Analytical approach for transverse vibration analysis of castellated beams

2014 ◽  
Vol 14 (03) ◽  
pp. 1350071 ◽  
Author(s):  
J. K. Chen ◽  
B. Kim ◽  
L. Y. Li
Keyword(s):  
Free Vibration ◽  
Analytical Study ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vibration Modes ◽  
Shear Effect ◽  
Vibration Frequencies ◽  
Beam Length ◽  
Cross Sectional ◽  
Simply Supported

This paper presents an analytical study on the dynamic characteristics of castellated beams. The study focuses on the effect of web shear on the free vibration frequencies of castellated beams. By using the Hamilton's principle, a simple closed-form solution for determining the free vibration frequencies of simply supported castellated beams is developed. The results show that the shear effect on the free vibration frequencies increases with the cross-sectional area and distance between the centroids of the two tee sections of castellated beams, but decreases with respect to increasing web thickness or increasing beam length. The shear effect is also found to be greater in higher vibration modes.

scholarly journals Displacement Formulations for Deformation and Vibration of Elastic Circular Torus

2021 ◽  
Author(s):  
bohua sun
Keyword(s):  
Free Vibration ◽  
Gaussian Curvature ◽  
Turning Point ◽  
Closed Form Solution ◽  
Complex Form ◽  
Form Solution ◽  
Element Analysis ◽  
Displacement Boundary ◽  
Engineering Mechanics ◽  
Maple Code

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

Bending and free vibration analysis of foam-filled truss core sandwich panel

2016 ◽  
Vol 20 (5) ◽  
pp. 617-638 ◽  
Author(s):  
MP Arunkumar ◽  
Jeyaraj Pitchaimani ◽  
KV Gangadharan
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Sandwich Panel ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Form Solution ◽  
Numerical Comparison ◽  
Truss Core ◽  
Foam Filled

This paper presents the studies carried out on bending and free vibration behavior of truss core sandwich panel filled with foam typically used in aerospace applications. Equivalent stiffness properties for foam-filled truss core sandwich panel are derived by idealizing 3D foam-filled sandwich panel to an equivalent 2D orthotropic thick plate continuum. The accuracy of the derived elastic property is ensured by the numerical comparison of free vibration response of 3D and its equivalent 2D finite element model. The derived stiffness constants were used in closed form solution to evaluate the maximum deflection of the continuum. The results show that the free vibration and static behavior of the sandwich panel can be enhanced in due consideration to the space constraint by filling foam in the empty space of core. The results also reveal that triangular core foam-filled sandwich panel deflects less compared to other cores. From the free vibration analysis, effect of filling foam is effective in cellular and trapezoidal core.

New continuum surgical robot based on hybrid concentric tube-tendon driven mechanism

2021 ◽  
pp. 095440622110424
Author(s):  
Mohammed Abdel-Nasser ◽  
Omar Salah
Keyword(s):  
Inverse Kinematics ◽  
High Performance ◽  
Analytical Study ◽  
Fuzzy Inference ◽  
Closed Form Solution ◽  
Form Solution ◽  
Robot Arm ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Intelligent Approach

Robotics technology is used widely in minimally invasive surgery (MIS) which provides high performance and accuracy. The most famous robot arm mechanisms, which are used in MIS, are tendon-driven mechanism (TDM), and concentric tube mechanism (CTM). Unfortunately, these mechanisms until now have some limitations, i.e. making friction with the tissue during extracting and retracting and strain limits, for TDM and CTM respectively. A new hybrid concentric tube-tendon driven mechanism (HCTDM) is proposed to overcome these limitations. HCTDM enables the end-effector to get close to and get away from the surgical area during the operation without harming the tissue and with more flexibility. In addition to that, the workspace increases as a result of this combination, too. This benefit serves MIS, especially endoscopic surgeries (ESs). We did an analytical study of this idea and got the forward kinematics. In the inverse kinematics, an intelligent approach which is called an adaptive neuro-fuzzy inference system (ANFIS) is used because the closed-form solution is more complicated for such these mechanisms. Finally, HCTDM is analyzed and evaluated by using a computer simulation. The simulation results show that the workspace becomes wider and has more dexterity than use TDM or CTM individually. Furthermore, various trajectories are used to test the mechanism and the kinematic analysis, which show the mechanism can follow and track the trajectories with maximum mean error 1.279, 0.7027, and [Formula: see text] for X, Y, and Z axes respectively.

