Numerical Dynamic Analysis of a Single Link Soft Robot Finger

2013 ◽  
Vol 459 ◽  
pp. 449-454 ◽  
Author(s):  
Elango Natarajan ◽  
Ahmad Athif Mohd Faudzi ◽  
Viknesh Malliga Jeevanantham ◽  
Muhammad Rusydi Muhammad Razif ◽  
Ili Najaa Aimi Mohd Nordin
Keyword(s):  
Room Temperature ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Mode Shapes ◽  
Soft Robot ◽  
Fundamental Frequencies ◽  
Single Link ◽  
Hyper Elastic ◽  
Finger Model ◽  
Strain Dependent

In this paper, a solid, single link soft robot finger was modeled with SILASTIC P-1 Silicone, supplied by Dow Corning®. The material is anon-linear hyper elastic, strain dependent, room temperature vulcanized (RTV) rubber. When the fingers are actuated for grasping and object manipulation, they vibrate with excessive amplitudes, which will disturb the precise positioning of the fingers. Vibration analysis through numerical simulation was conducted in ANSYS®V12. The first ten fundamental frequencies and their mode shapes were numerically computed and presented from modal analysis. The lowest natural frequency of the finger model was found to be 2.14 Hz. The dynamic stiffness of the finger model was then computed from the natural frequencies. It was found to be nonlinear in nature. The dynamic characteristics of the finger model during the excitation between 1 Hz and 1000 Hz were studied in transient analysis. The peak acceleration occurred at 9.3 Hz, while the peak velocity occurs at 3.75 Hz and 4.8 Hz with the magnitude of 0.013 mm/s.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

scholarly journals Modal analysis of spindles while accounting for system decay and its application to machine tool chatter prevention

2021 ◽  
Author(s):  
Seyed M. Hashemi ◽  
Omar Gaber
Keyword(s):  
Life Span ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Advanced Manufacturing ◽  
Machining Parameters ◽  
Fundamental Frequencies ◽  
Stability Lobes ◽  
Machine Tool Chatter ◽  
Vibrational Characteristics ◽  
The Stability

This paper investigates the vibrational characteristics of a machining spindle over its life span. The experimental investigation was carried out using tap testing, where the fundamental frequencies of the spindle system were recorded for different spindle categories, namely, ‘production’ and ‘prove-out’ spindles. Focussing on production spindles, the system ageing translated through a reduction in the system’s natural frequency is modelled as changes in the bearings’ stiffness. The experimentally evaluated natural frequencies were then used to calculate the equivalent bearings’ stiffness within the spindle by means of a calibrated dynamic stiffness method (CDSM) at various stages of spindle’s life. A comparison between the stability lobes generated for two different instances in time, in a full slotting cuts process, shows that over the life span of a spindle, the stability lobes would shift sufficiently to cause chatter after initially being stable. Therefore, as the spindle ages, the presented methodology can be exploited to predict the updated machining parameters necessary to avoid unstable chatter conditions.<div><br></div><div>This is a post-peer-review, pre-copyedit version of an article published in The International Journal of Advanced Manufacturing Technology. The final authenticated version is available online at: https://doi.org/10.1007/s00170-015-6979-4 <br></div>

EXACT VIBRATION FREQUENCIES AND MODES OF BEAMS WITH INTERNAL RELEASES

2002 ◽  
Vol 02 (01) ◽  
pp. 63-75 ◽  
Author(s):  
M. EISENBERGER
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Beam Element ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Dynamic Stiffness Matrix ◽  
Continuous Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

The exact vibration frequencies of continuous beams with internal releases are found using the dynamic stiffness method. Two types of releases are considered: hinge and sliding discontinuities. First, the exact dynamic stiffness matrix for a beam element with a release is derived and then used in the assembly of the structure dynamic stiffness matrix. The natural frequencies are found as the values of frequency that make this matrix singular. Then the mode shapes are found exactly. Examples are given for continuous beams with different releases.

Nanoscale Vibrational Behavior of Single-Layered Graphene Sheets

2007 ◽  
Author(s):  
A. Sakhaee-Pour ◽  
M. T. Ahmadian ◽  
A. Vafai
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Graphene Sheets ◽  
Empirical Equations ◽  
Atomistic Modeling ◽  
Vibrational Behavior ◽  
Fundamental Frequencies ◽  
Element Technique ◽  
Percent Accuracy

Molecular structural mechanics approach is implemented to investigate vibrational behavior of single-layered graphene sheets. By using the atomistic modeling, mode shapes and natural frequencies are obtained. Vibration analysis is performed under different chirality and boundary conditions. Numerical results from the finite element technique are applied to develop empirical equations via a statistical multiple nonlinear regression model. With the proposed empirical equations, fundamental frequencies of single-layered graphene sheets under considered boundary conditions can be predicted within 3 percent accuracy.

scholarly journals Modal analysis of spindles while accounting for system decay and its application to machine tool chatter prevention

2021 ◽  
Author(s):  
Seyed M. Hashemi ◽  
Omar Gaber
Keyword(s):  
Life Span ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Advanced Manufacturing ◽  
Machining Parameters ◽  
Fundamental Frequencies ◽  
Stability Lobes ◽  
Machine Tool Chatter ◽  
Vibrational Characteristics ◽  
The Stability

