Dynamic models for the contact analysis of a tensioned beam with a moving oscillator

2013 ◽  
Vol 228 (4) ◽  
pp. 676-689
Author(s):  
Kyuho Lee ◽  
Jintai Chung
Keyword(s):  
Natural Frequency ◽  
Nonlinear Model ◽  
Frequency Ratio ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Contact Analysis ◽  
Contact Forces ◽  
Accurate Analysis ◽  
Moving Oscillator ◽  
Velocity Decrease

Several dynamic models are proposed for the contact analysis of a tensioned beam with a moving oscillator. Depending on whether the strain and stress used to derive the equations of motion are nonlinear, four models are established to analyze the beam deflections and the contact force between the beam and moving oscillator. We find that the differences in the contact forces and deflections computed with the models become large as the beam tension and moving velocity decrease and the natural frequency ratio of the oscillator to the beam increases. The nonlinear model derived with nonlinear strain and stress is desirable for an accurate analysis.

scholarly journals The Study on Nonlinear Model of Pantograph-catenary Coupling system for Straddle-type Monorail

Mechanika ◽  
2020 ◽  
Vol 26 (3) ◽  
pp. 212-220
Author(s):  
Zixue DU ◽  
Zhen YANG ◽  
Zhouzhou XU ◽  
Junchao ZHOU* ◽  
Zhongwei HOU
Keyword(s):  
Dynamic Model ◽  
Nonlinear Model ◽  
Dynamic Models ◽  
Lagrange Equation ◽  
Contact Forces ◽  
Lateral Coupling ◽  
Coupling Dynamic ◽  
Nonlinear Dynamic Models ◽  
Lateral Excitation ◽  
Coupling Dynamic Model

Based on the Lagrange equation, the linear and nonlinear dynamic models of straddle monorail pantograph considering the lateral vibration of bogie are derived. On this basis, the lateral coupling dynamic model of pantograph-catenary is established. Newmark method is used to solve the pantograph-catenary coupling dynamic model. In order to evaluate the applicability of the two models，this paper analyzed the contact force response of two model with different speeds. The reasearch show that when the speed is below 40 km/h, the contact forces of nonlinear model and linear model can reflects the lateral excitation of the finger plate. When the speed exceeds 40 km/h, only the nonlinear model can reflect the lateral excitation of finger palte, the nonlinear pantograph-catenary coupling dynamics model is more suitable to the straddle-type monorail pantograph-catenary coupling research.

scholarly journals Vibration analysis of a sandwich cylindrical shell in hygrothermal environment

2021 ◽  
Vol 10 (1) ◽  
pp. 414-430
Author(s):  
Chunwei Zhang ◽  
Qiao Jin ◽  
Yansheng Song ◽  
Jingli Wang ◽  
Li Sun ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Single Layer ◽  
Functionally Graded ◽  
Sandwich Shell ◽  
Continuous Change ◽  
Multilayered Structures ◽  
Cylindrical Sandwich Shell ◽  
Vibrational Behavior

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

The elastic contact influences on passive walking gaits

Robotica ◽  
2010 ◽  
Vol 29 (5) ◽  
pp. 787-796 ◽  
Author(s):  
Feng Qi ◽  
Tianshu Wang ◽  
Junfeng Li
Keyword(s):  
Coulomb Friction ◽  
Dynamic Models ◽  
Contact Stiffness ◽  
Contact Forces ◽  
Hertz Contact ◽  
Walking Gait ◽  
Routes To Chaos ◽  
Coulomb Friction Law ◽  
Contact Parameters ◽  
Passive Model

SUMMARYThis paper presents a new planar passive dynamic model with contact between the feet and the ground. The Hertz contact law and the approximate Coulomb friction law were introduced into this human-like model. In contrast to McGeer's passive dynamic models, contact stiffness, contact damping, and coefficients of friction were added to characterize the walking model. Through numerical simulation, stable period-one gait and period-two gait cycles were found, and the contact forces were derived from the results. After investigating the effects of the contact parameters on walking gaits, we found that changes in contact stiffness led to changes in the global characteristics of the walking gait, but not in contact damping. The coefficients of friction related to whether the model could walk or not. For the simulation of the routes to chaos, we found that a small contact stiffness value will lead to a delayed point of bifurcation, meaning that a less rigid surface is easier for a passive model to walk on. The effects of contact damping and friction coefficients on routes to chaos were quite small.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

An Experimental and Theoretical Investigation of Nonlinear Vibrations of Piezoelectrically-Driven Microcantilevers

2006 ◽  
Author(s):  
S. Nima Mahmoodi ◽  
Nader Jalili
Keyword(s):  
Natural Frequency ◽  
Piezoelectric Layer ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Closed Form Solution ◽  
Cubic Form ◽  
Dynamic Representation ◽  
Microcantilever Beam

The nonlinear vibrations of a piezoelectrically-driven microcantilever beam are experimentally and theoretically investigated. A part of the microcantilever beam surface is covered by a piezoelectric layer, which acts as an actuator. Practically, the first resonance of the beam is of interest, and hence, the microcantilever beam is modeled to obtain the natural frequency theoretically. The bending vibrations of the beam are studied considering the inextensibility condition and the coupling between electrical and mechanical properties in piezoelectric materials. The nonlinear term appears in the form of quadratic due to presence of piezoelectric layer, and cubic form due to geometry of the beam (mainly due to the beam's inextensibility). Galerkin approximation is utilized to discretize the equations of motion. The obtained equation is simulated to find the natural frequency of the system. In addition, method of multiple scales is applied to the equations of motion to arrive at the closed-form solution for natural frequency of the system. The experimental results verify the theoretical findings very closely. It is, therefore, concluded that the nonlinear approach could provide better dynamic representation of the microcantilever than previous linear models.

A Study on Sensitivity of Maneuverability Performance on the Hydrodynamic Coefficients for Submerged Bodies

2000 ◽  
Vol 44 (03) ◽  
pp. 186-196
Author(s):  
Debabrata Sen
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Inertial Force ◽  
Axisymmetric Body ◽  
Hydrodynamic Coefficients ◽  
Damping Coefficients ◽  
Simulated Trajectory ◽  
Linear Damping

Based on a constant-coefficient dynamic model, a study was made to determine the influence of various hydrodynamic coefficients on the predicted maneuverability quality of submerged bodies. Two types of geometries were considered, a submarine and an axisymmetric slender geometry. For the submarine, the equations of motion used were the revised standard submarine equations (Feldman 1979) while for the latter geometry a dynamic model was developed. From computer simulation of a few selected definitive maneuvers based on these two different dynamic models for the two geometries, the sensitivity of the simulated trajectory on changes in different coefficients was found. The results quantified in form of sensitivity values are presented. It is found that the typical measures from the maneuvers do not depend significantly on most of the nonlinear coefficients. The coefficients having significant effects on the trajectories are found to be the linear damping coefficients for the submarine and the linear inertial force coefficients for the axisymmetric body.

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

Sign in / Sign up

Export Citation Format

Share Document