Identification of cracks in an Euler–Bernoulli beam using Bayesian inference and closed-form solution of vibration modes

2020 ◽  
pp. 146442072096971
Author(s):  
Tianyu Wang ◽  
Mohammad Noori ◽  
Wael A. Altabey
Keyword(s):  
Finite Element ◽  
Bayesian Inference ◽  
Finite Element Model ◽  
Crack Detection ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Vibration Modes ◽  
Vibration Data ◽  
The Finite Element Model

Over the past two decades, extensive research has been carried out in the field of structural health monitoring for damage detection in structural systems. Some crack detection methods are based on the finite element model of a beam and use vibration data are developed. These methods identify the crack by updating of the finite element model according to the vibration data of structure. This paper proposes a novel method for crack detection in Euler–Bernoulli beams based on the closed-form solution of mode shapes using Bayesian inference. The expression of vibration modes is derived analytically with the crack parameters as unknown variables. Subsequently, the Bayesian inference is used to obtain the probability density function of crack parameters and to evaluate the uncertainty of the modes. Finally, the method is applied to a series of numerical examples, including a beam with a single-crack and multi-cracks, to verify the effectiveness of this method.

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Natalie Waksmanski ◽  
Ernian Pan ◽  
Lian-Zhi Yang ◽  
Yang Gao
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Crystal Plate ◽  
Mode Shapes ◽  
Sandwich Plates ◽  
One Dimensional ◽  
Propagator Matrix ◽  
Multilayered Plates

An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation

2020 ◽  
pp. 108128652094777
Author(s):  
Giulio Maria Tonzani ◽  
Isaac Elishakoff
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Detailed Comparison ◽  
Vibration Frequencies ◽  
Pasternak Foundation ◽  
New Model ◽  
Simply Supported ◽  
Model Based

This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations of boundary conditions deriving from three typical end constraints, namely the simply supported end, clamped end, and free end. An interesting intermingling phenomenon is presented for a simply-supported (S-S) beam together with proof of the ‘non-existence’ of zero frequencies for free-free (F-F) and simply supported-free (S-F) beams on a Winkler–Pasternak foundation.

Analysis of Simply-Supported Orthotropic Cylindrical Shells Subject to Lateral Impact Loads

1990 ◽  
Vol 57 (2) ◽  
pp. 376-382 ◽  
Author(s):  
A. P. Christoforou ◽  
S. R. Swanson
Keyword(s):  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Double Fourier Series ◽  
Form Solution ◽  
Lateral Impact ◽  
Simply Supported ◽  
Response Characteristics ◽  
Simple Support ◽  
The Impact ◽  
Approximate Procedure

An analytic solution is given for the problem of simply-supported orthotropic cylindrical shells subject to impact loading. The closed-form solution has not been obtained previously. The analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support. Each expansion is assumed to be separable into a function of time and a function of position. By neglecting in-plane and rotary inertia the problem becomes a second-order ordinary differential equation in time for the Fourier coefficients of the radial deflection. For a given loading impulse the solution can be found by invoking the convolution integral. The results show that for impact by a heavy mass, the solution is equivalent to that obtained by an approximate procedure of neglecting the mass of the shell, which leads to a simple simple-degree-of-freedom analysis. For problems of impact by smaller masses, the higher response frequencies of the cylinder become important. The results show the importance of dynamic effects in the predicted impact duration, peak force, and peak deflection relative to the quasi-static response. The results show that the response amplitude varies linearly with the impact velocity, but the response characteristics depend on the mass of the impactor and the mass and stiffness of the cylinder.

Accurate Analytical-Type Solutions for the Free Vibration of Simply-Supported Parallelogram Plates

1991 ◽  
Vol 58 (1) ◽  
pp. 203-208 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Equal Length ◽  
Superposition Method ◽  
Vibration Modes ◽  
Type Solution ◽  
Simply Supported ◽  
Wide Range ◽  
Plate Geometry ◽  
Special Case ◽  
Comprehensive Study

A comprehensive study of the free vibration of simply-supported parallelogram plates is conducted. Solutions are obtained by utilizing the superposition method and by taking advantage of symmetry inherent in the problem. Toward this end a new alternating Le´vy-type solution is introduced. Verification tests are conducted by comparing computed eigenvalues with those of rhombic plates in the special case where all plate edges are of equal length. Eigenvalues are stored for eight vibration modes and for a wide range of plate geometry.

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