Vibration of Nonuniform Beams Under Moving Point Loads: An Approximate Analytical Solution in Time Domain

2017 ◽  
Vol 17 (03) ◽  
pp. 1750035 ◽  
Author(s):  
C. P. Sudheesh Kumar ◽  
C. Sujatha ◽  
K. Shankar
Keyword(s):  
Approximate Analytical Solution ◽  
Time Integration ◽  
Single Mode ◽  
Mode Analysis ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Require Time ◽  
Analytical Formulae ◽  
Clamped Beams ◽  
Forced Responses

The forced-free responses of nonuniform beams under moving point loads are analyzed in this paper. Simple approximate analytical formulae for the forced responses of undamped nonuniform beams, derived using the fundamental mode by the Rayleigh–Ritz (R–R) method, are presented. The responses of both simply supported and clamped–clamped beams are analyzed. The responses are also determined by the finite element method (FEM) in which nonuniform elements are used for fast convergence. It is found that the present method yields results that are very close to those obtained by the FEM. As this method does not require time integration, it is faster and computationally more efficient. Though the single-mode analysis of forced vibration of uniform beams under moving loads has been done by several researchers, its application to nonuniform beams has not been reported.

Prediction of Springback in Straight Flanging Operation

1999 ◽  
Author(s):  
Jian Cao ◽  
Zhihong Liu ◽  
Wing Kam Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Deformation Mechanism ◽  
The Finite Element Method ◽  
Moment Distribution ◽  
Analytical Formulae ◽  
Typical Distribution ◽  
Number Of Segments ◽  
Springback Angle ◽  
Energy Element

Abstract A straight flange problem is investigated with the expectation that this will lead to a better understanding of the deformation mechanism and to more complicated flanging problems. The “in-die” shape of the part is subdivided into a number of segments and individual springback of each segment is investigated, by releasing the elastic energy element by element, using the Finite Element Method (FEM). Typical distribution of the springback angle along the blank is obtained and found to be quite different from the widely used constant springback assumption for the curved part of the flange. A new model incorporating a non-uniform moment distribution at the curved part is proposed which reflects the above observation. Explicit analytical formulae are derived and the analytical predictions match with the experimental results very well.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

1998 ◽  
Vol 120 (2) ◽  
pp. 371-377 ◽  
Author(s):  
Huan Wang ◽  
Keith Williams ◽  
Wei Guan
Keyword(s):  
Finite Length ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Vibrational Modes ◽  
The Finite Element Method ◽  
Cylinder Length ◽  
Radial Thickness ◽  
Thick Cylinder

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

scholarly journals Stress Analysis of Polarization Maintaining Optical Fibers by the Finite Element Method

1970 ◽  
Vol 1 (1) ◽  
Author(s):  
M. H. Aly A. S. Farahat, M. S. Helmi and M. Farhoud
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optical Fibers ◽  
Radial Distance ◽  
Single Mode ◽  
The Finite Element Method ◽  
Modal Birefringence ◽  
Polarization Maintaining ◽  
External Forces ◽  
Element Method

Stress-induced birefringence in single mode polarization maintaining optical fibers has been investigated using the finite element method. The modal birefringence caused by external forces in the Panda and the Side Tunnel fibers are calculated. It is found that the modal birefringence is directly proportional to the radial distance from the fiber center. As expected, the modal birefringence vanishes with the variation in the magnitude of the applied external loads.Key Words: Birefringence, Polarization, Panda Fiber, Side-Pit Fiber, Finite Element Method.

scholarly journals Numerical and Circuit Modeling of the Low-Power Periodic WPT Systems

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2651 ◽  
Author(s):  
Adam Steckiewicz ◽  
Jacek Maciej Stankiewicz ◽  
Agnieszka Choroszucho
Keyword(s):  
Numerical Model ◽  
Low Power ◽  
Three Dimensional ◽  
Equivalent Circuit Model ◽  
Circuit Model ◽  
Wireless Power ◽  
The Finite Element Method ◽  
Charging System ◽  
Analytical Formulae ◽  
Similar Accuracy

This article presents a method for analysis of the low-power periodic Wireless Power Transfer (WPT) system, using field and circuit models. A three-dimensional numerical model of multi-segment charging system, with periodic boundary conditions and current sheet approximation was solved by using the finite element method (FEM) and discussed. An equivalent circuit model of periodic WPT system was proposed, and required lumped parameters were obtained, utilizing analytical formulae. Mathematical formulations were complemented by analysis of some geometrical variants, where transmitting and receiving coils with different sizes and numbers of turns were considered. The results indicated that the proposed circuit model was able to achieve similar accuracy as the numerical model. However, the complexity of model and analysis were significantly reduced.

