Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Intrinsic Curvature ◽  
Nonlinear Dynamic Response ◽  
Helical Springs ◽  
Secondary Resonances ◽  
Element Approach

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation and vice rotation (and displacement) interpolation and, thus, can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed, which captures coupling due to nonzero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate loading amplitudes lead to the presence of secondary resonances (not captured by linearized models), while large loading amplitudes lead to complex dynamics and transverse buckling.

Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

2010 ◽  
Author(s):  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Intrinsic Curvature ◽  
Amplitude Response ◽  
Nonlinear Dynamic Response ◽  
Helical Springs ◽  
Secondary Resonances ◽  
Element Approach

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation vice rotation (and displacement) interpolation, and thus can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed which captures coupling due to non-zero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate amplitude response leads to the presence of secondary resonances not captured by linearized models.

Nonlinear Dynamic Response of Piezoelectric Cylindrical Shell with Delamination under Hygrothermal Conditions

2012 ◽  
Vol 204-208 ◽  
pp. 4698-4701
Author(s):  
Jin Hua Yang ◽  
De Liang Chen
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference Method ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Transverse Motion ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
The Finite Difference Method ◽  
Delamination Length

Abstract. On the basis of the nonlinear plate-shell and piezoelectric theory, the governing equations of motion for axisymmetrical piezoelectric delaminated cylindrical shell under hygrothermal conditions were derived. The governing equation of transverse motion was modified by contact force and thus the penetration between two delaminated layers could be avoided. The whole problem was resolved by using the finite difference method. In calculation examples, the effects of delamination length, depth and amplitude of load on the nonlinear dynamic response of the axisymmetrical piezoelectric delaminated shell under hygrothermal conditions were discussed in detail.

The Motion Formalism for Flexible Multibody Systems

2021 ◽  
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Structural Elements ◽  
Governing Equations ◽  
Euclidean Group ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Element Approach

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the Special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Nonlinear Analysis of Vortex Induced Dynamic Response of Marine Riser

2013 ◽  
Vol 353-356 ◽  
pp. 2736-2740
Author(s):  
Lin Lin ◽  
Yan Ying Wang
Keyword(s):  
Dynamic Response ◽  
Cross Flow ◽  
Dynamic Responses ◽  
Marine Riser ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
Wake Oscillator Model ◽  
Wake Oscillator ◽  
Flow Profiles ◽  
Line Force

Vortex-induced dynamic response is the most important issue influencing marine riser. This paper presents an investigation on the vortex-induced nonlinear dynamic response of marine riser subjected to combined waves,currents and platform movement. The in-line force was solved by Morison equation under combined waves,currents and platform movement while cross-flow force was solved by wake oscillator model. Updated Lagrangianmethod was used to solve the nonlinear problem.The governing equations were discretized by finite element method and solved by Newmark-β method in time domain. Influence of nonlinearity, comparisons of vortex-induced dynamic responses under different boundary conditions and different flow profiles were discussed.

The Selection of the Linearized Natural Frequency for the Second-Order Normal Form Method

2011 ◽  
Author(s):  
Zhenfang Xin ◽  
S. A. Neild ◽  
D. J. Wagg
Keyword(s):  
Normal Form ◽  
Dynamic Response ◽  
Natural Frequency ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Second Order ◽  
Nonlinear Dynamic Response ◽  
Weakly Nonlinear ◽  
Selection Of ◽  
Normal Form Technique

The normal form technique is an established method for analysing weakly nonlinear vibrating systems. It involves applying a simplifying nonlinear transform to the first-order representation of the equations of motion. In this paper we consider the normal form technique applied to a forced nonlinear system with the equations of motion expressed in second-order form. Specifically we consider the selection of the linearised natural frequencies on the accuracy of the normal form prediction of sub- and superharmonic responses. Using the second-order formulation offers specific advantages in terms of modeling lightly damped nonlinear dynamic response. In the second-order version of the normal form, one of the approximations made during the process is to assume that the linear natural frequency for each mode may be replaced with the response frequencies. Here we will show that this step, far from reducing the accuracy of the technique, does not affect the accuracy of the predicted response at the forcing frequency and actually improves the predictions of sub and superharmonic responses. To gain insight into why this is the case, we consider the Duffing oscillator. The results show that the second-order approach gives an intuitive model of the nonlinear dynamic response which can be applied to engineering applications with weakly nonlinear characteristics.

Random Base Excitation of Timoshenko Beam Traversed by Moving Load

2011 ◽  
Author(s):  
Fahim Javid ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Base Excitation ◽  
Lateral Direction ◽  
Beam Dynamic

The study of dynamic response of Timoshenko beam traversed by moving load subjected to random base excitation is carried out. By applying the theory of dynamic response of Timoshenko beam as well as finite element theory, beam finite element governing equations of motion are developed and they are solved using Galerkin method. To validate the model, some results of the model are compared with those available in literatures and very close agreement is achieved. The beam is subjected to travelling load and random base excitation in lateral direction simultaneously. Three types of boundary conditions, namely, hinged-hinged, hinged-clamped, and the clamped-clamped ends, are considered and beam dynamic behavior; such as deflection, velocity, and bending moment of beam midpoint, with all so-called boundary conditions are studied. To get better understanding of base excitation effects on the beam dynamic performance, all the results are presented with and without base excitation, in which considerably difference is observed. Moreover, the effect of base excitation on beam with different span-length is monitored.

A Newly Developed Algorithm for Treating the Coupled Dynamic Response of Robotic Fixtureless Assembly

1996 ◽  
Author(s):  
Genady Shagal ◽  
Shaker A. Meguid
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Equations Of Motion ◽  
Time Integration ◽  
Integration Scheme ◽  
The Finite Element Method ◽  
Coupled Equations ◽  
Time Integration Scheme ◽  
Implicit Approach ◽  
Cooperating Robots

Abstract The coupled dynamic response of two cooperating robots handling two flexible payloads for the purpose of fixtureless assembly and manufacturing is treated using a new algorithm. In this algorithm, the equations describing the dynamics of the system are obtained using Lagrange’s method for the rigid robot links and the finite element method for the flexible payloads. A new time integration scheme is developed to treat the coupled equations of motion of the rigid links for a given displacement of the flexible payloads. The finite element equations of the flexible payloads are then treated using an implicit approach. The new algorithm was verified using simplified examples and was later used to examine the dynamic response of two cooperating robot arms manipulating flexible payloads which are typical of the automotive industry.

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