Free Vibration of Continuous Skin-Stringer Panels

1960 ◽  
Vol 27 (4) ◽  
pp. 669-676 ◽  
Author(s):  
Y. K. Lin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Structural Configuration ◽  
Modes Of Vibration ◽  
Fuselage Skin

The determination of the natural frequencies and normal modes of vibration for continuous panels, representing more or less typical fuselage skin-panel construction for modern airplanes, is discussed in this paper. The time-dependent boundary conditions at the supporting stringers are considered. A numerical example is presented, and analytical results for a particular structural configuration agree favorably with available experimental measurements.

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.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

NUMERICAL AND EXPERIMENTAL STUDY ON FREE VIBRATION OF DELAMINATED WOVEN FIBER GLASS/EPOXY COMPOSITE PLATES

2012 ◽  
Vol 12 (02) ◽  
pp. 377-394 ◽  
Author(s):  
J. MOHANTY ◽  
S. K. SAHU ◽  
P. K. PARHI
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Fiber Glass ◽  
Number Of Layers

This paper presents a combined experimental and numerical study of free vibration of industry-driven woven fiber glass/epoxy (G/E) composite plates with delamination. Using the first-order shear deformation theory, an eight-noded two-dimensional quadratic isoparametric element was developed, which has five degrees of freedom per node. In the experimental study, the influence of various parameters such as the delamination size, boundary conditions, fiber orientations, number of layers, and aspect ratio on the natural frequencies of delaminated composite plates are investigated. Comparison of the numerical results with experimental ones shows good agreement. Fundamental natural frequencies are found to decrease with the increase in the delamination size and fiber orientation and increases with the increase in the number of layers and aspect ratio of delaminated composite plates. The natural frequency of the delaminated composite plate varies significantly for different boundary conditions.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

2019 ◽  
Vol 55 (1-2) ◽  
pp. 42-52
Author(s):  
Milad Ranjbaran ◽  
Rahman Seifi
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

This article proposes a new method for the analysis of free vibration of a cracked isotropic plate with various boundary conditions based on Kirchhoff’s theory. The isotropic plate is assumed to have a part-through surface or internal crack. The crack is considered parallel to one of the plate edges. Existence of the crack modified the governing differential equations which were formulated based on the line-spring model. Generalized differential quadrature method discretizes the obtained governing differential equations and converts them into an algebraic system of equations. Then, an eigenvalue analysis was used to determine the natural frequencies of the cracked plates. Some numerical results are given to demonstrate the accuracy and convergence of the obtained results. To demonstrate the efficiency of the method, the results were compared with finite element solutions and available literature. Also, effects of the crack depth, its location along the thickness, the length of the crack and different boundary conditions on the natural frequencies were investigated.

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.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

Flexural and free vibration control of smart epoxy composite beams using shape memory alloy wires actuator

2020 ◽  
Vol 31 (13) ◽  
pp. 1557-1566 ◽  
Author(s):  
Mohsen Gol Zardian ◽  
Navid Moslemi ◽  
Farzin Mozafari ◽  
Soheil Gohari ◽  
Mohd Yazid Yahya ◽  
...  
Keyword(s):  
Shape Memory Alloy ◽  
Free Vibration ◽  
Shape Memory ◽  
Natural Frequencies ◽  
Composite Beams ◽  
Dynamic Responses ◽  
Beam Deflection ◽  
Engineering Structures ◽  
Fiber Fractions ◽  
Modes Of Vibration

Shape memory alloys are increasingly used in numerous smart engineering structures. This study experimentally investigates static flexural and free vibration characteristics of composite beams reinforced with shape memory alloy wires. The key to this study is using shape memory alloy fibers as a means for influencing and tuning the static and dynamic responses of structures. A series of static three-point bending and modal experiments is performed to capture the capability of shape memory alloy wires in controlling the static and dynamic responses of a reinforced beam. Static and dynamic behaviors of the fiber-reinforced beam with different volumetric fiber fractions are examined. Before heat excitation, increasing the number of shape memory alloy wires leads to higher beam stiffness and lower beam deflection. However, with both heat activation and the higher number of shape memory alloy wires, beam deflection is significantly reduced. The modal vibration tests demonstrated that when shape memory alloy wires are not activated, the magnitude of natural frequencies slightly decreases by increasing the number of shape memory alloy wires. However, with heat excitation, the higher number of shape memory alloy wires, in contrast, increases the magnitude of natural frequencies. Furthermore, the higher number of activated shape memory alloy wires shows to predominantly increase the magnitude of higher modes of vibration rather than lower modes.

Applications of Infrared Methods in the Structural Examination of Synthetic Rubber

1946 ◽  
Vol 19 (4) ◽  
pp. 1113-1123 ◽  
Author(s):  
J. E. Field ◽  
D. E. Woodford ◽  
S. D. Gehman
Keyword(s):  
Absorption Spectra ◽  
Organic Molecules ◽  
Normal Modes ◽  
Structural Variations ◽  
Structural Examination ◽  
Absorption Bands ◽  
Synthetic Rubber ◽  
Modes Of Vibration ◽  
Long Chain

Abstract Infrared absorption spectra have been long recognized as a convenient means for studying the structure of organic molecules. The interpretations of the spectra are based on the energy interactions of the molecule and the radiations which arise from the vibration of the constituent atoms and molecular rotations. For simple or highly symmetrical molecules, the determination of the normal modes of vibration and the calculation of the absorbing frequencies are relatively simple and straightforward. For more complicated organic molecules, this becomes increasingly difficult because with each additional atom, the number of degrees of freedom is increased by three and the determination of the normal modes of vibration becomes practically impossible. However, interpretations can be made to a useful extent through empirical comparisons with the absorption spectra of simpler known structures. The data that have been accumulated by investigators in this field have made it possible to assign rather definite absorption frequencies to some of the chemical linkages and functional groups. These correlations which have appeared in numerous places in the literature are partially reproduced in Table I. Organic compounds generally have strong absorption bands below 1300 cm−1, to which few definite assignments can be made with certainty because the vibrations of many of the atoms of the molecule may be involved rather than a specific part of it. It is clear that such empirical relationships must be relied upon in studying the structural variations of the long chain, complex molecules which occur in butadiene and isoprene polymers and copolymers and other synthetic rubbers. This procedure has been applied to determine the effects of oxidation and of variations in monomers and polymerizing conditions on the structure of synthetic rubber. It is practically certain that physical deficiencies of synthetic rubber are due principally to the structure of the long chain molecules rather than to the chemical nature of the monomers used.

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