共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate
the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials
(FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties
are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing equations of motion
for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom
nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance,
principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability
of steady state solutions is analyzed. The phase portrait, waveform and Poincaré map are used to analyze the periodic and
chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under
certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to
transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular
plate from periodic motion to the chaotic motion. 相似文献
2.
Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article.
The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law
distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through
the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order
shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically
for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal
loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy
of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio,
thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded
rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded
rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results
for researchers to validate their numerical and analytical methods in the future. 相似文献
3.
4.
研究Winkler地基上正交各向异性矩形薄板弯曲方程所对应的Hamilton正则方程, 计算出其对边滑支条件下相应Hamilton算子的本征值和本征函数系, 证明该本征函数系的辛正交性以及在Cauchy主值意义下的完备性, 进而给出对边滑支边界条件下Hamilton正则方程的通解, 之后利用辛叠加方法求出Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的解析解. 最后通过两个具体算例验证了所得解析解的正确性. 相似文献
5.
Joanna Sokół-Supel 《基于设计的结构力学与机械力学》2013,41(1):77-93
A rigid-plastic rectangular plate subjected to a moving transverse load is analyzed. The load is too large for the plate to be supported under static conditions. The present study indicates that there is a critical value for the moving load, above which the crossing cannot be made, irrespective of its speed. The relation between the moving load and its speed is given for values less than ciritical, as well as the distribution of displacement for a simply supported rectangular plate. 相似文献
6.
This paper presents a computational fluid–structure interaction analysis for a flexible plate in a free-stream to investigate the effects of flexibility and angle of attack on force generation. A Lattice Boltzmann Method with an immersed boundary technique using a direct forcing scheme model of the fluid is coupled to a finite element model with rectangular bending elements. We investigated the effects of various angles of attack of a flexible plate fixed at one of the end edges in a free-stream at a Reynolds number of 5000, which represents the wing flapping condition of insects and small birds in nature. The lift of the flexible plate is maintained at the large angle of attack, whereas the rigid plate shows the largest lift at angles of attack around 30–40° and then drastic reductions in the lift at the large angle of attack. If we consider the efficiency as the lift divided by the drag, the flexible plate shows better efficiency at angles of attack greater than 30° compared to the rigid plate. The better performance of the flexible plate at large angles of attack comes from the deformation of the plate, which produces an interaction between the trailing edge vortex and the short edge vortex. The horseshoe-shaped vortex produced by a large vortex interaction at the trailing edge side has an important role in increasing the lift, and the small projection area due to the deformation reduces the drag. Furthermore, we investigate the role of flexibility on the lift and the drag force of the rectangular plate in a free-stream as the Reynolds number increases. Whenever a large vortex interaction at the trailing edge side is shown, the efficiency of the rectangular plate is improved. Especially, the flexible plate shows better efficiency as the Reynolds number increases regardless of the angle of attack. 相似文献
7.
This paper investigates the multi-pulse global bifurcations and chaotic dynamics of the high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. Using the von Karman type equations, Reddy’s third-order shear deformation plate theory and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of 1:2 internal resonance and primary parametric resonance. From the averaged equations obtained, the theory of normal form is used to derive the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on the explicit expressions of normal form, the extended Melnikov method is used for the first time to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multi-pulse chaotic dynamics of the laminated composite piezoelectric rectangular plate are analytically obtained. Numerical simulations also illustrate that the Shilnikov type multi-pulse chaotic motions can also occur in the laminated composite piezoelectric rectangular plate. Overall, both theoretical and numerical studies demonstrate that the chaos in the Smale horseshoe sense exists for the laminated composite piezoelectric rectangular plate. 相似文献
8.
Resonant chaotic motions of a simply supported rectangular thin plate with parametrically and externally excitations are analyzed
using exponential dichotomies and an averaging procedure for the first time. The formulas of the rectangular thin plate are
derived by a von Karman type equation and the Galerkin’s approach. The critical condition to predict the onset of chaotic
motions for the full system is obtained by developing a Melnikov function containing terms from the non-hyperbolic mode. We
prove that the non-hyperbolic mode of the thin plate does not affect the critical condition for the occurrence of chaotic
motions in the resonant case. Simulations also show that the chaotic motions of the hyperbolic subsystem are shadowed by the
chaotic motions for the full system of the rectangular thin plate. 相似文献
9.
V. L. Karlash 《International Applied Mechanics》2007,43(5):547-553
An attempt is made to systematize experimental data for a rectangular piezoceramic plate and to compare them with those on
planar vibrations of a thin piezoceramic half-disk. Experimental data on planar vibrations of a half-disk are discussed for
the first time. Neighboring vibration modes of a rectangular plate with solid electrodes demonstrate strong superposition
and coupling
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 89–96, May 2007. 相似文献
10.
