modal analysis of rotating shafts a body fixed axis formulation approach abstract a spinning timoshenko beam subjected to a constant moving load is analyzed using a modal expansion technique the formulation is based on a body fixed axis reference system and thus should be applicable to handle any general cross sections using this alternative approach dynamic quantities such as natural frequencies mode shapes and system responses are easily computable it is shown that simply supported spinning timoshenko beams posses two pairs of natural frequencies corresponding to each mode shape through appropriate simplifications the coupled eighth order differential equations governing the problem are degenerated into a set of uncoupled fourth order equations with this simplified theory closed form expressions for natural frequencies and system transient response are derived however one pair of the natural frequencies is lost in the process but this is acceptable as the frequencies of this pair are much higher than those of the retained pair in addition a linearized approximation of the natural frequency similar to the one given for euler bernoulli beams is also proposed for a timoshenko shaft numerical simulations are performed to demonstrate the characteristics of the response

application of the principle of detailed balance to the random vibration of non linear oscillators abstract the principle of detailed balance which was developed in the field of statistical physics relates to the microscopic reversibility of a stochastic process it has recently been suggested that this principle may be used to expedite the solution of the fokker planck equation which arises when the response of a non linear system to white noise excitation is considered to investigate this the most general externally excited non linear oscillator which satisfies detailed balance is derived and it is found that the result coincides with a class of system for which there is an existing solution to the stationary form of the fokker planck equation in deriving this result the stationary response statistics of a slightly more general class of oscillator which does not satisfy detailed balance are found and a number of results regarding the probability current of the response are obtained

an exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping abstract this paper concerns the frequency response analysis of beams and plane frames with an arbitrary number of kelvin voigt viscoelastic dampers typical external and internal dampers are considered as grounded translational tuned mass rotational and axial dampers for bending and axial vibrations respectively using the theory of generalised functions within a 1d formulation of equations of motion exact closed form expressions are derived for beam dynamic green s functions and frequency response functions under arbitrary polynomial load for any number of dampers for a plane frame exact global frequency response matrix and load vector are built with size depending only on the number of beam to column nodes for any number of dampers and point polynomial loads along the frame members from the nodal displacement solution the exact frequency response in all frame members is also obtained in closed analytical form numerical applications show many of the advantages of the proposed method

deforming stanley reisner schemes we study the deformation theory of projective stanley reisner schemes associated to combinatorial manifolds we achieve detailed descriptions of first order deformations and obstruction spaces versal base spaces are given for certain stanley reisner surfaces

degenerations to unobstructed fano stanley reisner schemes we construct degenerations of mukai varieties and linear sections thereof to special unobstructed fano stanley reisner schemes corresponding to convex deltahedra this can be used to find toric degenerations of rank one index one fano threefolds furthermore we show that the stanley reisner ring of the boundary complex of the dual polytope of the associahedron has trivial t 2 this can be used to find new toric degenerations of linear sections of g 2 n

modal analysis of continuous rotor bearing systems abstract modal analysis is applied to continuous rotor systems with various boundary conditions which include isotropic and anisotropic natural boundary conditions the rotor includes the effects of rotary inertia and gyroscopic moment in particular the whirl speeds and mode shapes backward and forward of a rotating shaft are obtained as spin speed and boundary conditions vary and the unbalance responses are calculated by using modal analysis the effects of asymmetry in boundary conditions on the system dynamic characteristics are also investigated

deformations of equivelar stanley reisner abelian surfaces abstract the versal deformation of stanley reisner schemes associated to equivelar triangulations of the torus is studied the deformation space is defined by binomials and there is a toric smoothing component which i describe in terms of cones and lattices connections to moduli of abelian surfaces are considered the case of the mobius torus is especially nice and leads to a projective calabi yau 3 fold with euler number 6

