free vibration analysis of rotating beams by a variable order finite element method the free vibration of rotating beams is analyzed by means of a finite element method of variable order this method entails displacement functions that are a complete power series of a variable number of terms the terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and additionally displacements at certain points within the element the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series numerical results are presented for uniform beams with zero and nonzero hub radii tapered beams and a nonuniform beam with discontinuities since the present method reduces to a conventional beam finite element method for a cubic displacement function the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom indeed essentially exact eigenvalues and eigenvectors are obtained with this technique which is far more rapidly convergent than other approaches in the literature

the free vibration of a type of tapered beams this paper studies the vibrational characteristics of tapered beams with continuously varying rectangular cross section of depth and breadth proportional to xs and xt respectively where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co ordinate measured from the sharp end of the beam the bernoulli euler theory of bending is used to describe the motion of the beam a new set of beam functions are developed as the admissible functions which are the complete solution of the tapered beam under an arbitrary static load expanded into a taylor series the eigenfrequency equation is obtained by the rayleigh ritz method the accuracy is assured from the convergency and comparison studies the effect of the location of the taylor series expanding point on the convergency is discussed the analysis shows that the present approach is convergent for arbitrary truncation factor by taking the midpoint of the beam as the expanding point of the taylor series numerical results are tabulated for three different tapered beams with various boundary conditions and truncation factors it is shown that the eigenfrequencies can be obtained with high accuracy by using only a small number of terms of the static beam functions 2000 elsevier science s a all rights reserved

solutions of integral and integro differential equation systems by using differential transform method in this study differential transform method dtm is applied to both integro differential and integral equation systems the method is further expanded with a formulation to treat fredholm integrals if the system considered has a solution in terms of the series expansion of known functions this powerful method catches the exact solution so as to show this capability and robustness some systems of integral and integro differential equations are solved as numerical examples

a simplified canonical form algorithm with application to porous metal plasticity a canonical form for the representation of material constitutive equations within standard finite element codes has been developed which is deceptive in its simplicity substitution of different equation systems is trivial and a consistent material jacobian may be obtained automatically the process is essentially numerical and does not involve the difficult algebraic manipulation associated with more traditional approaches it is nevertheless exact because partial derivatives are derived analytically and simple because calculation of these derivatives is the only algebraic manipulation required the remainder of the process is generic in this paper the algorithm is simplified further a much more detailed and transparent explanation of the key to the method is given namely calculation of the consistent jacobian a trivial modification also extends the method to plane stress the original algorithm was validated for a simple material model the new form is used to implement the significantly more difficult modified gurson model for porous metal plasticity with hydrostatic yield dependence it is tested for single element cases involving total collapse and also used to simulate necking of a notched cylindrical bar copyright 2005 john wiley sons ltd

porous elastic system with nonlinear damping and sources terms abstract we study the long time behavior of porous elastic system focusing on the interplay between nonlinear damping and source terms the sources may represent restoring forces but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest by employing nonlinear semigroups and the theory of monotone operators we obtain several results on the existence of local and global weak solutions and uniqueness of weak solutions moreover we prove that such unique solutions depend continuously on the initial data under some restrictions on the parameters we also prove that every weak solution to our system blows up in finite time provided the initial energy is negative and the sources are more dominant than the damping in the system additional results are obtained via careful analysis involving the nehari manifold specifically we prove the existence of a unique global weak solution with initial data coming from the good part of the potential well for such a global solution we prove that the total energy of the system decays exponentially or algebraically depending on the behavior of the dissipation in the system near the origin we also prove the existence of a global attractor

flapwise bending vibration analysis of a rotating tapered cantilever bernoulli euler beam by differential transform method abstract this paper studies the vibration characteristics of a rotating tapered cantilever bernoulli euler beam with linearly varying rectangular cross section of area proportional to xn where n equals to 1 or 2 covers the most practical cases in this work the differential transform method dtm is used to find the nondimensional natural frequencies of the tapered beam numerical results are tabulated for different taper ratios nondimensional angular velocities and nondimensional hub radius the effects of the taper ratio nondimensional angular velocity and nondimensional hub radius are discussed the accuracy is assured from the convergence of the natural frequencies and from the comparisons made with the studies in the open literature it is shown that the natural frequencies of a rotating tapered cantilever bernoulli euler beam can be obtained with high accuracy by using dtm

an asymptotic solution to transverse free vibrations of variable section beams abstract the transverse free vibration of a class of variable cross section beams is investigated using the wentzel kramers brillouin wkb approximation here the governing equation of motion of the euler bernoulli beam including axial force distribution is utilized to obtain a singular differential equation in terms of the natural frequency of vibration and a wkb expansion series is applied to find the solution based on this formulation a closed form solution is obtained for determination of natural vibration mode shapes and the corresponding frequencies the first four terms of this asymptotic solution are simplified for homogenous beams to give a compact third order wkb approximation next the resulting solution is employed to determine the natural frequencies and mode shapes of some examples with and without axial force distribution the results are then been compared with those in the literature and very good agreement is achieved

