Effects of Rotational Elastic Edge Supports on Buckling and Free Vibration of Thin Rectangular Plates PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Effects of Rotational Elastic Edge Supports on Buckling and Free Vibration of Thin Rectangular Plates PDF full book. Access full book title Effects of Rotational Elastic Edge Supports on Buckling and Free Vibration of Thin Rectangular Plates by Hari Kishan Koduru. Download full books in PDF and EPUB format.
Author: Hari Kishan Koduru
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Rectangular plates are found in most structures of modern industry. Their two-dimensional structural action results in lighter structures and therefore offers numerous economic advantages. Recently interest in rectangular plates increased due to rapid growth in electronic technology where electronic circuit boards in the form of thin rectangular plates are employed. It is well known that while a clamped boundary condition along the edge of thin rectangular plates is easy to formulate mathematically, it is difficult to achieve, even under laboratory conditions. This is due in part to the fact that some rotational elasticity is likely to be found in such supports, whether it is introduced intentionally or inadvertently. In this study, the effects of such elasticity on the free vibration and buckling of plates subjected to uniform in-plane loading are examined. Loading is applied in a direction perpendicular to a pair of opposite edges where lateral displacement is forbidden and edge rotation is opposed by a moment proportional to the degree of edge rotation. The edges running parallel to the in-plane loading are free. Highly accurate solutions are obtained by the method of superposition. Two plates are analysed; one with rotational elastic support at one edge, the other edge being simply supported and, a second plate with rotational elastic support at the pair of opposite edges. Free vibration eigenvalues and buckling loads are computed for various plate geometries, dimensionless rotational stiffnesses with various in-plane loads. It is observed that in limiting cases, eigenvalues and buckling loads agree well in comparison with those of classical cases such as pinned and clamped boundary conditions. It is also found that the edges can be given any desired value of the rotational stiffness.
Author: Hari Kishan Koduru
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Rectangular plates are found in most structures of modern industry. Their two-dimensional structural action results in lighter structures and therefore offers numerous economic advantages. Recently interest in rectangular plates increased due to rapid growth in electronic technology where electronic circuit boards in the form of thin rectangular plates are employed. It is well known that while a clamped boundary condition along the edge of thin rectangular plates is easy to formulate mathematically, it is difficult to achieve, even under laboratory conditions. This is due in part to the fact that some rotational elasticity is likely to be found in such supports, whether it is introduced intentionally or inadvertently. In this study, the effects of such elasticity on the free vibration and buckling of plates subjected to uniform in-plane loading are examined. Loading is applied in a direction perpendicular to a pair of opposite edges where lateral displacement is forbidden and edge rotation is opposed by a moment proportional to the degree of edge rotation. The edges running parallel to the in-plane loading are free. Highly accurate solutions are obtained by the method of superposition. Two plates are analysed; one with rotational elastic support at one edge, the other edge being simply supported and, a second plate with rotational elastic support at the pair of opposite edges. Free vibration eigenvalues and buckling loads are computed for various plate geometries, dimensionless rotational stiffnesses with various in-plane loads. It is observed that in limiting cases, eigenvalues and buckling loads agree well in comparison with those of classical cases such as pinned and clamped boundary conditions. It is also found that the edges can be given any desired value of the rotational stiffness.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: American Society of Mechanical Engineers. Winter Annual Meeting
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: George E. Weeks
Publisher:
ISBN:
Category : Aeroelasticity
Languages : en
Pages : 46
Get Book Here
Book Description
Author: Hai Qi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
In the present study, it is demonstrated that the traditional superposition method lends itself successfully to obtaining of eigenvalues and mode shapes for rectangular shear deformable plates resting on uniform elastic edge supports. The effect of transverse shear deformation is taken into account by means of the first order shear deformation relationship developed by Mindlin. Uniform elastic rotational and translational supports of any stiffness magnitudes are considered to act simultaneously along the four edges. The effects of twisting edge restraint are investigated for the first time. The governing differential equations are satisfied exactly throughout the plate domain. Eigenvalues are tabulated for the first six vibration modes of square plates with identical stiffnesses along all edges. It is shown that all the three classical boundary conditions, namely, free, simply supported, and clamped, are approached when the stiffness coefficients are allowed to take on appropriate limits. These appear to be the first analytical solutions to these important elastically supported plate vibration problems obtained by the superposition method.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 636
Get Book Here
Book Description
Author: David J. Michelussi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Interest in the free vibration of thin rectangular plates has emerged due to the rapid growth in computer technology. Delicate electronic components mounted on circuit boards may be placed in environments under dynamic loadings. The designer may need to control the natural frequency or mode shape of a specific board if a known excitation is causing reliability problems in the hardware. Fortunately, constant in-plane loads can be applied to the plate, affecting its stiffness, and hence dynamic characteristics. This method of control is convenient since the circuit board does not need to be redesigned. The method of superposition is used to obtain analytical-type solutions for the free vibration of thin rectangular plates under constant in-plane loads in this thesis. A total of nine plate configurations are examined, each of which possess at least one free edge. Eight building blocks are derived and used to solve the plates under consideration. Each building block solution is of the Levy-type and is analytically exact. Since plate buckling is a limiting case of plate vibration, the solutions obtained can also be used to solve plate buckling problems. Results are calculated for nine plate aspect ratios. Buckling loads, frequencies, and mode shapes are shown. Excellent agreement is found in comparisons with other solution methods.
Author: Ziya Uddin
Publisher: CRC Press
ISBN: 1000599868
Category : Technology & Engineering
Languages : en
Pages : 251
Get Book Here
Book Description
This book presents the reader with comprehensive insight into various kinds of mathematical modeling and numerical computation for problems arising in several branches of engineering, such as mechanical engineering, computer science engineering, electrical engineering, electronics and communication engineering, and civil engineering. The book: • Discusses topics related to clean and green energy production and storage • Bridges the gap between core theory and costly industrial experiments • Covers advanced biomechanics and nanodrug delivery topics • Explores diversified applications of mathematical techniques to solve practical engineering problems The text in this book emphasizes mathematical treatment of soft computing, image and signal processing, fluid flows in various geometries, biomechanics, biological modeling, a mathematical description of the solar cell, analytical and numerical treatment of problems in fracture mechanics, and antenna design modeling. It also discusses the numerical computations of biomechanics problems and problems arising in cryptography. The text further covers optimization techniques that are useful for real-world problems. This material is primarily written for graduate students and academic researchers in a number of engineering fields, including electrical, electronics and communication, industrial, manufacturing, mechanical, computer science, and mathematics.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 236
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 974
Get Book Here
Book Description
