Free Vibration Analysis of Angle-ply Laminated Shallow Cylindrical Shell with Clamped Edges

2000 ◽  
Vol 123 (2) ◽  
pp. 188-197 ◽  
Author(s):  
Kenji Hosokawa ◽  
Minehiro Murayama ◽  
Toshiyuki Sakata
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Numerical Approach ◽  
Free Vibrations ◽  
Numerical Results ◽  
Mode Shapes ◽  
Shallow Cylindrical Shell ◽  
Plastic Composite ◽  
Vibration Tests

In a previous paper, the authors proposed a numerical approach for analyzing the free vibrations of a laminated FRP (fiber reinforced plastic) composite plate. In the present paper, this approach is modified for application to a symmetrically laminated shallow cylindrical shell having a rectangular planform. First, the natural frequencies of the shell are calculated for discussion of the convergence and accuracy of the solution. Next, the effects of the curvature ratio and stacking sequence on the natural frequencies and mode shapes of the shell are studied. Furthermore, to justify the numerical results, vibration tests of the clamped symmetrically laminated shallow cylindrical shell having a square planform are carried out. These experimental results are found to agree well with the numerical results computed using the measured material properties of the lamina.

Comparison of Vibration Characteristics of Stiffened Composite Shallow Circular Cylindrical Shell Panels

2002 ◽  
Author(s):  
V. O¨zerciyes ◽  
U. Yuceoglu
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Free Vibrations ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Shallow Cylindrical Shell ◽  
Parametric Studies ◽  
Complete Set ◽  
Hit And Run

The problem of “Free Vibrations Centrally and Non Centrally Stiffened Composite Shallow Cylindrical Shell Panels” are briefly considered and their vibration characteristics are compared, in detail, in terms of their natural frequencies and the corresponding mode shapes. First, the complete set of composite shallow cylindrical shell equations are reduced to a system of first order ordinary differential equations in “state-vector” form. Then, by making use of the “Modified Transfer Matrix Method”, the effects of the position and the width of the stiffening shell strip in the natural frequencies and the mode shapes of the panel system are plotted and compared. Some significant results of parametric studies and also the possibility of some kind of hit-and-run type of optimization are presented.

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.

scholarly journals Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

2011 ◽  
Vol 18 (5) ◽  
pp. 709-726 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural Elements ◽  
Mass System ◽  
Assembly Technique

The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1—Free Vibration Analysis

2012 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Centrifugal Stiffening

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.

Measurement of Young’s Modulus and Shear Modulus of Some Structures Welded Using Flux Cored Wire by Vibration Tests

2014 ◽  
Vol 216 ◽  
pp. 151-156 ◽  
Author(s):  
Liviu Bereteu ◽  
Mircea Vodǎ ◽  
Gheorghe Drăgănescu
Keyword(s):  
Shear Modulus ◽  
Arc Welding ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Vibration Modes ◽  
Cored Wire ◽  
Flux Cored Arc Welding ◽  
Longitudinal Elastic Modulus ◽  
Vibration Tests ◽  
Non Destructive

The aim of this work was to determine by vibration tests the longitudinal elastic modulus and shear modulus of welded joints by flux cored arc welding. These two material properties are characteristic elastic constants of tensile stress respectively torsion stress and can be determined by several non-destructive methods. One of the latest non-destructive experimental techniques in this field is based on the analysis of the vibratory signal response from the welded sample. An algorithm based on Pronys series method is used for processing the acquired signal due to sample response of free vibrations. By the means of Finite Element Method (FEM), the natural frequencies and modes shapes of the same specimen of carbon steel were determined. These results help to interpret experimental measurements and the vibration modes identification, and Youngs modulus and shear modulus determination.

Dynamic characteristics of horizontally curved bridges

2017 ◽  
Vol 24 (19) ◽  
pp. 4465-4483 ◽  
Author(s):  
Mohsen Amjadian ◽  
Anil K Agrawal
Keyword(s):  
Free Vibration ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Response Spectrum ◽  
Translational Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Curved Bridges ◽  
Horizontally Curved ◽  
Horizontally Curved Bridges

Horizontally curved bridges have complicated dynamic characteristics because of their irregular geometry and nonuniform mass and stiffness distributions. This paper aims to develop a simplified and practical method for the calculation of the natural frequencies and mode shapes of horizontally curved bridges that would be of interest to bridge engineers for the estimation of the seismic response of these types of bridges. For this purpose, a simple three-degree-of-freedom (3DOF) dynamic model for free vibration equation of this type of bridge has been developed. It is shown that the translational motion of the deck of horizontally curved bridges in the direction that is perpendicular to their axis of symmetry is always coupled with the rotational motion of the deck, regardless of the location of the stiffness center. The model is further exploited to develop closed-form formulas for the estimation of the maximum displacements of the corners of the deck of one-way asymmetric horizontally curved bridges. The accuracy of the model is verified by finite-element model of a horizontally curved bridge prototype in OpenSEES. Finally, the model is utilized to study the influence of the location of the stiffness center with respect to the deck curvature center on the natural frequency and the maximum displacements of the corners of the deck for different curvatures of the deck. The results of free vibration analysis show that the natural frequencies of one-way asymmetric horizontally curved bridges, in general, increase with the increase of the subtended angle of the deck. The results of earthquake response spectrum analysis show that the increase in the subtended angle of one-way asymmetric horizontally curved bridges decreases the radial displacements of the corners of the deck but increases the azimuthal displacement. These two responses both increase with the increase in the distance between the stiffness center and the curvature center.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

scholarly journals Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

2021 ◽  
Vol 11 (21) ◽  
pp. 10485
Author(s):  
Hao Yu ◽  
Feng Liang ◽  
Yu Qian ◽  
Jun-Jie Gong ◽  
Yao Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Band Gap ◽  
Cross Section ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Critical Parameters ◽  
Mode Shapes ◽  
Beam Model ◽  
The Impact ◽  
Fluid Conveying Pipes

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

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.

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