scholarly journals Analysis of a 4-span continuous plate in one direction using Matlab programming

2021 ◽  
Vol 27 (2) ◽  
pp. 203-207
Author(s):  
E. I. Adah ◽  
S. E Ubi ◽  
F. O. Idagu ◽  
P. A. Ubi
Keyword(s):  
Boundary Conditions ◽  
Bending Moments ◽  
Shape Functions ◽  
Study Program ◽  
Simply Supported ◽  
Maximum Value ◽  
Percentage Difference ◽  
Fixed End ◽  
Matlab Programming ◽  
Continuous Plate

The present study presents a computer approach based on polynomial shape functions application for analysis of continuous plate in one direction using Matlab. A 4-span continuous plate in the x-direction comprises of boundary conditions SSSC, SCSC, SCSC and SCSS single panels’ plate was analyzed. It was assumed that, the external edges were simply supported while the internal edges of each panel were clamped. The bending moments of the clamped edges were calculated for each panel using appropriate boundary conditions which formed the fixed end moments (FEMs). Stiffness method was used based on beam analogy to analyze the continuous plate. Matlab codes were applied to develop a computer program for this analysis. To validate the results of this present study, the values of the moments obtained were compared with those of earlier studies using manual method. The percentage difference for fixed end moments were all 0.00% and that of support moments had the maximum value of 0.016%. Thus, it was concluded that the present study program based on Matlab is adequate and a faster approach for a 4-span continuous plate in one direction analysis. Keywords: Matlab Programming, Continuous Plate, Polynomial Shape Functions, Beam Analogy, Fixed Edge Moment.

Standardization of Three Efficient Footbridges: Von Mises, Monocontentio and Bicontentio Prototypes.

2021 ◽  
Author(s):  
Mario Guisasola
Keyword(s):  
Boundary Conditions ◽  
Structural Characteristics ◽  
Structural Behavior ◽  
Bending Moments ◽  
Variable Depth ◽  
Constant Depth ◽  
Simply Supported ◽  
Vertical Walls ◽  
Basic Concepts ◽  
Von Mises

<p>The Von Mises, Monocontentio and Bicontentio footbridges are three parameterized metal bridge whose main structural characteristics are their variable depth depending on the applied stress and the embedding of abutments. Its use is considered suitable for symmetrical or asymmetrical topographies with slopes or vertical walls on one or both edges. The footbridges include spans spaced apart by 20 to 66 meters, and are between 2 to 4.5 meters wide.</p><p>Its design is based on five basic concepts: integration in the geometry of the environment; continuous search for simplicity; design based on a geometry that emanates from structural behavior; unitary and round forms; and long- lasting details.</p><p>The structural behavior of these prototypes has been compared with three types of constant-depth metal beams: the bridge simply supported, and the bridge embedded on one or both sides.</p><p>The embedding of abutments, and the adoption of a variation of depth adapted to the bending moments diagrams, allow for more efficient and elegant forms which are well-adapted to the boundary conditions.</p>

Vibration of Beam-Mass Systems With Time-Dependent Boundary Conditions

1959 ◽  
Vol 26 (3) ◽  
pp. 353-356
Author(s):  
T. C. Yen ◽  
S. Kao
Keyword(s):  
Boundary Conditions ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Simply Supported ◽  
Vibration Problems ◽  
Fixed End

Abstract Vibration problems of beams with time-dependent boundary conditions are solved by the method of Laplace transforms. The problems treated include the simply supported, cantilevered, and fixed beams carrying a single arbitrarily placed mass; two equal masses symmetrically placed on a simply supported or fixed-end beam and a beam carrying a mass at the center and two equal masses at tips, striking a spring.

scholarly journals An Electrostatic Self-Excited Resonator with Pre-Tension/Pre-Compression Constraint for Active Rotation Control