FINITE ELEMENT ANALYSIS OF TE AND TM MODES IN NONLINEAR PLANAR WAVEGUIDES

1994 ◽  
Vol 03 (01) ◽  
pp. 101-116 ◽  
Author(s):  
M. ZOBOLI ◽  
S. SELLERI
Keyword(s):  
Finite Element ◽  
Refractive Index ◽  
Transverse Magnetic ◽  
Planar Waveguides ◽  
Mode Analysis ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Transverse Magnetic Mode ◽  
Solution Convergence ◽  
Index Distribution

A general approach based on the finite element method for analyzing optical waves guided by dielectric planar waveguides with arbitrary nonlinear media and with arbitrary refractive index distribution is considered. A complete transverse-electric and transverse-magnetic mode analysis is presented and TM polarization solutions are obtained without approximations on the biaxial nature of the nonlinear refractive index. Solution convergence and stability is discussed and both film-guided and surface-guided modes are presented for symmetrical and asymmetrical structures. Bistability and hysteresis phenomena have been investigated for TE as well as for TM modes.

Comparison Between Numerical Simulation and Experimentation of Asymmetrical Three-Roll Bending Process

2010 ◽  
Author(s):  
Zhengkun Feng ◽  
Henri Champliaud
Keyword(s):  
Structural Dynamics ◽  
Metal Forming ◽  
Plastic Material ◽  
Time Integration ◽  
Material Model ◽  
Rigid Bodies ◽  
The Finite Element Method ◽  
Shell Elements ◽  
Roll Bending ◽  
Bending Process

Three-roll bending processes are widely used in metal forming manufacturing due to simple configurations. Asymmetrical three-roll bending is one of the processes. This paper deals with the simulation analyses based on the finite element method for cylindrical production. The components of the roll bending machine, such as the rolls were assumed to be rigid bodies and the 4-node shell elements were used in the modeling. The tensile test of the material was simulated to determine the elasto-plastic material model of the plate. Automatic node-surface contacts were chosen for the interfaces between the plate and the rigid bodies. The nonlinear equations which represent the structural dynamics with large displacement were resolved using explicit time integration. The simulations were performed under the well-known ANSYS/LS-DYNA environment. The numerical results agree well with the experimental ones.

scholarly journals Impact of Disabled Driver’s Mass Center Location on Biomechanical Parameters during Crash

2021 ◽  
Vol 11 (4) ◽  
pp. 1427 ◽  
Author(s):  
Kamil Sybilski ◽  
Jerzy Małachowski
Keyword(s):  
Head Injuries ◽  
Time Integration ◽  
Control Unit ◽  
Disable Person ◽  
Steering Wheel ◽  
The Finite Element Method ◽  
Time Integration Method ◽  
Additional Equipment ◽  
Biomechanical Parameters ◽  
Lateral Displacements

Adapting a car for a disable person involves adding additional equipment to compensate for the driver’s disability. During this process, the change in the driver’s position and kinematics and their impact on safety levels during crash is not considered. There is also a lack of studies in the literature on this problem. This paper describes a methodology for conducting a study of the behavior of a disabled driver during a crash using the finite element method, based on an explicit time integration method. A validated car model and a commercial dummy model were used. The results show that the use of a handle on the steering wheel and a hand control unit causes dangerous lateral displacements relative to the seat. Amputation of the left leg or right arm causes significant shoulder rotations, amputation of the left leg causes increased thoracic loads. Amputation or additional equipment have no significant impact on head injuries.

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