Dynamics of Elastic Systems

Nowacki, Witold; Zorski, Henryk; Miklowitz, Julius

doi:10.1115/1.3629767

Cited by 73 publications

(38 citation statements)

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“…Many solutions have been found in open literature for a simply supported square plate with a central point support [29][30][31][32][33][34][35][36]. Except for the results reported by Nowacki [30] and Johns and Nataraja [32], the DSC results are in excellent agreement with results from the other researchers [29,31,[33][34][35][36]. For square plates with other edge supporting conditions, the DSC results show close agreement with those by Leissa [29], Kim and Dickinson [33] and Liew et al [36].…”

Section: Convergence and Comparison Studiessupporting

confidence: 82%

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Xiang

Zhao

Wei

2002

Numerical Meth Engineering

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SUMMARYPart 2 of this series of two papers presents the applications of the discrete singular convolution (DSC) algorithm. The main purpose of this paper is to explore the utility, test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports. Both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions. The e ects of di erent size, shape and topology of the internal supports and di erent boundary conditions on the vibration response of plates are investigated. The partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports. Several closed-loop supports, such as ring, square and rhombus, and their combinations are studied for complex internal supports. Convergence and comparison studies are carried out to establish the correctness and accuracy of the DSC algorithm. The DSC results are compared with those in the available literature obtained by using other methods. Numerical results indicate that the DSC algorithm exhibits controllable accuracy for plate analysis and shows excellent exibility in handling complex geometries, boundary conditions and support conditions.

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Section: Convergence and Comparison Studiessupporting

confidence: 82%

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Xiang

Zhao

Wei

2002

Numerical Meth Engineering

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“…A rich bibliography on the dynamics of cylindrical shells has been presented by Grigolyuk andKabanov (1967, 1978) and Bert (1969). Linear vibrations were studied by Nowacki (1963). He pre- …”

Section: Cylindrical Shellsmentioning

confidence: 99%

Nonlinear vibrations of doubly-curved cross-ply shallow shells

Alhazza

Nayfeh

2001

19th AIAA Applied Aerodynamics Conference

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The objective of this work is to study the local and global nonlinear vibrations of isotropic single-layered and multi-layered cross-ply doubly curved shallow shells with simply supported boundary conditions. The study is based-on the full nonlinear partial-differential equations of motion for shells. These equations of motion are based-on the von Kármán-type geometric nonlinear theory and the first-order shear-deformation theory, they are developed by using a variational approach. Many approximate shell theories are presented.We used two approaches to study the responses of shells to a primary resonance: a direct approach and a discretization approach. In the discretization approach, the nonlinear partial-differential equations are discretized using the Galerkin procedure to reduce them to an infinite system of nonlinearly coupled second-order ordinary-differential equations. An approximate solution of this set is then obtained by using the method of multiple scales for the case of primary resonance. The resulting equations describing the modulations of the amplitude and phase of the excited mode are used to generate frequency-and force-response curves. The effect of the number of modes retained in the approximation on the predicted responses is discussed and the shortcomings of using low-order discretization models are demonstrated. In the direct approach, the method of multiple scales is applied directly to the nonlinear partial-differential equations of motion and associated boundary conditions for the same cases treated using the discretization approach. The results obtained from these two approaches are compared.For the global analysis, a finite number of equations are integrated numerically to calculate the limit cycles and their stability, and hence their bifurcations, using Floquet theory. The use of this theory requires integrating 2n + (2n) 2 nonlinear first-order ordinary-differential equations simultaneously, where n is the number of modes retained in the discretization. A convergence study is conducted to determine the number of modes needed to obtain robust results.The discretized system of equation are used to study the nonlinear vibrations of shells to subharmonic resonances of order one-half. The effect of the number of modes retained in the approximation is presented. Also, the effect of the number of layers on the shell parameters is shown.Modal interaction between the first and second modes in the case of a two-to-one internal resonance is investigated. We use the method of multiple scales to determine the modulation equations that govern the slow dynamics of the response. A pseudo-arclength scheme is used to determine the fixed points of the modulation equations and the stability of these fixed points is investigated. In some cases, the fixed points undergo Hopf bifurcations, which result in dynamic solutions. A combination of a long-time integration and Floquet theory is used to determine the detailed solution branches and chaotic solutions and their stability. The limit cycles may undergo...

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“…In constructing a general solution to Laplace's equation that satisfies the prescribed conditions, we resort to Fourier cosine transforms (Nowacki 1972)…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Modeling of Waves Propagating in Water with a Crushed Ice Layer on the Free Surface

Szmidt

2017

Archives of Hydro-Engineering and Environmental Mechanics

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A transformation of gravitational waves in fluid of constant depth with a crushed ice layer floating on the free fluid surface is considered. The propagating waves undergo a slight damping along their path of propagation. The main goal of the study is to construct an approximate descriptive model of this phenomenon. With regard to small displacements of the free surface, a viscous type model of damping is considered, which corresponds to a continuous distribution of dash-pots at the free surface of the fluid. A constant parameter of the dampers is assumed in advance as known parameter of damping. This parameter may be obtained by means of experiments in a laboratory flume.

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Dynamics of Elastic Systems

Cited by 73 publications

References 0 publications

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Nonlinear vibrations of doubly-curved cross-ply shallow shells

Modeling of Waves Propagating in Water with a Crushed Ice Layer on the Free Surface

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