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 650
Author(s):  
Ruide Yun ◽  
Yangsheng Zhu ◽  
Zhiwei Liu ◽  
Jianmei Huang ◽  
Xiaojun Yan ◽  
...  
Keyword(s):  
Maximum Velocity ◽  
Flapping Wings ◽  
Variable Velocity ◽  
Beam Length ◽  
Dc Voltage ◽  
Middle Position ◽  
Simply Supported ◽  
Maximum Value ◽  
Constraint Structure

We report a novel electrostatic self-excited resonator driven by DC voltage that achieves variable velocity-position characteristics via applying the pre-tension/pre-compression constraint. The resonator consists of a simply supported micro-beam, two plate electrodes, and two adjustable constraint bases, and it can be under pre-compression or pre-tension constraint by adjusting the distance L between two constraint bases (when beam length l > L, the resonator is under pre-compression and when l < L, it is under pre-tension). The oscillating velocity of the beam reaches the maximum value in the position around electrodes under the pre-compression constraint and reaches the maximum value in the middle position between two electrodes under the pre-tension condition. By changing the constraint of the microbeam, the position of the maximum velocity output of the oscillating beam can be controlled. The electrostatic self-excited resonator with a simple constraint structure under DC voltage has great potential in the field of propulsion of micro-robots, such as active rotation control of flapping wings.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Rayleigh-Ritz Analysis of Vibrating Plates Based on a Class of Eigenfunctions

2009 ◽  
Author(s):  
Giuseppe Catania ◽  
Silvio Sorrentino
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Linear Combination ◽  
Equation Of Motion ◽  
Extensive Literature ◽  
Shape Functions ◽  
Element Analysis ◽  
Vibrating Plates ◽  
General Basis

In the Rayleigh-Ritz condensation method the solution of the equation of motion is approximated by a linear combination of shape-functions selected among appropriate sets. Extensive literature dealing with the choice of appropriate basis of shape functions exists, the selection depending on the particular boundary conditions of the structure considered. This paper is aimed at investigating the possibility of adopting a set of eigenfunctions evaluated from a simple stucture as a general basis for the analysis of arbitrary-shaped plates. The results are compared to those available in the literature and using standard finite element analysis.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Vibrational Analysis of a Single-Layered Nanoporous Graphene Membrane

NANO ◽  
2016 ◽  
Vol 11 (04) ◽  
pp. 1650043 ◽  
Author(s):  
Haw-Long Lee ◽  
Win-Jin Chang
Keyword(s):  
Boundary Conditions ◽  
Vibrational Analysis ◽  
Atomic Scale ◽  
Good Correspondence ◽  
Graphene Layers ◽  
Simply Supported ◽  
Vibrational Behavior ◽  
Fundamental Frequencies ◽  
Nanoporous Graphene ◽  
New Applications

In this study, we use the atomic-scale finite element method to investigate the vibrational behavior of the armchair- and zigzag-structured nanoporous graphene layers with simply supported-free-simply supported-free (SFSF) and clamped-free-free-free (CFFF) boundary conditions. The fundamental frequencies computed for the graphene layers without pores are compared with the results of previous studies. We observe very good correspondence of our results with that of the other studies in all the considered cases. For the armchair- and zigzag-structured nanoporous graphenes with SFSF and CFFF boundary conditions, the frequencies decrease with increasing porosity. When the positions of the pores are symmetric with respect to the center of the graphene, the frequency of the zigzag nanoporous graphene is higher than that of the armchair one. To the best of our knowledge, this is first study investigating the relation between the vibrational behavior and porosity of nanoporous graphene layers, which is essential for tuning the material/structural design and exploring new applications for nanoporous graphenes.

Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

1992 ◽  
Author(s):  
L. T. Lee ◽  
W. F. Pon
Keyword(s):  
Boundary Conditions ◽  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Energy Functional ◽  
Comprehensive Treatment ◽  
Energy Functionals ◽  
Simply Supported ◽  
Cartesian Coordinate

Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

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