Free Vibration of Beams With Two Sections of Distributed Mass

1998 ◽  
Vol 120 (4) ◽  
pp. 944-948 ◽  
Author(s):  
Kwok-Tung Chan ◽  
Xiao-Quan Wang ◽  
Tin-Pui Leung
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Computational Results ◽  
Free Transverse Vibration

The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

Free Transverse Vibration of Thin Rotating Disks: Nonlinear Analysis

2005 ◽  
Author(s):  
Hamid R. Hamidzadeh
Keyword(s):  
Steady State ◽  
Free Vibration ◽  
Analytical Method ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Rotating Disks ◽  
Rotating Speed ◽  
Spinning Disk ◽  
Modes Of Vibration ◽  
Free Transverse Vibration

An analytical method is adopted to determine natural frequencies for a nonlinear spinning disk. The disk is assumed to be isotropic and rotating under steady state conditions. The effects of amplitude and rotating speed on natural frequencies are determined. The developed procedure is also capable of analyzing natural frequencies of linear free vibration, which is independent of amplitude. Attention is confined to determine natural frequencies for different numbers of nodal diameters. The developed procedure does not consider modes of vibration corresponding to nodal circles. Validity of this procedure is verified by comparing some of the computed results with those established for certain cases.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

Non-linear free transverse vibration of thin rotating discs

2007 ◽  
Vol 221 (3) ◽  
pp. 467-473 ◽  
Author(s):  
H R Hamidzadeh
Keyword(s):  
Steady State ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Rotating Speed ◽  
Rotating Discs ◽  
Non Linear ◽  
Modes Of Vibration ◽  
Free Transverse Vibration

An analytical method is adopted to determine modal characteristics of non-linear spinning discs. The disc is assumed to be isotropic and rotating under steady-state conditions. The effects of amplitude and rotating speed on natural frequencies are determined. The developed procedure is also capable of analysing natural frequencies of linear free vibration, which is independent of amplitude. Attention is confined to determine natural frequencies, mode shapes, stress distributions, and critical speeds for different numbers of nodal diameters. The developed procedure does not consider modes of vibration corresponding to nodal circles. Validity of this procedure is verified by comparing some of the computed results with those established for certain cases.

Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

2017 ◽  
Vol 17 (10) ◽  
pp. 1750111
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tufekci
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequencies ◽  
Plane Motion ◽  
Mode Shapes ◽  
Frame Structures ◽  
Crack Identification ◽  
Rotatory Inertia ◽  
Axial Extension

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

Transverse Free Vibration of Timoshenko Beams Resting on Viscoelastic Foundations

2014 ◽  
Vol 919-921 ◽  
pp. 275-279
Author(s):  
Li Peng ◽  
Ying Wang
Keyword(s):  
Free Vibration ◽  
Modal Analysis ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Complex Frequency ◽  
Pasternak Foundation ◽  
Timoshenko Beams ◽  
Numerical Examples ◽  
Complex Modal Analysis

The complex modal analysis is developed to study the transverse vibration of Timoshenko beams resting on viscoelastic Pasternak foundation. Complex frequency equations and modal function expressions are obtained for pinned-pinned ends. In numerical examples, the characteristics of natural frequencies and decrement coefficients of Timoshenko beams are compared with Euler-Bernoulli beams. The numerical results show that with increase in the length, the natural frequencies of Timoshenko beams are slightly less than Euler-Bernoulli beams, and the decrement coefficients of Timoshenko beams are not constant as that of Euler-Bernoulli beams.

Dynamic Modelling and Free Vibration Characteristics Analysis of Rotating Beams

2021 ◽  
Author(s):  
D. Sachin ◽  
Mallikarjuna Reddy
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Turbine Blades ◽  
Dynamic Modelling ◽  
Free Vibration Analysis ◽  
Beam Model ◽  
Plane Vibration

