Accurate Analytical-Type Solutions for the Free Vibration of Simply-Supported Parallelogram Plates

1991 ◽  
Vol 58 (1) ◽  
pp. 203-208 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Equal Length ◽  
Superposition Method ◽  
Vibration Modes ◽  
Type Solution ◽  
Simply Supported ◽  
Wide Range ◽  
Plate Geometry ◽  
Special Case ◽  
Comprehensive Study

A comprehensive study of the free vibration of simply-supported parallelogram plates is conducted. Solutions are obtained by utilizing the superposition method and by taking advantage of symmetry inherent in the problem. Toward this end a new alternating Le´vy-type solution is introduced. Verification tests are conducted by comparing computed eigenvalues with those of rhombic plates in the special case where all plate edges are of equal length. Eigenvalues are stored for eight vibration modes and for a wide range of plate geometry.

scholarly journals A Highly Accurate and Efficient Analytical Approach to Bridge Deck Free Vibration Analysis

2000 ◽  
Vol 7 (6) ◽  
pp. 399-412 ◽  
Author(s):  
D.J. Gorman ◽  
L. Garibaldi
Keyword(s):  
Free Vibration ◽  
Bridge Deck ◽  
Bridge Decks ◽  
Free Vibration Analysis ◽  
Free Edge ◽  
Mode Shapes ◽  
Superposition Method ◽  
Type Solution ◽  
Edge Type ◽  
Edge Conditions

The superposition method is employed to obtain an accurate analytical type solution for the free vibration frequencies and mode shapes of multi-span bridge decks. Free edge conditions are imposed on the long edges running in the direction of the deck. Inter-span support is of the simple (knife-edge) type. The analysis is valid regardless of the number of spans or their individual lengths. Exact agreement is found when computed results are compared with known eigenvalues for bridge decks with all spans of equal length. Mode shapes and eigenvalues are presented for typical bridge decks of three and four span lengths. In each case torsional and non-torsional modes are studied.

scholarly journals New Analytic Free Vibration Solutions of Rectangular Thick Plates With a Free Corner by the Symplectic Superposition Method

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Rui Li ◽  
Pengcheng Wang ◽  
Bo Wang ◽  
Chunyu Zhao ◽  
Yewang Su
Keyword(s):  
Free Vibration ◽  
Analytic Solutions ◽  
The Other ◽  
Superposition Method ◽  
Element Analysis ◽  
Thick Plates ◽  
Simply Supported ◽  
Vibrating Plates ◽  
First Time ◽  
Mathematical Derivation

Seeking analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges is of significance for an insight into the performances of related engineering devices and structures as well as their rapid design. A challenging set of problems concern the vibrating plates with a free corner, i.e., those with two adjacent edges free and the other two edges clamped or simply supported or one of them clamped and the other one simply supported. The main difficulty in solving one of such problems is to find a solution meeting both the boundary conditions at each edge and the condition at the free corner, which is unattainable using a conventional analytic method. In this paper, for the first time, we extend a novel symplectic superposition method to free vibration of rectangular thick plates with a free corner. The analytic frequency and mode shape solutions are both obtained and presented via comprehensive numerical and graphic results. The rigorousness in mathematical derivation and rationality of the method (without any predetermination for the solutions) guarantee the validity of our analytic solutions, which themselves are also validated by the reported results and refined finite element analysis.

Simply supported annular plates transversely loaded by a concentrated force applied at an arbitrary point

1995 ◽  
Vol 30 (3) ◽  
pp. 211-215
Author(s):  
A Strozzi ◽  
E Dragoni ◽  
V Ciavatti
Keyword(s):  
Series Solution ◽  
Annular Plate ◽  
Arbitrary Point ◽  
Experimental Tests ◽  
Concentrated Force ◽  
Simply Supported ◽  
Annular Plates ◽  
Aspect Ratios ◽  
Wide Range ◽  
Plate Geometry

An analysis is performed for a thin, annular plate, simply supported at its inner boundary, free at its periphery, and loaded by a concentrated force applied at any plate position. A purely flexural model is adopted, for which a series solution is obtained with the aid of an algebraic manipulator. Experimental tests are carried out for a specific plate geometry and the results obtained are compared to the analytical forecasts. A diagram is presented which summarizes the plate theoretical deflection by the loaded point for a wide range of aspect ratios of the annular plate and of normalized loaded positions.

Vibration Frequencies of Tapered Bars and Circular Plates

1964 ◽  
Vol 31 (2) ◽  
pp. 329-331 ◽  
Author(s):  
H. D. Conway ◽  
E. C. H. Becker ◽  
J. F. Dubil
Keyword(s):  
Free Vibration ◽  
Test Cases ◽  
Cantilever Beams ◽  
Vibration Frequencies ◽  
Circular Plates ◽  
Approximate Methods ◽  
Resonant Frequencies ◽  
Simply Supported ◽  
Tapered Plates ◽  
Special Case

Calculations are made of the values of the transverse vibrationa resonant frequencies for truncated-cone cantilever beams for a number of geometries, the boundary conditions being clamped/free, clamped/simply supported, and clamped/clamped. After noting an analogy which exists between the free vibration of cones and linearly tapered plates for the special case when Poisson’s ratio = 1/3, data are also given for the resonant axisymmetrical frequencies of clamped tapered circular plates. Some data for partially tapered plates are also computed. Aside from their value for design purposes, these data can be used as test cases for assessing the accuracy of various approximate methods of solution.

scholarly journals New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xinran Zheng ◽  
Mingqi Huang ◽  
Dongqi An ◽  
Chao Zhou ◽  
Rui Li
Keyword(s):  
Hamiltonian System ◽  
Free Vibration ◽  
Eigenvalue Problems ◽  
Analytic Solutions ◽  
Symplectic Space ◽  
Superposition Method ◽  
Mathematical Solution ◽  
Simply Supported ◽  
Solution Methods ◽  
Symplectic Eigenvalue

AbstractNew analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where the mathematical solution framework involves the construction of symplectic eigenvalue problems and symplectic eigen expansion. The analytic symplectic solutions are derived for several elaborated fundamental subproblems, the superposition of which yields the final analytic solutions. Besides Lévy-type solutions, non-Lévy-type solutions are also obtained, which cannot be achieved by conventional analytic methods. Comprehensive numerical results can provide benchmarks for other solution methods.

