scholarly journals Bending Vibration Analysis of Tensioned Ball Screw under Nonuniform Stress during the Cutting Process

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Cheng Zhang ◽  
Jianrun Zhang
Keyword(s):  
Differential Equation ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Cutting Process ◽  
Ball Screw ◽  
Segmentation Method ◽  
Bending Vibration ◽  
Nonuniform Stress ◽  
Euler Bernoulli Beam ◽  
Force Data

The bending vibration of tensioned ball screw under nonuniform stress in the cutting process is analyzed in this paper. Differential equation of a beam under nonuniform prestress is derived according to Euler–Bernoulli beam theory. A method to solve the differential equation under different boundary conditions is proposed based on the segmentation method. The correctness of the method is verified by comparison with the traditional method and experiment, respectively. The dynamic analysis of tensioned ball screw under nonuniform stress in the cutting process is carried out with this method. The influence of the location on the ball screw and amplitude of the axial force produced in the cutting process on natural frequencies of ball screw is researched. Results show that the greater the force, the greater the change in natural frequencies. Furthermore, the change of first two natural frequencies presents a simple harmonic trend with the force moving along the ball screw. Taking a set of cutting force data as an example, the instantaneous frequency of tensioned ball screw in the cutting process is calculated in the end.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

On the Vibrational Behavior of Piezoelectric Nano-Beams

2013 ◽  
Vol 829 ◽  
pp. 790-794 ◽  
Author(s):  
Omid Rahmani ◽  
Mohammad Hosein Noroozi Moghaddam
Keyword(s):  
Electromechanical Coupling ◽  
Natural Frequencies ◽  
Surface Effect ◽  
Beam Theory ◽  
Load Effect ◽  
Coupling Behavior ◽  
Article Surface ◽  
Non Local ◽  
Euler Bernoulli Beam ◽  
Exact Term

In this article surface effects are considered to study the electromechanical coupling behavior of piezoelectric nanobeams with the non-local Euler-Bernoulli beam theory. The equation of motion for piezoelectric nanobeams with considering both surface effect and nonlocal effect is achieved and exact term for natural frequencies is derived for simply supported conditions. In the following the axial load effect on the natural frequencies piezoelectric nanobeams has been studied.

Damping of Vibrations of Layered Elastic-Viscoelastic Beams

1993 ◽  
Vol 46 (11S) ◽  
pp. S305-S311 ◽  
Author(s):  
Richard B. Hetnarski ◽  
Ray A. West ◽  
Joseph S. Torok
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Bernoulli Beam ◽  
Viscoelastic Effects ◽  
Viscoelastic Layers ◽  
Euler Bernoulli Beam ◽  
Damping Of Vibrations ◽  
Fourth Order Differential Equation

A five-layer cantilever beam consisting of an elastic core, two symmetric viscoelastic layers, and two elastic constraining layers is considered. The viscoelastic effects are incorporated in the Euler-Bernoulli beam theory. If the contraction and extension of the constraining layers is neglecterd a fourth order differential equation of motion is received. Inclusion of contraction and extension of the constraining layers results in a more accurate sixth order differential equation. Appropriate boundary conditions are derived. Laplace transforms are used extensively. Both the analytical solution and the numerical results are presented.

scholarly journals On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature

On the Analytical Lumped-Mass Model of an Elastic Four-Bar Mechanism

1975 ◽  
Vol 97 (2) ◽  
pp. 561-565 ◽  
Author(s):  
J. P. Sadler
Keyword(s):  
Nonlinear Differential Equations ◽  
Beam Theory ◽  
Parameter Method ◽  
Lumped Mass ◽  
Mass Model ◽  
Bending Vibration ◽  
Lumped Parameter ◽  
Lumped Mass Model ◽  
Four Bar Linkage ◽  
Euler Bernoulli Beam

The lumped-parameter method for the elastodynamic analysis of mechanisms is applied to a particular case for which existing experimental evidence is available. The mechanism analyzed is a planar four-bar linkage, and the calculated results include steady-state deflection and stress and strain responses associated with the bending vibration of the three moving links. The analytical model is based on nonlinear differential equations derived by way of Euler-Bernoulli beam theory, and numerical solution is obtained through the use of a digital computer. Comparison of the analytical and experimental results shows very good agreement, supporting the use of the lumped-parameter approach in analyses of this type.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

Nonlinear Free Vibration of Nanobeams With Surface Effects Considerations

2011 ◽  
Author(s):  
Ali Fallah ◽  
Keikhosrow Firoozbakhsh ◽  
Mohammad Hossein Kahrobaiyan ◽  
Abdolreza Pasharavesh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Partial Differential Equation ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Nonlinear Ordinary Differential Equation ◽  
Euler Bernoulli Beam ◽  
Analytical Expressions ◽  
Equations Of Motions

In this paper, simple analytical expressions are presented for geometrically non-linear vibration analysis of thin nanobeams with both simply supported and clamped boundary conditions. Gurtin-Murdoch surface elasticity together with Euler-Bernoulli beam theory is used to obtain the governing equations of motions of the nanobeam with surface effects consideration. The governing nonlinear partial differential equation is reduced to a single nonlinear ordinary differential equation using Galerkin technique. He’s variational approach is employed to obtain analytical solution for the resulted nonlinear governing equation. The effects of different parameters such as vibration amplitude, boundary conditions, and beam dimensions on the natural frequencies of nanobeams are investigated and results are presented for future studies.

scholarly journals On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature

Dynamic Responses of Two Beams Connected by a Spring-Mass Device

2012 ◽  
Vol 29 (1) ◽  
pp. 143-155 ◽  
Author(s):  
H.- P. Lin ◽  
D. Yang
Keyword(s):  
Natural Frequencies ◽  
Beam Theory ◽  
Free Vibrations ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Entire System ◽  
Bernoulli Beam ◽  
Continuous Beams ◽  
Experimental Validations ◽  
Euler Bernoulli Beam

AbstractThis paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring con-nection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

Sign in / Sign up

Export Citation Format

Share Document