This paper investigates the vibrational characteristics of a machining spindle over its life span. The experimental investigation was carried out using tap testing, where the fundamental frequencies of the spindle system were recorded for different spindle categories, namely, ‘production’ and ‘prove-out’ spindles. Focussing on production spindles, the system ageing translated through a reduction in the system’s natural frequency is modelled as changes in the bearings’ stiffness. The experimentally evaluated natural frequencies were then used to calculate the equivalent bearings’ stiffness within the spindle by means of a calibrated dynamic stiffness method (CDSM) at various stages of spindle’s life. A comparison between the stability lobes generated for two different instances in time, in a full slotting cuts process, shows that over the life span of a spindle, the stability lobes would shift sufficiently to cause chatter after initially being stable. Therefore, as the spindle ages, the presented methodology can be exploited to predict the updated machining parameters necessary to avoid unstable chatter conditions.<div><br></div><div>This is a post-peer-review, pre-copyedit version of an article published in The International Journal of Advanced Manufacturing Technology. The final authenticated version is available online at: https://doi.org/10.1007/s00170-015-6979-4 <br></div>

scholarly journals Riser Dynamic Analysis Using WKB-Based Dynamic Stiffness Method

2012 ◽  
Author(s):  
Yongming Cheng ◽  
J. Kim Vandiver
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Shape Function ◽  
Dynamic Stiffness ◽  
Mode Shapes ◽  
Marine Riser ◽  
Theoretical Formulation ◽  
Eigen Value ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

Risers are fluid conduits from subsea equipment to surface floating production platforms. The integrity of a riser system plays a very important role in deepwater developments. Riser dynamic analysis is an important part to the system design. This paper investigates riser dynamic analysis using the WKB-Based dynamic stiffness method. This paper first presents a theoretical formulation of the dynamic stiffness method. It then combines the dynamic stiffness method with the WKB theory, which assumes that the coefficients in the differential equation of motion are slowly varying. The WKB-based dynamic stiffness method is derived and a frequency dependent shape function is expressed implicitly. The Wittrick and Williams (W-W) algorithm is further extended to solve eigen value problem for a general non-uniform marine riser. Examples of non-uniform riser are analyzed and the results show the efficiency of this method. In addition, a pipe-in-pipe riser system is analyzed for natural frequencies and mode shapes using the WKB-based dynamic stiffness method with the W-W algorithm. The characteristic of the mode shapes is described for such a riser system.

Free Vibration Behavior of Angle-Ply Laminated Composite Stiffened Plates

2021 ◽  
pp. 2150187
Author(s):  
Leena Sinha ◽  
Amaresh Tripathy ◽  
Amar N. Nayak ◽  
Shishir K. Sahu
Keyword(s):  
Free Vibration ◽  
Numerical Investigation ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Stiffened Plates ◽  
Vibration Behavior ◽  
Fundamental Frequencies ◽  
Aspect Ratios ◽  
Support Conditions

This paper reports for the first time the experimental investigation on the free vibration characteristics of angle-ply laminated composite stiffened plates along with the numerical investigation. The natural frequencies of these plates are computed experimentally using an FFT analyzer and numerically by employing the finite element method with combination of isoparametric nine nodded plate and three nodded beam elements. Angle-ply laminated stiffened plates are fabricated using woven glass fiber fabrics and epoxy by hand layup technique. The effects of various support conditions; number, orientation and types of stiffeners; aspect ratios of plates and different fiber orientations on the fundamental frequencies of the angle-ply laminated stiffened plates are investigated. These parameters significantly influence the natural frequencies. It is found that there is a very good agreement observed between the fundamental frequencies obtained from both experimental and numerical investigation. Mode shapes are also presented for angle-ply laminated square stiffened plates with three different support conditions to justify the trend of increasing/decreasing of the modal frequency with the addition of stiffeners. It is observed that the enhancement of the frequencies of the angle-ply plates due to addition of stiffeners is influenced significantly by the position of stiffeners and consequently mode shapes. As the research on the free vibration behavior of angle-ply stiffened plates with experimental analysis is very rare, this study can be considered as the benchmark for future research.

Calculation of the natural frequencies and mode shapes of a Euler–Bernoulli beam which has any combination of linear boundary conditions

2019 ◽  
Vol 25 (18) ◽  
pp. 2473-2479 ◽  
Author(s):  
Paulo J. Paupitz Gonçalves ◽  
Michael J. Brennan ◽  
Andrew Peplow ◽  
Bin Tang
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
New Method ◽  
Mode Shapes ◽  
Linear Boundary ◽  
Bernoulli Beam ◽  
Classical Boundary ◽  
Euler Bernoulli Beam

There are well-known expressions for natural frequencies and mode shapes of a Euler-Bernoulli beam which has classical boundary conditions, such as free, fixed, and pinned. There are also expressions for particular boundary conditions, such as attached springs and masses. Surprisingly, however, there is not a method to calculate the natural frequencies and mode shapes for a Euler–Bernoulli beam which has any combination of linear boundary conditions. This paper describes a new method to achieve this, by writing the boundary conditions in terms of dynamic stiffness of attached elements. The method is valid for any boundaries provided they are linear, including dissipative boundaries. Ways to overcome numerical issues that can occur when computing higher natural frequencies and mode shapes are also discussed. Some examples are given to illustrate the applicability of the proposed method.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Sign in / Sign up

Export Citation Format

Share Document