Optimal Forms of Shallow Cylindrical Panels With Respect to Vibration and Stability

1986 ◽  
Vol 53 (1) ◽  
pp. 135-140 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Surface Area ◽  
Fundamental Frequency ◽  
Axial Load ◽  
Cylindrical Panel ◽  
Buckling Load ◽  
Material Surface ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Cylindrical Panels

Thin, shallow, elastic, cylindrical panels with rectangular planform are considered. We seek the midsurface form which maximizes the fundamental frequency of vibration, and the form which maximizes the buckling value of a uniform axial load. The material, surface area, and uniform thickness of the panel are specified. The curved edges are simply supported, while the straight edges are either simply supported or clamped. For the clamped case, the optimal panels have zero slope at the edges. In the examples, the maximum fundamental frequency is up to 12 percent higher than that of the corresponding circular cylindrical panel, while the buckling load is increased by as much as 95 percent. Most of the solutions are bimodal, while the rest are either unimodal or trimodal.

Optimal Forms of Shallow Shells With Circular Boundary, Part 3: Maximum Enclosed Volume

1984 ◽  
Vol 51 (3) ◽  
pp. 536-539 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Spherical Shell ◽  
Surface Area ◽  
Material Surface ◽  
Uniform Thickness ◽  
Base Plane ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part ◽  
Uniformly Distributed Loads

In Parts 1 and 2, we determined optimal forms of shallow shells with respect to vibration and stability, respectively. In this final part, we consider a given load and find the shell form for which the volume between the base plane and the deflected shell is a maximum. As before, the shell is assumed to be thin, elastic, and axisymmetric, with a given circular boundary that is either clamped or simply supported. The material, surface area, and uniform thickness of the shell are specified. Both uniformly distributed loads and concentrated central loads are treated. In the numerical results, the maximum enclosed volume is on the order of 10 percent higher than that for the corresponding spherical shell.

Optimal Forms of Shallow Shells With Circular Boundary, Part 1: Maximum Fundamental Frequency

1984 ◽  
Vol 51 (3) ◽  
pp. 526-530 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson ◽  
R. Parbery
Keyword(s):  
Boundary Conditions ◽  
Fundamental Frequency ◽  
Iterative Procedure ◽  
Material Surface ◽  
Uniform Thickness ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Axisymmetric Shell ◽  
Boundary Part

Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.

scholarly journals Post-Buckling Behaviour of laminated Cylindrical Panels with/without Cut-Outs

2019 ◽  
Vol 8 (3) ◽  
pp. 8026-8030
Keyword(s):  
Compressive Load ◽  
Laminated Composite ◽  
Cylindrical Panel ◽  
Buckling Load ◽  
Equilibrium Path ◽  
Cylindrical Panels ◽  
Post Buckling ◽  
The Impact ◽  
Generalized Finite Element ◽  
Composite Cylindrical Panel

Buckling and post-buckling analysis of isotropic and laminated composite cylindrical plates/panels under compressive load has been done by equilibrium path approach (arc-length technique). The impact of cut outs on buckling and post-buckling load of an isotropic and laminated composite cylindrical plates/panels has been assessed by utilizing summed up generalized finite element programming ANSYS. In post-buckling Eigen mode imperfection shape is picked for creating geometric undulations on cylindrical panels with/without circular cut-outs. The impact of the area and size of the cut out and furthermore the composite utilize point on the buckling load of laminated composite cylindrical panel is explored with simply supported boundary conditions. The post-buckling consequences of laminated cylindrical panels have been validated with existing appropriate writing (18) and are additionally stretched out for analysis of sheets/plates with cutouts. It has been seen that the as the curvature of the panel increases load bearing capacity is increasing irrespective of the material and with/without cut out.

Influence of Modal Coupling on the Nonlinear Vibration of Simply Supported Cylindrical Panels

2016 ◽  
Vol 849 ◽  
pp. 106-118 ◽  
Author(s):  
Frederico Martins Alves da Silva ◽  
Henrique Araújo Rodrigues Sattler ◽  
Paulo Batista Gonçalves ◽  
Zenón José Guzmán Nunñez del Prado
Keyword(s):  
Lateral Displacement ◽  
Equations Of Motion ◽  
Basins Of Attraction ◽  
Cylindrical Panel ◽  
Simply Supported ◽  
Modal Coupling ◽  
Cylindrical Panels ◽  
Circumferential Displacement ◽  
Low Dimensional ◽  
Standard Galerkin Method

The aim of this paper is to analyse the influence of the nonlinear modal coupling on the nonlinear vibrations of a simply supported cylindrical panel excited by a time dependent transversal load. The cylindrical panel is modeled by the Donnell nonlinear shallow shell theory and the lateral displacement field is based on a perturbation procedure. The axial and circumferential displacement are described in terms of the obtained lateral displacement, generating a precise low-dimensional model that satisfies all transversal boundary conditions. The discretized equations of motion in time domain are determined by applying the standard Galerkin method. Various numerical techniques are employed to obtain the cylindrical panel resonance curves, bifurcation scenario and basins of attraction. The results show the influence of geometry and the nonlinear modal coupling on the nonlinear response of the cylindrical panel.

