Nonlinear stiffness characteristics of the annular ligament

2014 ◽  
Vol 136 (4) ◽  
pp. 1756-1767 ◽  
Author(s):  
M. Lauxmann ◽  
A. Eiber ◽  
F. Haag ◽  
S. Ihrle
Keyword(s):  
Annular Ligament ◽  
Nonlinear Stiffness ◽  
Stiffness Characteristics

Nonlinear Response of a Dynamic System due to Oscillatory Flow

1987 ◽  
Vol 109 (4) ◽  
pp. 345-356 ◽  
Author(s):  
Y. M. Huang ◽  
C. M. Krousgrill ◽  
A. K. Bajaj
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Response ◽  
Oscillatory Flow ◽  
Nonlinear Stiffness ◽  
Method Of Averaging ◽  
Secondary Resonances ◽  
Incremental Harmonic Balance ◽  
Nonzero Mean ◽  
Stiffness Characteristics ◽  
Solution Formulation

The dynamic response of a structure exhibiting nonlinear stiffness characteristics and excited by a nonzero mean oscillatory fluid flow is investigated. Both the method of averaging and a multi-frequency incremental harmonic balance approach are used in understanding the primary and secondary resonances in the response. Several parameter studies are presented where the results of these two methods are compared with those obtained by numerical integration and are discussed in detail. The results point to the need for a multi-frequency solution formulation for accurate representation of the response offset and to the difficulties of using the standard method of averaging formulation for investigation of secondary resonances in the response of this system.

scholarly journals Predicting Nonlinear Stiffness, Motion Range, and Load-Bearing Capability of Leaf-Type Isosceles-Trapezoidal Flexural Pivot Using Comprehensive Elliptic Integral Solution

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Aimei Zhang ◽  
Yanjie Gou ◽  
Xihui Yang
Keyword(s):  
Elliptic Integral ◽  
Integral Solution ◽  
Leaf Spring ◽  
Nonlinear Stiffness ◽  
Load Bearing ◽  
Large Rotation ◽  
Leaf Type ◽  
Proposed Model ◽  
Motion Range ◽  
Stiffness Characteristics

A leaf-type isosceles-trapezoidal flexural (LITF) pivot consists of two leaf springs that are situated in the same plane and intersect at a virtual center of motion outside the pivot. The LITF pivot offers many advantages, including large rotation range and monolithic structure. Each leaf spring of a LITF pivot subject to end loads is deflected into an S-shaped configuration carrying one or two inflection points, which is quite difficult to model. The kinetostatic characteristics of the LITF pivot are precisely modeled using the comprehensive elliptic integral solution for the large-deflection problem derived in our previous work, and the strength-checking method is further presented. Two cases are employed to verify the accuracy of the model. The deflected shapes and nonlinear stiffness characteristics within the range of the yield strength are discussed. The load-bearing capability and motion range of the pivot are proposed. The nonlinear finite element results validate the effectiveness and accuracy of the proposed model for LITF pivots.

A Spatial Parametric Model for the Nonlinear Stiffness Characteristics of Flexure Strips

2018 ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Dannis M. Brouwer
Keyword(s):  
Closed Form ◽  
Nonlinear Effects ◽  
Geometrically Nonlinear ◽  
Nonlinear Stiffness ◽  
Mechanism Analysis ◽  
Compliance Matrix ◽  
Closed Form Solutions ◽  
Flexure Mechanism ◽  
Stiffness Characteristics ◽  
Torsion Deformation

The flexure strip is commonly used to provide support stiffness in flexure mechanisms for precision applications. While the flexure strip is often treated in a simplified form, e.g. by assuming planar deformation or linearized stiffness, the deformation in practice is spatial and sufficiently large that nonlinear effects due to the geometrical stiffness are significant. This paper presents an understandable analytical model for the nonlinear stiffness characteristics of flexure strips that deform spatially due to a general 3-D loading condition. This model provides closed-form expressions in a mixed stiffness and compliance matrix format that is tailored to flexure mechanism analysis. The effects of bending, elongation, and torsion deformation are taken into account. The geometrically nonlinear effects of the model are verified numerically. The approach for deriving closed-form solutions in a nonlinear context is detailed in this paper. Based on the Hellinger–Reissner variational principle, it can also be extended to the analysis of multi-flexure strip mechanisms. This is demonstrated with the case of a spatially deforming parallelogram flexure mechanism.

