Linear and nonlinear stiffness and friction in biological rhythmic movements

1995 ◽  
Vol 73 (6) ◽  
pp. 499-507 ◽  
Author(s):  
P. J. Beek ◽  
R. C. Schmidt ◽  
A. W. Morris ◽  
M. -Y. Sim ◽  
M. T. Turvey
Keyword(s):  
Nonlinear Stiffness ◽  
Rhythmic Movements ◽  
Linear And Nonlinear

Linear and nonlinear stiffness and friction in biological rhythmic movements

1995 ◽  
Vol 73 (6) ◽  
pp. 499-507 ◽  
Author(s):  
P. J. Beek ◽  
R. C. Schmidt ◽  
A. W. Morris ◽  
M.-Y. Sim ◽  
M. T. Turvey
Keyword(s):  
Nonlinear Stiffness ◽  
Rhythmic Movements ◽  
Linear And Nonlinear

Optimization of Axial Vibration Attenuation of Periodic Structure With Nonlinear Stiffness Without Addition of Mass

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Diego P. Vasconcellos ◽  
Marcos Silveira
Keyword(s):  
Periodic Structure ◽  
Total Mass ◽  
Periodic Structures ◽  
Original Structure ◽  
Dynamical Response ◽  
Nonlinear Stiffness ◽  
Optimal Position ◽  
Simplified Approach ◽  
Vibration Attenuation ◽  
Linear And Nonlinear

Abstract We explore the vibration attenuation of a periodic structure when one absorber with nonlinear cubic stiffness is included without increasing the total mass. Metastructures, and specifically periodic structures, present interesting characteristics for vibration attenuation that are not found in classical structures. These characteristics have been explored for automotive and aerospace applications, among others, as structures with low mass are paramount for these industries, and keeping low vibration levels in wide frequency range is also desirable. It has been shown that the addition of vibration absorbers in a periodic arrangement can provide vibration attenuation for shock input without increasing the total mass of a structure. In this work, the dynamical response of a metastructure with one nonlinear vibration absorber, with same mass as original structure, optimized for vibration attenuation under harmonic input is compared with a base metastructure without absorbers and a metastructure with linear absorbers via the evaluation of the H2 norm of the frequency response. A simplified approach is used to compare linear and nonlinear stiffness based on deformation energy, by considering linear and nonlinear restoring forces to be equal at mean deformation. The dynamical response of the optimal system is obtained numerically, and an optimization procedure based on sequential quadratic programming (SQP) is proposed to find the optimal position and stiffness coefficients of only one nonlinear absorber, showing that it results in lower level of vibrations than original structure and than structure with linear absorbers, while almost the same level as a structure with all nonlinear absorbers.

Effect of Negative Stiffness Content on the Periodic Motion of Nonlinearly Coupled Oscillators

2021 ◽  
Vol 16 (11) ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Coupled Oscillators ◽  
Dynamical Behavior ◽  
Negative Stiffness ◽  
Nonlinear Frequency ◽  
Nonlinear Stiffness ◽  
Nonlinear Coupling ◽  
Nonlinear Dynamical ◽  
Wide Range ◽  
Coupling Force ◽  
Linear And Nonlinear

Abstract The linear and nonlinear stiffness coupling forces in dynamical oscillators are usually dominated by positive stiffness components. Therefore, plotting the resultant force in y-axis with respect to the change in displacement in x-axis results in an odd symmetry in the first and third quadrants of the xy-plane. However, the appearance of negative stiffness content in coupling elements between dynamical oscillators generates a force that can be dominated by an odd symmetry in the second and fourth quadrants. The underlying nonlinear dynamical behavior of systems employing this kind of force has not been well-studied in the literature. Accordingly, the considered system here is composed of two linear oscillators that are nonlinearly coupled by a force of which the negative stiffness content is dominant. Therefore, the underlying dynamical behavior of the considered system in physical and dimensionless forms is studied on the frequency-energy plots where many backbone curves of periodic solution have been obtained. It is found that within a wide range of nonlinear frequency levels, the nonlinear coupling force is dominated by a strong negative stiffness content at the obtained frequency-energy plots backbones.

scholarly journals A novel stiffness model for a wall-climbing hexapod robot based on nonlinear variable stiffness

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401775248 ◽  
Author(s):  
Bin He ◽  
Shoulin Xu ◽  
Zhipeng Wang
Keyword(s):  
Structural Parameters ◽  
Variable Stiffness ◽  
Load Force ◽  
Nonlinear Stiffness ◽  
Hexapod Robot ◽  
Maximum Stiffness ◽  
Stiffness Model ◽  
Linear And Nonlinear ◽  
Serial Mechanism ◽  
Selection Of