Abstract Turbine blades are ideally modeled as cantilever beams on a disc rotating at a constant angular velocity. A study is made to understand the dynamic relationships between a rotating cantilever beam and various factors like hub radius, rotation speed, and slenderness ratio in in-plane vibration (Chordwise motion) and out-of-plane vibration (Flapwise motion). Hub is assumed to be rigid in the study. Using Hamilton’s principle, governing differential equations of movement for free vibration analysis of Euler-Bernoulli beam (EB) and Timoshenko (TB) beam under rotation are derived. The effects of the Gyroscopic couple are taken into account in the equations. The beam model is discretized using the Finite element approach. Derived differential equations are transformed into dimensionless quantities in which dimensionless parameters are identified. Under rotation, it is observed that the natural frequencies increase with the increase in rotational speed for both flapwise and chordwise motions of the beam. An interesting phenomenon is observed in the chordwise motion results, where Natural frequencies veer off at certain rotational speeds and certain modes. Slenderness ratios also influence this phenomenon, which shifts the veer-off region and the tuned angular frequency. Numerical results are obtained for different rotational speeds with various hub radius ratios, and it was observed that hub radius directly influences the natural frequencies of the rotating uniform cantilever beam. A thorough study on the influence of the slenderness ratio showed that, for lower slenderness ratio, frequency veering region occurs at the fundamental natural frequency, but for higher slenderness ratios’ there is a shift in frequency veering region for higher modes.

Free Vibration of Initially Stressed Circular Disks

1965 ◽  
Vol 87 (2) ◽  
pp. 258-264 ◽  
Author(s):  
C. D. Mote
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Variable Thickness ◽  
Transverse Vibration ◽  
Fundamental Mode ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Vibration Characteristics ◽  
Initial Stresses ◽  
Circular Disks

The approximate free vibration characteristics of centrally clamped, variable thickness disks are analyzed by the Rayleigh-Ritz technique. Natural frequencies of transverse vibration are computed, taking into consideration rotational and thermal in-plane stresses as well as purposely induced initial stresses. Initial stresses can significantly raise the minimum disk natural frequency throughout a prescribed rotational and thermal environment. The fundamental mode of disk vibration is one of zero nodal circles and either zero, one, or two nodal diameters, depending upon the disk geometry and the rotational-thermal environment.

The Study of the Vibration Characteristics of the Cantilever Beam with a Surface Crack

2013 ◽  
Vol 394 ◽  
pp. 121-127
Author(s):  
Li Hua Chen ◽  
Jian Wei Duan ◽  
Yue Sun ◽  
Jing Li
Keyword(s):  
Theoretical Analysis ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Surface Crack ◽  
Natural Frequencies ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Internal Boundary ◽  
Cracked Beam

In this paper, the physical model of the cantilever beam with a surface crack is established to study the free vibration of the cracked beam from three aspects that are theoretical analysis, FEM analysis, and experiment. At the same time, the relation between the crack parameter and the vibration characteristics, which are natural frequencies and the modes of each order, is obtained through analysis. The theoretical analysis is on the basis of the mode analysis theory and applied mechanics. The crack is regarded as a flexible hinge. Utilizing the external boundary conditions and internal boundary conditions at the crack, the free vibration characteristics are obtained combining with the vibration mechanics. With the ANSYS software, a finite element model of the cracked beam is established by the beam element. During the process of calculation, it calculates the natural frequencies and the modes of cracked beam with different parameters of crack. The results obtained from the experiment are in agreement with the results obtained from the theoretical and the FEM analysis. So the accuracy of the theoretical analysis and the numerical simulation is verified by the experiment. At last, the effects of the crack location and depth on the natural frequencies and modes of each order are shown, and it could provide the theoretical, numerical and experimental basis for the identification of cracked materials and the relevant study.

Hybrid Imidazole-Pyridine Derivatives: An Approach to Novel Anticancer DNA Intercalators

2020 ◽  
Vol 27 (1) ◽  
pp. 154-169 ◽  
Author(s):  
Claudiu N. Lungu ◽  
Bogdan Ionel Bratanovici ◽  
Maria Mirabela Grigore ◽  
Vasilichia Antoci ◽  
Ionel I. Mangalagiu
Keyword(s):  
Experimental Data ◽  
Antimicrobial Properties ◽  
Qsar Model ◽  
Therapeutic Effectiveness ◽  
Computational Results ◽  
Pyridine Derivatives ◽  
Quadruplex Dna ◽  
Dna Intercalators ◽  
Structure Activity ◽  
G Quadruplex

Lack of specificity and subsequent therapeutic effectiveness of antimicrobial and antitumoral drugs is a common difficulty in therapy. The aim of this study is to investigate, both by experimental and computational methods, the antitumoral and antimicrobial properties of a series of synthesized imidazole-pyridine derivatives. Interaction with three targets was discussed: Dickerson-Drew dodecamer (PDB id 2ADU), G-quadruplex DNA string (PDB id 2F8U) and DNA strain in complex with dioxygenase (PDB id 3S5A). Docking energies were computed and represented graphically. On them, a QSAR model was developed in order to further investigate the structure-activity relationship. Results showed that synthesized compounds have antitumoral and antimicrobial properties. Computational results agreed with the experimental data.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

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