The Experts below are selected from a list of 62952 Experts worldwide ranked by ideXlab platform
A. Y. T. Leung - One of the best experts on this subject based on the ideXlab platform.
-
Dynamic Stiffness for thin-walled structures by power series
Journal of Zhejiang University-SCIENCE A, 2006Co-Authors: Bin Zhu, A. Y. T. LeungAbstract:The Dynamic Stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A Dynamic Stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam Dynamic Stiffness matrices, the thin-walled frame Dynamic Stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilibrium, a method which is similar to the finite element method (FEM). Then the thin-walled structure natural frequencies can be found by equating the determinant of the system Dynamic Stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. The natural frequencies and buckling loads of these thin-walled structures are computed.
-
Dynamic Stiffness analysis of non-uniform timoshenko beams
Journal of Sound and Vibration, 1995Co-Authors: A. Y. T. Leung, W.e. ZhouAbstract:Abstract A Dynamic Stiffness method is introduced to analyze non-uniform Timoshenko beams with various boundary conditions. A Dynamic Stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. This eliminates spatial discretization error and is capable of predicting many natural modes with use of a small number of degrees of freedom. The method is now widely used in various Dynamic problems [1-4]. In this study it is not necessary to reduce the two coupled governing differential equations into one equation, as has been done by many authors [5-8]. The natural frequencies of the non-uniform beams can be found by equating to zero the determinant of the Dynamic Stiffness matrix of the system. Several cases are studied and the results are compared with those obtained by the finite element method.
-
Dynamic Stiffness and Substructures
1993Co-Authors: A. Y. T. LeungAbstract:1 Harmonic Analysis.- 1.1 Steady State.- 1.2 Multiple Degrees of Freedom.- 1.3 Modal Analysis and Acceleration.- 2 Finite Elements and Continuum Elements.- 2.1 Formulation.- 2.2 Bar Elements.- 2.3 Beam Elements.- 2.4 Continuous Mass Model.- 2.5 Rectangular Plate.- 2.6 Interaction Between Beams and Plates.- 2.7 Leung's Theorem.- 2.8 Simpson's Hypothesis.- 2.9 Sturm's Theorem.- 2.10 Wittrick-Williams Algorithm.- 2.11 Derivatives of the Dynamic Stiffness.- 3 Dynamic Substructures.- 3.1 Exact Dynamic Condensation.- 3.2 Dynamic Substructures.- 3.3 Dynamic Flexibility.- 3.4 Dynamic Transformation.- 3.5 Damped Substructures.- 3.6 Multilevel Substructures.- 3.7 Non-conservative Substructures.- 3.8 Substructure Response.- 3.9 Periodic Structures.- 3.10 Derivatives of Substructure.- 4 Dynamic Stiffness.- 4.1 Follower Force.- 4.2 Parametrically Excited Members.- 4.3 Effects of In-Plane Moment.- 4.4 Reponse Analysis.- 4.5 Non-conservative Modal Analysis.- 4.6 Exponentially Varying Harmonic Excitations.- 5 General Formulation.- 5.1 Initial Stress Formulation.- 5.2 Finite Element Method.- 5.3 Dynamic Stiffness Method.- 5.4 Thin-Walled Beam.- 5.5 Shear Deformable Thin-Walled Beam.- 5.6 Analytical Dynamic Stiffness.- 5.7 Curved Thin-Walled Beam.- 5.8 Helix.- 5.9 Curvature Effect.- 5.10 Extensions.- 5.11 Symmetry of the Dynamic Stiffness Matrix.
-
Dynamic Stiffness Analysis of Curved Thin-Walled Beams
Shock and Vibration, 1993Co-Authors: A. Y. T. Leung, W.e. ZhouAbstract:The natural vibration problem of curved thin-walled beams is solved by the Dynamic Stiffness method. The Dynamic Stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized.
-
Dynamic Stiffness Analysis of Curved Thin-Walled Beams
Shock and Vibration, 1993Co-Authors: A. Y. T. Leung, W.e. ZhouAbstract:The natural vibration problem of curved thin-walled beams is solved by the Dynamic Stiffness method. The Dynamic Stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized. © 1993 John Wiley & Sons, Inc.
W.e. Zhou - One of the best experts on this subject based on the ideXlab platform.
-
Dynamic Stiffness analysis of laminated composite plates
Thin-Walled Structures, 1996Co-Authors: Andrew Y. T. Leung, W.e. ZhouAbstract:An analysis is presented for the vibration and stability problem of composite laminated plates by using the Dynamic Stiffness matrix method. A Dynamic Stiffness matrix is formed by frequency dependent shape functions which are exact solutions of the governing differential equations. It eliminates spatial discretization error and is capable of predicting several natural modes by means of a small number of degrees of freedom. The natural frequencies and buckling loads of composite laminated plates are calculated numerically. The effects of the boundary conditions, the number of layers, the orthotropicity ratio, the side to thickness ratio, and the aspect ratio are studied. It is also illustrated that connected composite plate structures can be handled without difficulty by the present method.
