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51.
In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper. 相似文献
52.
A. Montanaro 《Journal of Elasticity》1999,57(1):25-53
By extending the procedure of linearization for constrained elastic materials in the papers by Marlow and Chadwick et al., we set up a linearized theory of constrained materials with initial stress (not necessarily based on a nonlinear theory).
The conditions of propagation are characterized for small-displacement waves that may be either of discontinuity type of any
given order or, in the homogeneous case, plane progressive. We see that, just as in the unconstrained case, the laws of propagation
of discontinuity waves are the same as those of progressive waves. Waves are classified as mixed, kinematic, or ghost. Then we prove that the analogues of Truesdell"s two equivalence theorems on wave propagation in finite elasticity hold for
each type of wave.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
53.
54.
In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation
is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and
a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop
system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries
are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore,
the second-order solution is presented and the corresponding results are compared with those of the first-order solution.
It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant
and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding
numerical results. Good agreement between the two sets of results is observed. 相似文献
55.
轴压作用下充液圆柱壳屈曲的实验研究 总被引:2,自引:0,他引:2
本文从实验及理论两个方面对充满液体的圆柱壳在轴向压力作用下液体内压的变化进行了实际测试及理论定性分析.采用薄壳理论分析了屈曲前液体内压随轴向压力的变化规律,讨论了壳材料、几何参数及边界约束对内压的影响.通过实验实际测定了内压随轴向压力的变化规律.通过实验手段测定了充满液体的圆柱壳临界载荷、屈曲模态,讨论了充满液体的圆柱壳的承载能力等问题. 相似文献
56.
ChenJnnming HuangYuying 《Acta Mechanica Solida Sinica》2003,16(3):210-219
Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here. 相似文献
57.
Internal waves from a body accelerating in a thermocline 总被引:1,自引:0,他引:1
Many papers study the steady wave system around bodies moving in thermoclines but little attention has been given to unsteady wave systems. This paper concentrates on the unsteady wave systems around accelerating bodies in thermoclines. The wave shapes are calculated using a theory derived from a dispersion relation based on an exp-tanh density profile. All modes of oscillation can be determined and it is shown that for the lowest mode both oblique and transverse waves occur whereas for the higher modes the presence of transverse waves depends on the background conditions and on the speed of the body. Cauchy-Poisson impulsive start waves are included. The theoretical wave shapes compare quite well with those calculated using finite-difference formulations of the full Navier-Stokes equations when a body accelerates from rest.It is also shown how the dispersion relation =N sin together with the WKB approximation can produce the same plan-view wave forms as those obtained using the thermocline wave dispersion relation given by [17, 30]. 相似文献
58.
A new three-dimensional transducer system is introduced in this paper, which enables the measurement of six internal components
of strain tensor in concrete members. Laboratory tests and strain analyses were carried out to evaluate this tranducer system.
The results show that the system is effective in measuring internal strains of concrete members. It was then embedded in a
reinforced concrete bridge deck in Macomb County, Michigan. Field tests were conducted to measure the strains in the deck
under truck wheel load. The results were used to understand the deck's strain and stress behavior under truck wheel load. 相似文献
59.
In order to develop criteria for the physical evaluation of wood for soundboards of musical instruments, measurements were made of dynamic Young's modulusE, static Young's modulusE, internal frictionQ
–1 in longitudinal direction, and specific gravity for numerous species of broad-leaved wood. From the results obtained, including those of our previous paper on coniferous wood [1], it was found that the suitability of wood for soundboards could be evaluated by the quantity ofQ
–1/(E/), and that there were very high correlations betweenQ
–1/(E/) andE/, and betweenE andE, regardless of wood species. Consequently, it becomes possible to select practically any wood suitable for soundboards by using the value ofE/, which can be measured easily, and it was derived that the relation betweenE/ andQ
–1 of wood could be expressed by an exponential equation regardless of wood species. 相似文献
60.
非惯性参考系中弹性薄板动力系统在纵横振动相互耦合时的全局分岔及混沌性质 总被引:3,自引:0,他引:3
讨论非惯性参考系中弹性薄板动力系统1∶1内共振时的全局分岔及其混沌性质.首先对系统的奇点进行了分析,进而得到了奇点附近同宿轨的参数方程,再用Melnikov方法研究了系统的同宿轨分岔及其混沌运动.研究表明,对各种不同共振情形,系统将由同宿轨分岔过渡到混沌运动.最后用数值仿真证实了理论分析的结果. 相似文献