Stiffness and Deflection Analysis of Complex Structures
01 Sep 1956-Journal of the Aeronautical Sciences (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 23, Iss: 9, pp 805-823
About: This article is published in Journal of the Aeronautical Sciences.The article was published on 1956-09-01. It has received 1397 citations till now. The article focuses on the topics: Deflection (engineering) & Bending stiffness.
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TL;DR: In this article, the authors proposed a method for reducing the size of the stiffness matrix by eliminating coordinates at which no forces are applied, based on the procedure used in Ref. 1 for stiffness matrix reduction.
Abstract: Just as it is often necessary to reduce the size of the stiffness matrix in statical structural analysis, the simultaneous reduction of the nondiagonal mass matrix for natural mode analysis may also be required. The basis for one such reduction technique may follow the procedure used in Ref. 1 for the stiffness matrix, namely, the elimination of coordinates at which no forces are applied.
2,418 citations
TL;DR: In this article, a method is developed for analyzing complex structural systems that can be divided into interconnected components, where displacement of the separate components are expressed in generalized coordinates that are defined by displacement modes.
Abstract: A method is developed for analyzing complex structural systems that can be divided into interconnected components. Displacements of the separate components are expressed in generalized coordinates that are defined by displacement modes. These are generated in three categories: rigid-body, "constraint," and "normal" modes. Rigid-body modes are convenient where displacements are denned in inertial space for dynamic analysis. "Constraint" modes are included to treat redundancies in the interconnection system. "Normal" modes define displacements relative to the connections. Generalized mass, stiffness, and damping matrices are determined for each component, as are generalized forces. The requirement of system continuity gives rise to equations of displacement compatibility at the connections. These serve as equations of constraint among the component coordinates and are used to construct a transformation relating component coordinates to system coordinates. This transformation is used to derive system properties and forces from component properties and forces. System equations of motion are formulated and solved to determine system response. Component responses are found using the transformation. Connection forces are computed from the component equations. Each component can then be isolated and treated separately.
1,166 citations
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17 Jul 2000TL;DR: In this article, the Fourier series is used to measure the response of a single-degree-of-freedom system to initial and non-periodic oscillations, respectively.
Abstract: 1 Concepts from Vibrations 2 Response of Single-Degree-of-Freedom Systems to Initial Excitations 3 Response of Single-Degree-of-Freedom Systems to Harmonic and Periodic Excitations 4 Response of Single-Degree-of-Freedom Systems to Nonperiodic Excitations 5 Two-Degree-of-Freedom Systems 6 Elements of Analytical Dynamics 7 Multi-Degree-of-Freedom Systems 8 Distributed-Parameter Systems: Exact Solutions 9 Distributed-Parameter Systems: Approximate Mathods 10 The Finite Element Method 11 Nonlinear Oscilations 12 Random Vibrations Appendix A. Fourier Series Appendix B. Laplace Transformation Appendix C. Linear Algebra
1,133 citations
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TL;DR: In this paper, the authors present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics and discuss the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations.
976 citations
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TL;DR: In this paper, it was pointed out that the reduction of the two viscosity coefficients to one according to the Stokes' relation is not justified except in the special case of a monatomic gas.
Abstract: It is pointed out that the reduction of the two viscosity coefficients to one according to the Stokes' relation $2\ensuremath{\mu}+3\ensuremath{\lambda}=0$ is not justified except in the special case of a monatomic gas. The generalization of this relation by the re-introduction of the second independent viscosity coefficient $\ensuremath{\kappa}=\frac{2}{3}\ensuremath{\mu}+\ensuremath{\lambda}$ makes it possible to develop the phenomenological theory of the absorption and dispersion of sound, in agreement with experiment in complete analogy to the corresponding optical phenomena. The connection of the well-known relaxation theory with classical hydrodynamics can be established and in the case of polyatomic gases $\ensuremath{\kappa}$ is expressed by the characteristic constants of this theory. The case of liquids is discussed. In polyatomic gases and liquids one has generally $\ensuremath{\kappa}\ensuremath{\gg}\ensuremath{\mu}$. Other hydrodynamical consequences of the introduction of $\ensuremath{\kappa}$ are discussed.
142 citations