scholarly journals Natural Frequencies of a Heated Plate: Theory and Experiment

AIAA Journal ◽  
2020 ◽  
Vol 58 (11) ◽  
pp. 4969-4973 ◽  
Author(s):  
Maxim Freydin ◽  
Dani Levin ◽  
Earl H. Dowell ◽  
Santosh Vaibhav Varigonda ◽  
Venkateswaran Narayanaswamy
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Heated Plate ◽  
Theory And Experiment

Correction: Natural Frequencies of a Heated Plate: Theory and Experiment

AIAA Journal ◽  
2021 ◽  
pp. 1-1
Author(s):  
Maxim Freydin ◽  
Dani Levin ◽  
Earl H. Dowell ◽  
Santosh Vaibhav Varigonda ◽  
Venkateswaran Narayanaswamy
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Heated Plate ◽  
Theory And Experiment

Vibroacoustic behavior of a plate surrounded by a cavity containing an inclined part–through surface crack with arbitrary position

2019 ◽  
Vol 25 (17) ◽  
pp. 2365-2379 ◽  
Author(s):  
F. Motaharifar ◽  
M. Ghassabi ◽  
R. Talebitooti
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Surface Crack ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Flexible Plate ◽  
Partial Differential ◽  
Cavity Depth ◽  
Cracked Plate ◽  
Arbitrary Position

Acoustical investigation of a thin plate having a part–through surface crack surrounded by an air enclosure is studied in this paper. The enclosure comprises five rigid walls and a flexible plate based on the Kirchhoff plate theory. It is also assumed that the crack is located at an arbitrary position and orientation with a specific length. Accordingly, partial differential equation related to the coupled cracked plate–cavity system is presented. In order for the partial differential equation (PDE) to be solved, firstly, the sound pressure inside the cavity is estimated by a suitable number of the plate modes. Then, the coupled PDE decomposes to some ordinary differential equations in the time-domain by employing the Galerkin method for three different boundary conditions. In addition, the linear natural frequencies are obtained in vacuo and coupled conditions for an uncracked plate and then, a similar procedure is performed for a cracked plate. Furthermore, comparing the results with available data in the literature shows the reliability and accuracy of the present work. Finally, the influences of the crack angle, crack length, crack position, and cavity depth on the natural frequencies are investigated.

Free Vibration Analysis of Lock Gate Structure

2020 ◽  
Vol 36 (4) ◽  
pp. 507-520
Author(s):  
Deepak Kumar Singh ◽  
Priyaranjan Pal ◽  
S. K. Duggal
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Computer Code ◽  
Computational Error ◽  
Surface Conditions ◽  
Cosine Series ◽  
Gate Structure ◽  
Convergence Study ◽  
Lock Gate

ABSTRACTThe effect of fluid on the natural frequencies of a vertical rectangular lock gate is investigated. The fluid is assumed to be inviscid and incompressible having an irrotational flow field. The far boundary of fluid domain is truncated near the lock gate structure by solving the Laplace equation using Fourier half range cosine series expansion. The formulation of lock gate structure is governed using Mindlin’s plate theory. The coupled interaction between the fluid domain and the lock gate structure is established using finite element method (FEM) and a computer code is written using FORTRAN. Convergence study and validation of the formulation are carried out to minimise the computational error. The natural frequencies of lock gate coupled with and without fluid are determined for undisturbed and linearised free surface conditions. By varying extent of fluid domain, the effect on the natural frequencies of lock gate is evaluated. The results of natural frequencies obtained may be useful to the designer when the reservoir lock gate structure is exposed to the natural disasters.

Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination

2000 ◽  
Vol 123 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Le-Chung Shiau ◽  
Yuan-Shih Chen
Keyword(s):  
Mach Number ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Compressive Load ◽  
Two Dimensional ◽  
Plate Model ◽  
Laminated Beam ◽  
Simply Supported ◽  
Flutter Boundary ◽  
Homogeneous Beam

The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

scholarly journals Realization of mutually unbiased bases for a qubit with only one wave plate: theory and experiment

2015 ◽  
Vol 23 (8) ◽  
pp. 10018 ◽  
Author(s):  
Zhibo Hou ◽  
Guoyong Xiang ◽  
Daoyi Dong ◽  
Chuan-Feng Li ◽  
Guang-Can Guo
Keyword(s):  
Plate Theory ◽  
Mutually Unbiased Bases ◽  
Wave Plate ◽  
Theory And Experiment

Free Bending Vibrations of Adhesively Bonded Orthotropic Plates With a Single Lap Joint