V. L. Karlash 《International Applied Mechanics》2007,43(7):786-793
The evolution of the planar vibrations of a rectangular piezoceramic plate as its aspect ratio is changed starting with 1
is studied. Experimental data are obtained using an integrated technique based on Meson’s circuit, Onoe’s circuit, and a piezotransformer
transducer. As the aspect ratio increases (square plate becomes rectangular), the intensity of electromagnetic vibrations
rapidly increases at the first longitudinal resonance and gradually decreases in the first radial mode. When the aspect ratio
is changed so that the length of one of the plate sides remains constant, the resonant frequencies of all vibration modes
change too
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 98–106, July 2007. 相似文献
11.
A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform
tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical
imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the
effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to
determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the
performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by
the thin plate theory. 相似文献
12.
The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson’s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness. 相似文献
13.
14.
张福范 《应用数学和力学(英文版)》1981,2(4):403-410
The cantilever rectangular plates discussed previously are all loaded continuously. For example, the load may be either a uniform or a concentrated load at the free ledge of the plate. Now we go a step further to deal with the case of a discontinuously loaded rectangular cantilever plate. The problem to be solved will involve a concentrated load at the center of the plate, as shown in Fig. 1. The method of solution used is the same as before. 相似文献
15.
Zhi-Min Li Ping Zhu Zhong-Qin Lin 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(5):585-603
Nonlinear bending behavior of 3D braided rectangular plates subjected to transverse loads is investigated. A new micro-macro-mechanical
model of unit cells is suggested. In this model, a 3D braided composite may be considered as a cell system and the geometry
of each cell is deeply dependent on its position in the cross-section of the plate. The material properties of the epoxy are
expressed as a linear function of temperature. Based on Reddy’s higher-order shear deformation plate theory and general von
Kármán-type equations, analytical solutions for nonlinear bending behavior of simply supported 3D braided rectangular plates
are obtained using mixed Galerkin-perturbation method. The numerical examples concern effects of geometric parameters, of
fiber volume fraction, braiding angle and load boundary condition. 相似文献
16.
黄炎 《应用数学和力学(英文版)》1988,9(11):1057-1065
A general solution of differential equation for lateral displacement lunction of rectangular elastic thin plates in free vibration
is established in this paper. It can be used to solve the vibration problem of rectangular plate with arbitrary boundaries.
As an example, the frequency and its vibration mode of a rectangular plate with four edges free have been solved. 相似文献
17.
Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method.The rectangular thin plate is subject to transversal and in-plane excitation.A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach.A one-toone internal resonance is considered.An averaged equation is obtained with a multi-scale method.After transforming the averaged equation into a standard form,the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics,which can be used to explain the mechanism of modal interactions of thin plates.A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits.Furthermore,restrictions on the damping,excitation,and detuning parameters are obtained,under which the multi-pulse chaotic dynamics is expected.The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate. 相似文献
18.
In this paper, an analysis on the nonlinear dynamics and chaos of a simply supported orthotropic functionally graded material
(FGM) rectangular plate in thermal environment and subjected to parametric and external excitations is presented. Heat conduction
and temperature-dependent material properties are both taken into account. The material properties are graded in the thickness
direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on the
Reddy’s third-order share deformation plate theory, the governing equations of motion for the orthotropic FGM rectangular
plate are derived by using the Hamilton’s principle. The Galerkin procedure is applied to the partial differential governing
equations of motion to obtain a three-degree-of-freedom nonlinear system. The resonant case considered here is 1:2:4 internal
resonance, principal parametric resonance-subharmonic resonance of order 1/2. Based on the averaged equation obtained by the
method of multiple scales, the phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions
of the orthotropic FGM rectangular plate. It is found that the motions of the orthotropic FGM plate are chaotic under certain
conditions. 相似文献
19.
Shaukat Mirza 《Experimental Mechanics》1976,16(10):392-396
The present investigation deals with the stress distribution in the vicinity of rectangular inserts in finite rectangular plates. This problem is more complex due to the singularities at the corners of the inserts. In this paper, the finite-element technique is used to determine the deformations and, subsequently, the stresses. The paper treats the problem in a generalized form in the sense that the size and orientation of the insert are taken as variables. The finite rectangular plate is subjected to a uniform axial tensile load. The material of the plate and that of the insert are considered to be different. Element selections are made which are optimal with regard to accuracy and computational effort. The local element stresses which generate considerable discontinuity at the element nodes are plotted. Averaging process for the local stress calculations is discussed and these are compared with the results available1 which are obtained by experimental techniques. 相似文献
20.
An analysis for vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness subjected to thermal
gradient has been discussed in the present investigation. For visco-elastic, the basic elastic and viscous elements are combined.
We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here
the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion
has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement at different points for the first
two modes of vibration are calculated for various values of thermal gradients, non homogeneity constant, taper constant and
aspect ratio for non-homogenous visco-elastic rectangular plate which is clamped on two parallel edges and simply supported
on remaining two edges. Comparison studies have been carried out with homogeneous visco-elastic rectangular plate to establish
the accuracy and versatility. 相似文献