Vibration of an Infinitely Extending Plate Resting on an Elastic Foundation

1963 ◽  
Vol 30 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Kazuyosi Ono
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
The Other ◽  
Damped Oscillation

Free vibrations and forced vibrations of an infinitely extending plate resting on an elastic foundation and carrying a mass are solved. Then the amplitudes of the free vibrations produced by an impulse applied to the mass on the plate are determined, and it is found that two kinds of vibration are produced in the plate: One is a free vibration and the other is a special vibration, which consists of an infinite number of free vibrations and resembles a damped oscillation.

Transfer Matrices for Beams Loaded Axially and Laid on an Elastic Foundation

1969 ◽  
Vol 20 (3) ◽  
pp. 281-306 ◽  
Author(s):  
B. A. Djodjo
Keyword(s):  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Transfer Matrices ◽  
Homogeneous Case ◽  
Simultaneous Treatment ◽  
Modified Model ◽  
Continuous Beams ◽  
Axially Loaded

SummaryUsing a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.

scholarly journals Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 2090
Author(s):  
Avey Mahmure ◽  
Francesco Tornabene ◽  
Rossana Dimitri ◽  
Nuri Kuruoglu
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Composite Shell ◽  
Free Vibrations ◽  
Shell Structures ◽  
Pasternak Foundation ◽  
Thin Walled ◽  
Basic Equations ◽  
Benchmark Solutions

In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account for different distributions of CNTs (with uniform or nonuniform linear patterns), together with the presence of an elastic foundation, and von-Karman type nonlinearities. The basic equations of the problem are solved by using the Galerkin and Grigolyuk methods, in order to determine the frequencies associated with linear and nonlinear free vibrations. The reliability of the proposed methodology is verified against further predictions from the literature. Then, we examine the model for the sensitivity of the vibration response to different input parameters, such as the mechanical properties of the soil, or the nonlinearities and distributions of the reinforcing CNT phase, as useful for design purposes and benchmark solutions for more complicated computational studies on the topic.

An Integral Equation Method for Free Vibration of Circular Plate with Concentrated Mass at Arbitrary Positions

2011 ◽  
Vol 255-260 ◽  
pp. 1830-1835 ◽  
Author(s):  
Gang Cheng ◽  
Quan Cheng ◽  
Wei Dong Wang
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Concentrated Mass

The paper concerns on the free vibrations of circular plate with arbitrary number of the mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green’s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

scholarly journals Experimental Procedure Used To Determine The Flexural Rigidity For Composite Sandwich Bars With Various Thickness Values

2015 ◽  
Vol 67 (1) ◽  
pp. 7-12
Author(s):  
Cosmin Mihai Miriţoiu
Keyword(s):  
Carbon Fiber ◽  
Flexural Rigidity ◽  
Free Vibrations ◽  
The Other ◽  
Honeycomb Core ◽  
Experimental Procedure ◽  
Composite Sandwich

Abstract In this paper there is presented an experimental procedure used to determine the flexural rigidity for composite sandwich bars with polypropylene honeycomb core with various thickness values: 1, 1,5 and 2 cm. The composite bars will be reinforced with one layer of carbon fiber. The width value of the composite bars will be of 6 cm. In order to obtain the flexural rigidity the composite bars will be clamped at one end and left free at the other. An accelerometer will be placed at the free end used to record the free vibrations of these bars. The simplifying assumption of “bar” will be used in this research, so I have chosen several free lengths for the bars: 29, 32 and 35 cm. The eigenfrequency of the first eigenmode will be used to determine the flexural rigidity of the bars.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

scholarly journals Reflections on the Hysteretic Damping Model

2009 ◽  
Vol 16 (5) ◽  
pp. 529-542 ◽  
Author(s):  
Nuno Maia
Keyword(s):  
Free Vibration ◽  
Point Of View ◽  
The Other ◽  
Hysteretic Damping ◽  
Engineering Problems ◽  
Practical Engineering ◽  
The Subject ◽  
The One ◽  
Damping Model ◽  
Free Vibration Response

This paper presents a reflection on a recently proposed solution to the problem of the free vibration response with the constant hysteretic damping model, that has been presented in some conferences in recent years, by the author himself and some of his colleagues. On the one hand, as expected, the subject has been received with natural criticism, mainly due to the well-known non-causal behaviour of the model in free vibration. On the other hand, it was not easy to understand what could be wrong in that proposal, as apparently everything was perfect from a mathematical point of view. The author decided that this subject deserved a more careful and detailed analysis and – in this kind of tutorial paper – the issue seems to have been clarified. It is concluded that the proposed solution involving the constant hysteretic damping corresponds in fact to an equivalent viscously damped model; it is therefore concluded that the application of the constant hysteretic damping to model the free vibration of practical engineering problems should be considered only in the perspective of an equivalent viscously damped model.

Dynamic Analysis of Steel-Concrete Composite Frames with Partial Interaction

2012 ◽  
Vol 594-597 ◽  
pp. 904-907 ◽  
Author(s):  
Jun Xia ◽  
Z. Shen ◽  
Bin Chen
Keyword(s):  
Boundary Condition ◽  
Free Vibration ◽  
Dynamic Analysis ◽  
Free Vibration Analysis ◽  
Slip Boundary Condition ◽  
Composite Beams ◽  
Free Vibrations ◽  
Frame Structures ◽  
Shear Connection ◽  
Slip Boundary

The finite element formulations of steel-concrete composite (SCC) beams considering interlayer slip with end shear restraint were established. Free vibrations of SCC beams and frame structures under different slip boundary conditions were examined. The influences of the shear connection stiffness and the slip boundary condition on dynamic characteristics were analyzed. It is shown that the low order 8-DOF element may exhibit slip locking phenomenon in free vibration analysis for very stiff connection. The free vibration frequencies of composite beams and frame structures increase with the shear connection stiffness increasing. Besides, it is found that the natural vibration properties of SCC frame structures are significantly affected by the slip boundary condition, and it should be suitably imposed on all composite beams in dynamic analysis.

Orthonormal basis of wavelets with customizable frequency bands

2016 ◽  
Vol 14 (06) ◽  
pp. 1650050 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Frequency Domain ◽  
Infinite Number ◽  
Orthonormal Basis ◽  
The Other ◽  
Just Intonation ◽  
Frequency Bands ◽  
Orthonormal Bases ◽  
Major Scale ◽  
Dilation Factor ◽  
New Type

We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation factor, and the other is designed based on the major scale in just intonation.

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