Vibration Propagation in Ordered and Disordered Orthotropic Single-Leaf Rib-Stiffened Panels

2011 ◽  
Vol 317-319 ◽  
pp. 287-291 ◽  
Author(s):  
Da Ye Yu ◽  
Gui Lan Yu
Keyword(s):  
Periodic Structures ◽  
Plate Theory ◽  
Torsional Rigidity ◽  
Span Length ◽  
Bending Rigidity ◽  
Stiffened Panels ◽  
Vibration Localization ◽  
Single Leaf ◽  
Thin Plate Theory ◽  
Relative Bending Rigidity

Abstract Based on the thin plate theory and the transfer matrix method, the vibration propagation in periodical orthotropic single-leaf rib-stiffened panels is studied. The localization factors of the ordered and disordered periodic systems are calculated. The numerical results show that the anisotropy of the plate affects the propagation of vibration in the pannels. With the relative bending rigidity increasing, or with the relative torsional rigidity increasing, the width of stopbands increases in low dimenionless frequencies. The vibration localization phenomenon occurs in the span-length disordered periodic structures and it is enhanced with the increasing disorder of span-length.

scholarly journals Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

2021 ◽  
Vol 43 (5) ◽  
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Thin Plate ◽  
Strain Gradient ◽  
Plate Theory ◽  
Laminated Composite ◽  
Equilibrium Equations ◽  
Thin Plate Theory ◽  
Bending Behavior ◽  
Hygrothermal Environment ◽  
Load Types ◽  
Novel Applications

AbstractIn this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

2007 ◽  
Vol 129 (5) ◽  
pp. 559-566 ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Vibration Suppression ◽  
Periodic Structures ◽  
Electric Circuit ◽  
Forced Response ◽  
Bladed Disks ◽  
Vibration Localization ◽  
Network Concept ◽  
Engine Order ◽  
The Individual ◽  
Local Circuits

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Study on Gradual Deformation and Prediction Model of the Mined Overburden

2012 ◽  
Vol 524-527 ◽  
pp. 699-704
Author(s):  
Xiao Gang Xia ◽  
Yun Feng Yang
Keyword(s):  
Boundary Condition ◽  
Plate Theory ◽  
Surface Expression ◽  
Rock Deformation ◽  
Double Trigonometric Series ◽  
Mechanics Model ◽  
Thin Plate Theory ◽  
Gradual Deformation ◽  
Exchange Condition ◽  
Gradual Transformation

Based on the overburden three caving feature, the deformation of mining rock process was devided and the criterion of gradual transformation of each stages deformation were given. Then , combined the thin-plate theory, the differential models were derived for rock deformation in level and similar to level bured condition. The boundary condition of each models and exchange condition between different models were put forward and the gradual mechanics model was set up.The subsidence model before roof collapse was solved by Navier double trigonometric series and the deflection surface expression of rock deformation was put forword. At last, the reliability and practicality of the models was verified by engineering examples.

Normal Loading on a Wedge-Shaped Plate

1955 ◽  
Vol 6 (3) ◽  
pp. 196-204 ◽  
Author(s):  
D. E. R. Godfrey
Keyword(s):  
Thin Plate ◽  
Mellin Transform ◽  
Plate Theory ◽  
Normal Loading ◽  
Thin Plate Theory

SummaryThe equations of thin plate theory are expressed in polar co-ordinates and transformed using the Mellin transform. Problems involving discontinuous and isolated normal loadings may then be solved in the case of the built-in or freely supported wedge-shaped boundary.

On the Vibration of Layered Sandwich Elastic Plates

2008 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku
Keyword(s):  
Plate Theory ◽  
Impact Damage ◽  
Local Buckling ◽  
Recent Analysis ◽  
Sandwich Plates ◽  
Elastic Plates ◽  
Interface Pressure ◽  
Engineering Structures ◽  
Thin Plate Theory ◽  
Operational Methods

Sandwich elastic plates have found increasing applications in civil, aerospace, military and offshore industries to enhance superior resistance to fatigue crack propagation, impact damage, local buckling and are very effective for vibration damping and noise reduction. Such structural application has significantly led to reduction in vulnerability of warships to blasts, ballistics, bomb and fire attacks. In engineering structures, one of the effective ways of damping vibration and noise attenuation, is to exploit the occurrence of slip at the interface of structural laminates where such members are held together in a pressurised environment. Recent analysis and experimental investigation of vibration characteristics and damping properties of layered sandwich structures, are mostly limited to elastic beams. This paper is an attempt to extend such analytical investigations to layered sandwich plates. By employing contact mechanics and laminated thin plate theory, the generalised equation governing the vibration of two layered sandwich plates that are held together in pressurised environment is presented. In particular, by invoking operational methods for the case of linear interface pressure distribution, closed form analytical results for the system natural frequency and dynamic response under external excitation are reported for design analysis and applications.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

Prediction of Vibration Properties of Sandwich Panel Using Thick Plate Theory

2001 ◽  
Author(s):  
Qunli Liu ◽  
Yi Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Principle ◽  
Free Vibration ◽  
Thick Plate ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Vibration Properties ◽  
Proposed Model ◽  
Thin Plate Theory

Abstract The vibration of a sandwich panel with two identical isotropic facesheets and an orthotropic core was studied. The governing partial differential equation was derived using variational principle. Kirchhoff’s theory was applied to describe the deformation of the panel, and the rotational effect was taken into consideration. The frequencies of free vibration of a rectangular panel can be predicted based on the proposed analytical model. Results based on the proposed model were compared with those from thin plate theory. The effect of orthotropic core on frequencies was also discussed.

On the Transient Response of a Two-Dimensional Floating Runway During Airplane Take-Off

2007 ◽  
Author(s):  
Dingwu Xia ◽  
R. Cengiz Ertekin
Keyword(s):  
Transient Response ◽  
Plate Theory ◽  
Moving Load ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Jump Conditions ◽  
Thin Plate Theory ◽  
Parametric Studies ◽  
The Finite Difference Method ◽  
Level I

The transient response of a two-dimensional floating runway subject to dynamic moving load due to airplane landing and take-off is studied in this paper. This hydroelastic problem is formulated by directly coupling the structure with fluid, by use of the Level I Green-Naghdi theory for the fluid motion and the Kirchhoff thin plate theory for the runway. The coupled fluid-structure system, together with the appropriate jump conditions are solved by the finite difference method. The results, including hydroelastic deformation of the runway and the drag force on the airplane are predicted and compared with the available results. Favorable agreements are observed. Parametric studies are carried out to identify the important factors for the design of floating runways.

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