1996 ◽  
Vol 118 (1) ◽  
pp. 122-134 ◽  
Author(s):  
U. Yuceoglu ◽  
F. Toghi ◽  
O. Tekinalp
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Lap Joint ◽  
Orthotropic Plates ◽  
Adhesively Bonded ◽  
Bending Vibrations ◽  
Free Bending

This study is concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The influence of shear deformation and rotatory inertia in plates are taken into account in the equations according to the Mindlin plate theory. The effects of both thickness and shear deformations in the thin adhesive layer are included in the formulation. Plates are assumed to have simply supported boundary conditions at two opposite edges. However, any boundary conditions can be prescribed at the other two edges. First, equations of motion at the overlap region are derived. Then, a Levy-type solution for displacements and stress resultants are used to formulate the problem in terms of a system of first order ordinary differential equations. A revised version of the Transfer Matrix Method together with the boundary and continuity conditions are used to obtain the frequency equation of the system. The natural frequencies and corresponding mode shapes are obtained for identical and dissimilar adherends with different boundary conditions. The effects of some parameters on the natural frequencies are studied and plotted.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

Nonlinear Vibration of Rotating Thin Disks

2000 ◽  
Vol 122 (4) ◽  
pp. 376-383 ◽  
Author(s):  
Albert C. J. Luo ◽  
C. D. Mote,
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlinear Effects ◽  
Linear Vibration ◽  
Rotating Disks ◽  
Nodal Diameter ◽  
Von Karman ◽  
Thin Disks ◽  
Von Kármán

The response and natural frequencies for the linear and nonlinear vibrations of rotating disks are given analytically through the new plate theory proposed by Luo in 1999. The results for the nonlinear vibration can reduce to the ones for the linear vibration when the nonlinear effects vanish and for the von Karman model when the nonlinear effects are modified. They are applicable to disks experiencing large-amplitude displacement or initial flatness and waviness. The natural frequencies for symmetric and asymmetric responses of a 3.5-inch diameter computer memory disk as an example are predicted through the linear theory, the von Karman theory and the new plate theory. The hardening of rotating disks occurs when nodal-diameter numbers are small and the softening of rotating disks occurs when nodal-diameter numbers become larger. The critical speeds of the softening disks decrease with increasing deflection amplitudes. [S0739-3717(00)02004-3]

scholarly journals The Effect of Using Different Elastic Moduli on Vibration of Laminated CFRP Rectangular Plates

2019 ◽  
Vol 2 (1) ◽  
pp. 19-27
Author(s):  
Yoshihiro Narita ◽  
Michio Innami ◽  
Daisuke Narita
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Linear Regression Analysis ◽  
Laminated Composite ◽  
Thin Layers ◽  
Test Accuracy ◽  
Rectangular Plates ◽  
Classical Boundary ◽  
Definition Of

This paper deals with effects of using different sets of material constants on the natural frequencies of laminated composite rectangular plates. The plate is symmetrically laminated by thin layers composed of recently developed carbon fiber reinforced plastic (CFRP) materials. Numerical experiments are conducted by using a semi-analytical solution based on the thin plate theory and the lamination theory. The displacements are assumed to accommodate any combination of classical boundary conditions. The material property is expressed by a set of four elastic constants, and some typical sets of values are cited from the recent literature. Furthermore, a new standard set of discretized constants is proposed to uncover the underlying characteristics of the existing constants. The convergence study is carried out first, and the lowest five natural frequencies are calculated for five sets of classical boundary conditions including totally free through totally clamped cases. Next, a new definition of frequency parameters is introduced to promote more physically meaningful comparison among the obtained results, and the effect of using slightly different constants is clarified for unified comparison and insights. It is also discussed to derive approximate frequency formulas by linear regression analysis and to test accuracy of the formulas.

Multi-Frequency Multi-Modal Excitation of a Heated Annular Plate

2006 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Nonlinear Dynamics ◽  
Internal Resonance ◽  
Radial Direction ◽  
Natural Frequencies ◽  
Annular Plate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Plate Theory ◽  
Frequency Excitation ◽  
The Difference

The forced nonlinear dynamics of a pre-buckled thermally loaded annular plate are investigated. The plate is modeled using the von Ka´rma´n plate theory and the heat equation. The heat, which is generated by the difference between the uniformly distributed temperatures at the inner and outer boundaries, is assumed to symmetrically flow in the radial direction. The amount of heat affects the natural frequencies, which may give rise to different internal resonance conditions. The method of multiple scales is used to examine the system axisymmetric responses when it is driven by an external multi-frequency excitation. The plate responses could be very complex exhibiting Hopf and cyclic-fold bifurcations, quasi-periodicity, chaos, and multiplicity of attractors.

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