Analytical approach for transverse vibration analysis of castellated beams

2014 ◽  
Vol 14 (03) ◽  
pp. 1350071 ◽  
Author(s):  
J. K. Chen ◽  
B. Kim ◽  
L. Y. Li
Keyword(s):  
Free Vibration ◽  
Analytical Study ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vibration Modes ◽  
Shear Effect ◽  
Vibration Frequencies ◽  
Beam Length ◽  
Cross Sectional ◽  
Simply Supported

This paper presents an analytical study on the dynamic characteristics of castellated beams. The study focuses on the effect of web shear on the free vibration frequencies of castellated beams. By using the Hamilton's principle, a simple closed-form solution for determining the free vibration frequencies of simply supported castellated beams is developed. The results show that the shear effect on the free vibration frequencies increases with the cross-sectional area and distance between the centroids of the two tee sections of castellated beams, but decreases with respect to increasing web thickness or increasing beam length. The shear effect is also found to be greater in higher vibration modes.

A Comprehensive Study of the Free Vibration of Rectangular Plates Resting on Symmetrically-Distributed Uniform Elastic Edge Supports

1989 ◽  
Vol 56 (4) ◽  
pp. 893-899 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Comprehensive Treatment ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Rapid Convergence ◽  
Linear Elastic ◽  
Modes Of Vibration ◽  
Elastic Edge ◽  
Comprehensive Study

An analytical-type solution is developed for the free vibration analysis of rectangular plates with uniform elastic edge support symmetrically distributed about the plate central axes. Both linear elastic rotational and translational support are considered to act simultaneously. Rapid convergence is encountered. Because of the symmetry of the problem, the free vibration modes fall into three distinct families. Eigenvalues are tabulated for the first four modes of vibration of a square plate with identical stiffnesses on each edge and with various ratios of translational to rotational stiffnesses. This represents, to the author’s knowledge, the first comprehensive treatment of this problem.

scholarly journals Effects of Precast Cladding Systems on Dynamic Characteristics of Steel Frame Buildings by Ambient and Free Vibration Tests

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Jun Ma ◽  
Shinji Nakata ◽  
Akihito Yoshida ◽  
Yukio Tamura
Keyword(s):  
Free Vibration ◽  
Dynamic Characteristics ◽  
Steel Frame ◽  
Ambient Vibration ◽  
Test Cases ◽  
Vibration Method ◽  
External Wall ◽  
Wide Range ◽  
Cladding Panels ◽  
Vibration Tests

Full-scale tests on a one-story steel frame structure with a typical precast cladding system using ambient and free vibration methods are described in detail. The cladding system is primarily composed of ALC (Autoclaved Lightweight Concrete) external wall cladding panels, gypsum plasterboard interior linings, and window glazing systems. Ten test cases including the bare steel frame and the steel frame with addition of different parts of the precast cladding system are prepared for detailed investigations. The amplitude-dependent dynamic characteristics of the test cases including natural frequencies and damping ratios determined from the tests are presented. The effects of the ALC external wall cladding panels, the gypsum plasterboard interior linings, and the window glazing systems on the stiffness and structural damping of the steel frame are discussed in detail. The effect of the precast cladding systems on the amplitude dependency of the dynamic characteristics and the tendencies of the dynamic parameters with respect to the structural response amplitude are investigated over a wide range. Furthermore, results estimated from the ambient vibration method are compared with those from the free vibration tests to evaluate the feasibility of the ambient vibration method.

scholarly journals Controlling Teleportation-Based Locomotion in Virtual Reality with Hand Gestures: A Comparative Evaluation of Two-Handed and One-Handed Techniques

Electronics ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 715
Author(s):  
Alexander Schäfer ◽  
Gerd Reis ◽  
Didier Stricker
Keyword(s):  
Virtual Reality ◽  
Virtual Worlds ◽  
User Preferences ◽  
Interaction Techniques ◽  
Hand Gestures ◽  
Wide Range ◽  
Effectiveness And Efficiency ◽  
High Degree ◽  
Additional Hardware ◽  
Comprehensive Study

Virtual Reality (VR) technology offers users the possibility to immerse and freely navigate through virtual worlds. An important component for achieving a high degree of immersion in VR is locomotion. Often discussed in the literature, a natural and effective way of controlling locomotion is still a general problem which needs to be solved. Recently, VR headset manufacturers have been integrating more sensors, allowing hand or eye tracking without any additional required equipment. This enables a wide range of application scenarios with natural freehand interaction techniques where no additional hardware is required. This paper focuses on techniques to control teleportation-based locomotion with hand gestures, where users are able to move around in VR using their hands only. With the help of a comprehensive study involving 21 participants, four different techniques are evaluated. The effectiveness and efficiency as well as user preferences of the presented techniques are determined. Two two-handed and two one-handed techniques are evaluated, revealing that it is possible to move comfortable and effectively through virtual worlds with a single hand only.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

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