽  
Vtol Aircraft ◽  
Vertical Takeoff

This paper presents the flight dynamics simulation and analysis of a tilt-rotor vertical takeoff and landing (VTOL) aircraft on transition phase, that is conversion from vertical or hover to horizontal or level flight and vice versa. The model of the aircraft is derived from simplified equations of motion comprising the forces and moments working on the aircraft in the airplane's longitudinal plane of motion. This study focuses on the problem of the airplane's dynamic response during conversion phase, which gives an understanding about the flight characteristics of the vehicle. The understanding about the flight dynamics characteristics is important for the control system design phase. Some simulation results are given to provide better visualization about the behaviour of the tilt-rotor. The simulation results show that both transition phases are quite stable, although an improved stability can give better manoeuver and attitude handling. Improvement on the simulation model is also required to provide more accurate and realistic dynamic response of the vehicle.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

scholarly journals Dynamic Response of Single Pile Subjected to Different Frequencies in Gypseous Soil

2020 ◽  
Vol 13 (4) ◽  
pp. 50-57
Author(s):  
Noor D. Abd ◽  
Safa H. AbidAwn
Keyword(s):  
Experimental Study ◽  
Dynamic Response ◽  
Slenderness Ratio ◽  
Vibration Source ◽  
Single Pile ◽  
Collapsible Soil ◽  
Dynamic Movement ◽  
Steel Container ◽  
Gypsum Content ◽  
Gypseous Soil

This paper exhibits an experimental study on dynamic response of a single pile under dynamic load which comes from motor placed on cap pile called a vibration source. This study used the effect of the dynamic movement of vibration on one pile, collapsible soil (gypseous soil) used in this study with 30% gypsum content. The experiment is performed in a dry and soak state. A solid steel pile with a slenderness ratio of 27 was inserted into the soil after preparing it in layers in a steel container (30 * 30 * 60) cm. The test was performed under a dynamic response to the different frequencies 10, 15, 20, and 25 Hz. The results showed that the speed, acceleration and displacement increase with increasing frequency of the vibration source in addition to that the values of speed, acceleration and displacement amplitude are less in the case of soaking compared to their values in the dry state.

scholarly journals Quantitative Support for Borowski’s Theory of Gravitation

2013 ◽  
Vol 17 ◽  
pp. 67-71 ◽  
Author(s):  
Michael A. Persinger
Keyword(s):  
Dark Matter ◽  
Gravitational Constant ◽  
Planetary Motion ◽  
Free Oscillations ◽  
Energy Equivalence ◽  
Order Of Magnitude ◽  
Theory Of Gravitation

The Borowski Theory of Gravitation (BTG) indicates that movements of mass such as planets through space are determined by differential pressures from dark matter. One of the consequences of the final epoch is that there would be no matter but only distance. Quantitative solutions indicate that the tensor to set universal average dark matter pressure equal to G, the gravitational constant, would require that the terminal length would be ~2.2∙1069 m or effectively identical to current estimates of energy equivalence of the universal mass. For the earth’s orbit the force from the dark pressure is the same order of magnitude as the force associated with the product of the planet’s mass and background free oscillations whose origins are still ambiguous. The convergences of solutions suggest that the BTG may reveal alternative interpretations and mechanisms for the role of gravitation in planetary motion.

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