Nonlinear dynamic behaviors of viscoelastic shallow arches

The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches sub- jected to external excitation are investigated. Based on the d＇Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical in- tegration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch viscoelastic shallow arches may appear to have a are investigated. The results show that chaotic motion for certain conditions.

Nonlinear Bending Analysis of Functionally Graded CNT-Reinforced Shallow Arches Placed on Elastic Foundations

This research explores the nonlinear bending behaviors of functionally graded carbon nanotube-reinforced(FG-CNTR)shallow arches with unmovable simply supported ends and clarnped-clamped ends;these arches are subjected to a uniform radial pressure and rest on a nonlinear elastic foundation.The temperature-dependent material properties of the arches are considered.Within the framework of Reddy shear deformation theory possessing von Karman nonlinearity,the motion equations and boundary conditions for the FG-CNTR arches are determined by the Euler-Lagrange variational principle.Then,a two-step perturbation technique is adopted to determine the load-deflection relationship analytically.To verify the validity of the developed model and related perturbation solutions,a numerical investigation is conducted for shallow arches with five distribution patterns of carbon nanotube(CNT)reinforcements uniaxially aligned in the axial direction.Finally,the influences of various factors,including the elastic foundation,layout type,and volume fraction of CNTs and geometric factors,on the nonlinear behaviors of FG-CNTR shallow arches are examined.The obtained results show that the load deflection curves exhibit less snap-through instability as the CNT volume fraction increases.The transverse shear stress versus the thickness of FG-CNTR shallow arches is markedly affected by the layout type and content of reinforcements.

Elastic stability of shallow pin-ended parabolic arches subjected to step loads

Buckling could be induced when shallow arches were subjected to vertical step loads. In-plane static and dynamic buckling of shallow pin-ended parabolic arches with a horizontal cable was investigated. Based on the equations of motion derived from Hamilton's principle, nonlinear equilibrium equations and static buckling equilibrium equations were deduced. Through the pseudo-static analysis, approximate solutions to the lower and upper dynamic buckling loads under step loads were obtained, for shallow parabolic arches. The results show that dynamic buckling and snap-through buckling are impossible when modified slenderness ratio λ<λc and λ>λs, where λc and λs denote critical slenderness ratios of bucking and snap-through buckling, respectively; effects of the stiffness of the horizontal cable on the dynamic buckling are significant; and the dynamic buckling loads under a equivalent central concentrated step load are lower than the loads under a distributed load appreciably.

STEADY STATE MOTIONS OF SHALLOW ARCH UNDER PERIODIC FORCE WITH 1:2 INTERNAL RESONANCEON THE PLANE OF PHYSICAL PARAMETERS

The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1:2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to lire types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end.

LINEAR FINITE ELEMENT APPROXIMATIONS FOR THE TIMOSHENKO BEAM AND THE SHALLOW ARCH PROBLEMS

Focuses on a study that discusses the linear finite element approximations for the Timoshenko beam and the shallow arch problems with shear dampening and reduced integration. Information on the Timoshenko beam; Details on the shallow arch problem; Factors that lead to the explicit formulation of the exact solution.