-
Dynamic Stiffness analysis of non-uniform timoshenko beams
Journal of Sound and Vibration, 1995Co-Authors: A. Y. T. Leung, W.e. ZhouAbstract:Abstract A Dynamic Stiffness method is introduced to analyze non-uniform Timoshenko beams with various boundary conditions. A Dynamic Stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. This eliminates spatial discretization error and is capable of predicting many natural modes with use of a small number of degrees of freedom. The method is now widely used in various Dynamic problems [1-4]. In this study it is not necessary to reduce the two coupled governing differential equations into one equation, as has been done by many authors [5-8]. The natural frequencies of the non-uniform beams can be found by equating to zero the determinant of the Dynamic Stiffness matrix of the system. Several cases are studied and the results are compared with those obtained by the finite element method.
-
Dynamic Stiffness Analysis of Curved Thin-Walled Beams
Shock and Vibration, 1993Co-Authors: A. Y. T. Leung, W.e. ZhouAbstract:The natural vibration problem of curved thin-walled beams is solved by the Dynamic Stiffness method. The Dynamic Stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized.
-
Dynamic Stiffness Analysis of Curved Thin-Walled Beams
Shock and Vibration, 1993Co-Authors: A. Y. T. Leung, W.e. ZhouAbstract:The natural vibration problem of curved thin-walled beams is solved by the Dynamic Stiffness method. The Dynamic Stiffness of a curved open thin-walled beam is given. The computed natural frequencies of the beam are compared with those obtained by a completely analytical method to show the high accuracy of the present method. The interaction of in-plane and out-of-plane modes is emphasized. © 1993 John Wiley & Sons, Inc.
Hongxing Hua - One of the best experts on this subject based on the ideXlab platform.
-
Exact Dynamic Stiffness matrix of a Timoshenko three-beam system
International Journal of Mechanical Sciences, 2008Co-Authors: Yong Chen, Hongxing HuaAbstract:An exact Dynamic Stiffness matrix is established for an elastically connected three-beam system, which is composed of three parallel beams of uniform properties with uniformly distributed-connecting springs among them. The formulation includes the effects of shear deformation and rotary inertia of the beams. The Dynamic Stiffness matrix is derived by rigorous use of the analytical solutions of the governing differential equations of motion of the three-beam system in free vibration. The use of the Dynamic Stiffness matrix to study the free vibration characteristics of the three-beam system is demonstrated by applying the Muller root search algorithm. Numerical results for the natural frequencies and mode shapes of the illustrative examples are discussed for 10 interesting boundary conditions and three different Stiffness constants of springs.
M. Haddar - One of the best experts on this subject based on the ideXlab platform.
-
In-plane Dynamic Stiffness matrix for a free orthotropic plate
Journal of Sound and Vibration, 2016Co-Authors: O. Ghorbel, L. Hammami, Imad Tawfiq, Jean-baptiste Casimir, M. HaddarAbstract:Abstract The aim of this paper is to describe a procedure for computing the Dynamic Stiffness matrix relative to the in-plane effect for an orthotropic rectangular plate. The Dynamic Stiffness matrix is calculated for free edge boundary conditions. The formulation is based on strong solutions for the equations of motion for an orthotropic plate obtained with the Levy series and a Gorman decomposition of the free boundary conditions. The results obtained for the in-plane harmonic response are validated by the Finite Element Method.
-
Dynamic Stiffness formulation for free orthotropic plates
Journal of Sound and Vibration, 2015Co-Authors: O. Ghorbel, J. B. Casimir, L. Hammami, Imad Tawfiq, M. HaddarAbstract:This paper presents a procedure for developing the Dynamic Stiffness matrix of a free orthotropic Kirchhoff plate. The Dynamic Stiffness matrix is computed for free edge boundary conditions of the plate that allow assembly procedures. The method is based on a strong formulation of Kirchhoff plate equations and series solutions, taking advantage of the symmetry and Gorman type decomposition of the free boundary conditions. The performances of the so-called Dynamic Stiffness Method (DSM) are evaluated by comparing the harmonic responses of an orthotropic Kirchhoff plate with those obtained from the Finite Element Method using four noded quadrilateral elements.
-
Dynamic Stiffness formulation and response analysis of stiffened shells
Computers & Structures, 2014Co-Authors: D. Tounsi, J. B. Casimir, Imad Tawfiq, S. Abid, M. HaddarAbstract:This work presents a Dynamic analysis of a stiffened cylindrical shell using the Dynamic Stiffness Method, also known as the Continuous Element Method. This approach is based on the determination of the Dynamic Stiffness matrix of an unmeshed structure. A method for calculating the Dynamic Stiffness matrix of an axisymmetric shell stiffened with multiple stiffeners at arbitrary locations is given. Thus a stiffened cylindrical shell is subjected to free-free boundary conditions and three types of loads. A finite element model is used in order to validate the numerical results obtained from the method.