In this article, the most contribution is to propose a novel general stiffness model to analyze the stiffness of a wall-climbing hexapod robot. First, we propose a new general stiffness model of serial mechanism, which includes the linear and nonlinear stiffness models. By comparison, the nonlinear stiffness model is a variable stiffness model which introduces the external load force as a variable, obtaining that the nonlinear stiffness model can greatly improve the accuracy of stiffness model than linear stiffness model. Then, the stiffness model of one leg of the robot and the overall stiffness model of the robot are derived based on the general stiffness model. Next, to improve the stiffness of the robot, a new minimum and maximum stiffness are introduced, which provide with effective reference for the selection and optimization of the structural parameters of the robot. Finally, we develop a new wall-climbing hexapod robot based on selection and optimization of the structural parameters, then the experiments are used to show that the selection of structure parameters of the robot effectively improve the stiffness of the robot.

Modeling and Simulation for the Feed System of CNC Machine

2014 ◽  
Vol 496-500 ◽  
pp. 1024-1027
Author(s):  
Qin Wu ◽  
Jian Jun Yang ◽  
Chun Li Lei
Keyword(s):  
Driving Force ◽  
Simulation Analysis ◽  
Multiple Solution ◽  
Ball Screw ◽  
Nonlinear Stiffness ◽  
Cnc Machine ◽  
Feed System ◽  
Damping Force ◽  
System Use ◽  
Linear And Nonlinear

Study the linear and nonlinear stiffness dynamic characteristics of ball screw in feed system. According to the structure and the stiffness of ball screw, considering the influence of damping force, elastic force, friction force, driving force and load, establish the dynamic model of feed system. Use Linz Ted- Poincare (L-P) Method of singular perturbation to solve the model, obtain the quadratic approximate solution of the free vibration, analyze the multiple solution phenomenon of the model, and also conduct the numerical simulation analysis for the model.

The Effect of Material Nonlinearity on the Dynamics of Hull/Mooring Coupled System

2013 ◽  
Author(s):  
Jiayu Qian ◽  
Liping Sun ◽  
Linfeng Song
Keyword(s):  
Viscoelastic Properties ◽  
Steel Wire ◽  
Coupled System ◽  
Nonlinear Stiffness ◽  
Time Domain Simulation ◽  
Mooring Lines ◽  
Linear And Nonlinear ◽  
The Difference ◽  
The Time Domain ◽  
Nonlinear Elastic

The dynamics of a turret-moored FPSO with 12 catenary chain-steel wire-chain mooring lines are studied to investigate the influence of the hull/mooring coupled system from both linear and nonlinear stiffness of steel wire. The two simulated results are compared with experimental statistics, it indicated that the results using nonlinear stiffness are slightly larger than using linear stiffness and closer when compared with the experimental statistics. Then it illustrates that the polynomial approximation of nonlinearity for steel wire is applicable. The difference between linear and nonlinear results of steel wire is not apparent due to steel wire doesn’t belong to the viscoelastic material. This paper also researches the motion of FPSO with taut chain-polyester-chain mooring lines because polyester rope has viscoelastic properties. The results are unstable when using lower and upper linear stiffness in the time-domain simulation. But the dynamic response of FPSO is good by nonlinear stiffness. Thus, the nonlinear elastic method should be used in engineering works to decrease the damaged risk of the structure.

Analytic Study of Linear and Nonlinear Mode Localization

1993 ◽  
Vol 60 (2) ◽  
pp. 555-557 ◽  
Author(s):  
A. F. Vakakis
Keyword(s):  
Nonlinear Systems ◽  
Analytical Method ◽  
Normal Modes ◽  
Nonlinear Stiffness ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems ◽  
Exact Analytical Method ◽  
Vibrating Systems

The localization of the normal modes of weakly coupled vibrating systems is examined with a new exact, analytical method. Both linear and nonlinear systems are considered and the mode localization is examined by means of “balancing diagrams.” This study complements previous studies of the author and co-workers on investigating mode localization in systems with nonlinear stiffness elements.

Dynamical Behaviors of a Coupled Cushioning Packaging Model with Linear and Nonlinear Stiffness

2013 ◽  
Vol 38 (6) ◽  
pp. 1625-1629 ◽  
Author(s):  
Jun Wang ◽  
Yasir Khan ◽  
Rui-Hua Yang ◽  
Li-Xin Lu ◽  
Zhi-wei Wang
Keyword(s):  
Nonlinear Stiffness ◽  
Dynamical Behaviors ◽  
Linear And Nonlinear
Sign in / Sign up

Export Citation Format

Share Document