Design of Composite Cylindrical Panels for Maximum Axial and Shear Buckling Capacity

1991 ◽  
Vol 113 (3) ◽  
pp. 204-209 ◽  
Author(s):  
N. Kumar ◽  
T. R. Tauchert
Keyword(s):  
Composite Material ◽  
Nonlinear Programming ◽  
Aspect Ratio ◽  
Ritz Method ◽  
Cylindrical Panel ◽  
Geometrical Parameters ◽  
Simply Supported ◽  
Design Variables ◽  
Cylindrical Panels ◽  
Shear Buckling

Response of a cylindrical panel made of layers of composite material and subjected to in-plane loads is investigated. Prebuckling deformations are determined for antisymmetric angle-ply and cross-ply panels having simply supported boundary conditions. Buckling solutions are obtained via the Rayleigh-Ritz method. Nonlinear programming is used to optimize the designs. Design variables are taken as fiber orientations and/or thicknesses of different layers. Numerical results are presented for different materials and different geometrical parameters, including aspect ratio and curvature-to-length ratio.

Nonlinear dynamic response and vibration of imperfect eccentrically stiffened sandwich third-order shear deformable FGM cylindrical panels in thermal environments

2017 ◽  
Vol 21 (8) ◽  
pp. 2816-2845 ◽  
Author(s):  
Nguyen D Duc ◽  
Ngo Duc Tuan ◽  
Phuong Tran ◽  
Tran Q Quan ◽  
Nguyen Van Thanh
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Geometrical Nonlinearity ◽  
Cylindrical Panel ◽  
Geometrical Parameters ◽  
Third Order ◽  
Nonlinear Dynamic Response ◽  
Elastic Foundations ◽  
Thermal Environments ◽  
Cylindrical Panels

This study follows an analytical approach to investigate the nonlinear dynamic response and vibration of eccentrically stiffened sandwich functionally graded material (FGM) cylindrical panels with metal–ceramic layers on elastic foundations in thermal environments. It is assumed that the FGM cylindrical panel is reinforced by the eccentrically longitudinal and transversal stiffeners and subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution. Based on the Reddy’s third-order shear deformation shell theory, the motion and compatibility equations are derived taking into account geometrical nonlinearity and Pasternak-type elastic foundations. The outstanding feature of this study is that both FGM cylindrical panel and stiffeners are assumed to be deformed in the presence of temperature. Explicit relation of deflection–time curves and frequencies of FGM cylindrical panel are determined by applying stress function, Galerkin method and fourth-order Runge-Kutta method. The influences of material and geometrical parameters, elastic foundations and stiffeners on the nonlinear dynamic and vibration of the sandwich FGM panels are discussed in detail. The obtained results are validated by comparing with other results in the literature.

Spatial Actuation Effectiveness of Segmented Actuators on Parabolic Cylindrical Panels

2012 ◽  
Author(s):  
S. D. Hu ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Shape Control ◽  
Cylindrical Panel ◽  
Design Parameters ◽  
Modal Control ◽  
Control Force ◽  
Optimal Position ◽  
Meridional Direction ◽  
Cylindrical Panels ◽  
Active Vibration ◽  
Control Forces

With the distinct capability of line-focusing, open parabolic cylindrical panels are commonly used as key components of radar antennas, space reflectors, solar collectors, etc. These structures suffer unexpected vibrations from the fluctuation of base structure, non-uniform heating and air flow. The unwanted vibration will reduce the surface reflecting precision and even result in structure damages. To explore active vibration and shape control of parabolic cylindrical panels, this study focuses on actuation effectiveness induced by segmented piezoelectric patches laminated on a flexible parabolic cylindrical panel. The mathematical model of a parabolic cylindrical panel laminated with distributed actuators is formulated. The segmentation technique is developed and applied to parabolic cylindrical panels, and the piezoelectric layer is segmented uniformly in the meridional direction. The distributed actuator patches induced modal control forces are evaluated. As the area of actuator patch varies in the meridional direction, modal control force divided by actuator area, i.e., actuation effectiveness, is investigated. Spatial actuation effectiveness, including its membrane and bending components are evaluated with respect to design parameters: actuator size and position, shell curvature, shell thickness and vibration mode in case studies. The actuation component induced by the membrane force in the meridional direction mainly contributes to the total actuation effectiveness for lower modes. Average and cancellation effect of various actuator sizes and the optimal actuator position are also discussed. Results suggest that for odd vibration modes, the maximal actuation effectiveness locates at the ridge of the panel; while for even modes, the peak/valley closest to the ridge is the optimal position to obtain the maximal actuation effectiveness. A segmentation scheme of the meridian interval angle 0.0464rad for the investigated standard panel is a preferred tradeoff between the actuation effectiveness and practical feasibility. The modal actuation effectiveness increases with the shell curvature, whereas decreases when the shell thickens.

Computation of natural frequencies of skewed slabs using equivalent rectangular slab concept

1980 ◽  
Vol 7 (2) ◽  
pp. 384-388 ◽  
Author(s):  
T. I. Campbell ◽  
W. H. Siu
Keyword(s):  
Isotropic Material ◽  
Natural Frequencies ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Linear Elastic ◽  
Rectangular Slab

The natural frequencies of skewed slabs (in the shape of a parallelogram) of uniform thickness and linear elastic isotropic material are considered. It is shown that the natural frequencies of a skewed slab can be related to those of the corresponding rectangular slab by means of an equivalent rectangular slab concept. Charts are presented to allow the computation of the natural frequencies of one-, two-, and three-span symmetric skewed slabs, which are simply supported at each end and free along each edge.

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