-
Dynamic Stiffness formulation for circular rings
Computers & Structures, 2012Co-Authors: D. Tounsi, J. B. Casimir, M. HaddarAbstract:This paper describes a procedure for calculating the Dynamic Stiffness matrix of a circular ring. The basis of the Dynamic Stiffness method resides in determining the Dynamic Stiffness matrix of such structural elements. The solution of the elementary problem is derived using Hamilton's principle and a Fourier series expansion of the solution. Concentrated and distributed loads are applied to the ring along several directions in order to determine the response of the system. The performances of the method are evaluated using comparisons with the harmonic responses of a circular ring obtained using the finite element method.
J.r. Banerjee - One of the best experts on this subject based on the ideXlab platform.
-
Dynamic Stiffness matrix of a rectangular plate for the general case
Journal of Sound and Vibration, 2015Co-Authors: J.r. Banerjee, S O Papkov, David KennedyAbstract:The Dynamic Stiffness matrix of a rectangular plate for the most general case is developed by solving the bi-harmonic equation and finally casting the solution in terms of the force–displacement relationship of the freely vibrating plate. Essentially the frequency dependent Dynamic Stiffness matrix of the plate when all its sides are free is derived, making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions. Previous research on the Dynamic Stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported. This restriction is quite severe and made the general purpose application of the Dynamic Stiffness method impossible. The theory developed in this paper overcomes this long-lasting restriction. The research carried out here is basically fundamental in that the bi-harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense, leading to the development of the Dynamic Stiffness method. It is significant that the ingeniously sought solution presented in this paper is completely general, covering all possible cases of elastic deformations of the plate. The Wittrick–Williams algorithm is applied to the ensuing Dynamic Stiffness matrix to provide solutions for some representative problems. A carefully selected sample of mode shapes is also presented.
-
Dynamic Stiffness Modeling of Composite Plate and Shell Assemblies
2013Co-Authors: F A Fazzolari, J.r. Banerjee, M BoscoloAbstract:Abstract : This grant sought to develop the Dynamic Stiffness method for composite shell assemblies. In the first part an exact Dynamic Stiffness element based on higher order shear deformation theory and extensive use of symbolic algebra is developed for the first time to carry out buckling analysis of composite plate assemblies. The principle of minimum potential energy is applied to derive the governing differential equations and natural boundary conditions. The effects of significant parameters such as thickness-to-length ratio, orthotropy ratio, number of layers, lay-up and stacking sequence and boundary conditions on the critical buckling loads and mode shapes are investigated. In the second part of the grant an exact free vibration analysis of laminated composite doubly-curved shallow shells was carried out by combining the Dynamic Stiffness method (DSM) and a higher order shear deformation theory (HSDT) for the first time. The Wittrick-Williams algorithm is used as a solution technique to compute the eigenvalues of the overall DS matrix.
-
Dynamic Stiffness matrix development and free vibration analysis of a moving beam
Journal of Sound and Vibration, 2007Co-Authors: J.r. Banerjee, W.d. GunawardanaAbstract:Abstract The Dynamic Stiffness matrix of a moving Bernoulli–Euler beam is developed and used to investigate its free flexural vibration characteristics. In order to develop the Dynamic Stiffness matrix, it is necessary to derive and solve the governing differential equation of motion of the moving beam in closed analytical form. The solution is then used to obtain the general expressions for both responses and loads. Boundary conditions are applied to determine the constants in the general solution, leading to the formation of the frequency dependent Dynamic Stiffness matrix of the moving beam, relating the amplitudes of the harmonically varying loads to those of the corresponding responses. The application of the resulting Dynamic Stiffness matrix using the Wittrick–Williams algorithm is demonstrated by some illustrative examples. Numerical results for both simply supported and fixed–fixed end conditions of the beam are discussed, and wherever possible, some are compared with those available in the literature.
-
Dynamic Stiffness formulation and free vibration analysis of spinning beams
2002Co-Authors: J.r. BanerjeeAbstract:In this paper, the Dynamic Stiffness matrix of a spinning beam is developed and subsequently used to investigate its free vibration characteristics. First, the governing differential equations are derived using Hamilton's principle. Then, for harmonic oscillation, exact solutions for the displacement, rotation, bending moment and shear force at any cross-section of the beam are obtained in explicit analytical form. Next, the Dynamic Stiffness matrix which relates the amplitudes of the forces to that of the displacements at the end of the spinning beam in free vibration is derived by imposing the boundary conditions. Finally, the natural frequencies and mode shapes for some illustrative examples are computed by applying the Wittrick-Williams algorithm to the ensuing Dynamic Stiffness matrix. These results are discussed and wherever possible, compared with published ones. The paper concludes with some remarks.
-
Dynamic Stiffness formulation for structural elements: A general approach
Computers & Structures, 1997Co-Authors: J.r. BanerjeeAbstract:Abstract A general theory to develop the Dynamic Stiffness matrix of a structural element is outlined. Substantial saving in computer time can be achieved if explicit analytical expressions for the elements of the Dynamic Stiffness matrix are used instead of numerical methods. Such expressions can be derived with the help of symbolic computation. The application of the Dynamic Stiffness matrix to calculate the natural frequencies of a structure is discussed with particular reference to the Wittrick-Williams algorithm. The method presented is fairly general.