free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method abstract starting from the governing differential equations of motion in free vibration the dynamic stiffness matrix of a uniform rotating bernoulli euler beam is derived using the frobenius method of solution in power series the derivation includes the presence of an axial force at the outboard end of the beam in addition to the existence of the usual centrifugal force arising from the rotational motion this makes the general assembly of dynamic stiffness matrices of several elements possible so that a non uniform or tapered rotating beam can be analyzed for its free vibration characteristics by idealizing it as an assemblage of many uniform rotating beams the application of the derived dynamic stiffness matrix is demonstrated by investigating the free vibration characteristics of uniform and non uniform tapered rotating beams with particular reference to the wittrick williams algorithm the results from the present theory are compared with published results it is shown that the proposed dynamic stiffness method offers an accurate and effective method of free vibration analysis of rotating beams

a finite beam element for vibration analysis of rotating tapered timoshenko beams a finite beam element for vibration analysis of a rotating tapered beam including shear deformations and rotary inertia is derived in this paper the finite element has four degrees of freedom and accounts for linear tapering in two planes this formulation permits any combination of taper ratios as well as unequal element lengths explicit expressions for the finite element mass and stiffness matrices are derived using the consistent mass approach while accounting for the centrifugal stiffness effects the generalized eigenvalue problem is defined and numerical solutions are generated for a wide range of rotational speed and taper ratios results obtained include the first ten free vibrational modes for both fixed and hinged end conditions comparisons are made whenever possible with exact solutions and with numerical results available in the literature the results display high accuracy when compared with other numerical results

dynamic analysis of a rotating cantilever beam by using the finite element method a finite element analysis for a rotating cantilever beam is presented in this study based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation three linear partial differential equations are derived from hamilton s principle two of the linear differential equations are coupled through the stretch and chordwise deformations the other equation is an uncoupled one for the flapwise deformation from these partial differential equations and the associated boundary conditions are derived two weak forms one is for the chordwise motion and the other is for the flapwise motion the weak forms are spatially discretized with newly defined two node beam elements with the discretized equations the behaviours of the natural frequencies are investigated for the variation of the rotating speed in addition the time responses and distributions of the deformations and stresses are computed when the rotating speed is prescribed the effects of the rotating speed profile on the vibrations of the beam are also investigated

global well posedness and stability of semilinear mindlin timoshenko system abstract we study long term behavior of reissner mindlin timoshenko rmt plate systems focusing on the interplay between nonlinear viscous damping and source terms the sources may represent restoring forces but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest this work complements 28 which established local well posedness of this problem global well posedness when damping dominates the sources in an appropriate sense and a blow up in the complementary scenario assuming negative total initial energy the current paper develops the potential well theory for the rmt system it proves global existence for potential well solutions without restricting the source exponents derives explicit energy decay rates dependent on the order of the damping exponents and verifies a blow up result for positive total initial energy

characteristics of steady vibration in a rotating hub beam system abstract a rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub s inertia and its rotating speed to highlight the essential nature behind the vibration phenomena we analyze the steady vibration of a rotating euler bernoulli beam with a quasi steady state stretch newton s law is used to derive the equations governing the beam s elastic motion and the hub s rotation a combination of these equations results in a nonlinear partial differential equation pde that fully reflects the mutual interaction between the two kinds of motion via the fourier series expansion within a finite interval of time we reduce the pde into an infinite system of a nonlinear ordinary differential equation ode in spatial domain we further nondimensionalize the ode and discretize it via a difference method the frequencies and modal shapes of a general rotating beam are then determined numerically for a low speed beam where the ignorance of geometric stiffening is feasible the beam s vibration characteristics are solved analytically we validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature finally systematic simulations are performed to demonstrate how the beam s eigenfrequencies vary with the hub s inertia and rotating speed

implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity abstract uniform exponential decay of solution is established for the elastodynamic system of elasticity using boundary feedback control energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces two primary goals are achieved first these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary thus extending earlier work which required that the domain be star shaped second the feedback is only a function of velocity as opposed to also containing the tangential derivative of the displacement resulting in a physically viable feedback proof is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system

nonlinear boundary feedback stabilization for a semilinear kirchhoff plate with dissipation acting only via moments limiting behavior abstract a semilinear kirchhoff plate with a nonlinear dissipation acting via moments only is considered it is shown that the plate is uniformly stabilizable with uniform energy decay rates with respect to the parameter 0 representing rotational forces assumed small moreover it is shown that the solutions of the kirchhoff plate converge to solutions of the semilinear euler bernoulli plate when 0 which is also uniformly stable in finite energy norm

flexural torsional coupled vibration analysis of axially loaded closed section composite timoshenko beam by using dtm abstract this study introduces the differential transform method dtm to analyse the free vibration response of an axially loaded closed section composite timoshenko beam which features material coupling between flapwise bending and torsional vibrations due to ply orientation the governing differential equations of motion are derived using hamilton s principle and solved by applying dtm the mode shapes are plotted the natural frequencies are calculated and the effects of the bending torsion coupling the axial force and the slenderness ratio on the natural frequencies are investigated using the computer package mathematica wherever possible comparisons are made with the studies in open literature

general stability result for a viscoelastic plate equation with past history and general kernel abstract in this paper we consider the following plate problem u t t u t t 2 u 0 k s 2 u t s d s 0 and we show that the stability of this problem holds for a much larger class of kernels more precisely we consider the kernel k 0 0 satisfies k t t k t t 0 where and are functions satisfying some specific properties under this very general assumption on the behavior of k at infinity we establish a relation between the decay rate of the solution and the growth of k at infinity this work generalizes and improves earlier results in the literature moreover we drop the boundedness assumption on the history data usually made in the literature