An Analogue Simulation of the Nonlinear Vibration of a Plate with a Central Opening Subjected to Tension Loading

1981 ◽  
Vol 23 (2) ◽  
pp. 103-106 ◽  
Author(s):  
P. K. Datta
Keyword(s):  
Random Excitation ◽  
Analogue Computer ◽  
Nonlinear Stiffness ◽  
Single Degree Of Freedom ◽  
Response Characteristics ◽  
Single Degree ◽  
Central Opening ◽  
Frequency Response Characteristics ◽  
Stiffness Characteristics ◽  
Tension Loading

The complicated, nonlinear stiffness characteristics of a tensioned plate with a central opening are studied via analogue computer simulation. Associated frequency response characteristics and statistical properties of the response to random excitation are examined using a single degree of freedom model.

Influence of Nonlinear Stiffness on the Dynamics of a Slender Elastic Beam under Torsional Oscillations

2014 ◽  
Vol 706 ◽  
pp. 159-169
Author(s):  
Marcos Silveira ◽  
Bento R. Pontes ◽  
José M. Balthazar
Keyword(s):  
Numerical Algorithms ◽  
Elastic Beam ◽  
Basins Of Attraction ◽  
Torsional Stiffness ◽  
Nonlinear Stiffness ◽  
Torsional Oscillations ◽  
Before And After ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Helical Buckling

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams

scholarly journals A Method to Identify the Nonlinear Stiffness Characteristics of an Elastic Continuum Mechanism

2018 ◽  
Vol 3 (3) ◽  
pp. 1450-1457 ◽  
Author(s):  
Bastian Deutschmann ◽  
Tong Liu ◽  
Alexander Dietrich ◽  
Christian Ott ◽  
Dongheui Lee
Keyword(s):  
Nonlinear Stiffness ◽  
Elastic Continuum ◽  
Stiffness Characteristics

Design and Optimization of an Origami-Inspired Jumping Mechanism With Nonlinear Stiffness Properties

2019 ◽  
Author(s):  
Sahand Sadeghi ◽  
Blake D. Betsill ◽  
Suyi Li
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Displacement Curve ◽  
Nonlinear Stiffness ◽  
Design And Optimization ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
New Generation ◽  
Force Displacement

Abstract This research investigates the feasibility of utilizing origami folding techniques to create an optimized jumping mechanism. As a theoretical example, we study the dynamic characteristics of a jumping mechanism consisting of two masses connected by a Tachi-Miura Polyhedron (TMP) origami structure with nonlinear stiffness characteristics. We show how the desired “strain-softening” effects of the TMP structure can lead to design of jumping mechanisms with optimized performance. The kinematics of TMP origami structure is reviewed and a modified model of its reaction-force displacement curve is presented. We derive the equations of motion of the jumping process and use their numerical solutions extensively for design optimization. Through this process we are able to obtain optimum geometrical configurations for two different objectives: The maximum time spent in the air and the maximum clearance off the ground. Results of this study can lead to emergence of a new generation of more efficient jumping mechanisms with optimized performance in the future.

scholarly journals Reconfigurable Trusses of Nonlinear Morphing Elements

2018 ◽  
Author(s):  
Chrysoula Aza ◽  
Alberto Pirrera ◽  
Mark Schenk
Keyword(s):  
Double Helix ◽  
Nonlinear Stiffness ◽  
Helical Pitch ◽  
Reconfigurable Mechanisms ◽  
Wide Range ◽  
Stiffness Characteristics ◽  
Constituent Elements

Reconfigurable mechanisms are capable of changing their behavior during operation and perform different tasks through changes of their configuration. A compliant, multistable, reconfigurable mechanism is introduced which consists of nonlinear morphing elements assembled in a truss-like configuration. These constituent elements are made of composite strips assembled to form a double-helix and exhibit tailorable nonlinear stiffness characteristics, including bistability. The mechanism’s behavior can be tailored by tuning the inherent properties of the helical components, leading to a wide range of responses. This work explores the reconfigurability of the mechanism, based on the ability to change the helical pitch and the resulting stiffness.

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