modal analysis of multi span timoshenko beams connected or supported by resilient joints with damping the present paper proposes an exact modelling and modal analysis method for non uniform multi span beam type structure supported and or connected by resilient joints with damping to this end an exact dynamic matrix for a timoshenko beam element is derived by means of the spatial domain laplace transform a generalized modal analysis method is also proposed and applied to the derivation of frequency response and time response formulas for general beam structures three examples are provided for validating and or illustrating the proposed method in the first numerical example the proposed method is compared with fem the second example deals with a three stepped beam structure supported by joints with damping property in the final example a dynamic analysis of a multi span beam under moving load is demonstrated the numerical study proves that the proposed method is useful for the dynamic analysis of multi span beam type structures

vibration of multi span timoshenko frames due to moving loads abstract an analytical method is presented in this paper to study the vibration of multi span timoshenko frames the combined effects of axial inertia rotatory inertia and shear deformation of each branch of those frames are simultaneously considered any two distinct sets of the mode shape functions are shown to be orthogonal the method of modal analysis is then adopted to investigate the forced vibration of the frames a concentrated load and a uniformly distributed load moving on these frames are treated as two examples results show that as the span number gets larger the first modal frequency gets smaller furthermore the longer column implies a smaller first modal frequency the absolute maximum deflection of the timoshenko frame is larger than that of the bernoulli euler frame

equations of 1 d polarized abelian surfaces in this paper we study the equations of projectively embedded abelian surfaces with a polarization of type 1 d classical results say that given an ample line bundle l on an abelian surface a the line bundle l n is very ample for n 3 and furthermore in case n is even and n 4 the generators of the homogeneous ideal ia of the embedding of a via l n are all quadratic a possible choice for a set of generators of ia are the riemann theta relations on the other hand much less is known about embeddings via line bundles l of type 1 d that is line bundles l which are not powers of another line bundle on a it is well known that if d 5 and a is a general abelian surface then l is very ample while l can never be very ample for d 5 however even if d 5 l may not be very ample for special abelian surfaces we will restrict our attention in what follows only to the general abelian surface and wish to know what form the equations take for such a projectively embedded abelian surface a few special cases are well documented in the literature d 4 in which case the general surface is a singular octic in p3 cf blvs and d 5 in which case the abelian surface is described as the zero set of a section of the horrocks mumford bundle hm whereas its homogeneous ideal is generated by 3 heisenberg invariant quintics and 15 sextics cf ma also recent work by manolache and schreyer ms and by ranestad ra provides a description of the equations and syzygies in the case d 7

dynamic analysis of multi stepped distributed parameter rotor bearing systems exact solutions for a distributed parameter system are of great use for the physical understanding of the system or the sensitivity analysis and design of the system however exact or closed form solutions for multi stepped rotor bearing systems with distributed parameters have been rarely investigated the present paper proposes a modelling and analysis method to obtain exact solutions for multi stepped rotor bearing systems with distributed parameters to this end a modelling procedure to obtain an exact dynamic matrix for a timoshenko shaft element is presented by using a spatial state equation and the laplace transformation the assembling procedure for constructing the global matrix can be accomplished in the same manner as the finite element method the proposed method can readily provide exact eigensolutions frequency responses and unbalance responses for multi stepped rotor bearing systems with distributed parameters three numerical examples are also presented for validating or illustrating the proposed method the numerical study shows that the proposed method is very useful for the analysis of rotor bearing systems

on the natural frequencies and mode shapes of a multispan timoshenko beam carrying a number of various concentrated elements abstract the purpose of this paper is to utilize the numerical assembly method nam to determine the exact natural frequencies and mode shapes of the multispan timoshenko beam carrying a number of various concentrated elements including point masses rotary inertias linear springs rotational springs and spring mass systems first the coefficient matrices for an intermediate pinned support an intermediate concentrated element left and right end support of a timoshenko beam are derived next the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method finally the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions respectively the effects of distribution of in span pinned supports and various concentrated elements on the dynamic characteristics of the timoshenko beam are also studied

approximate eigenfunction analysis of first order non linear systems with application to a cubic system for stochastic systems excited by white gaussian noise the transition probability density is the solution to the fokker planck kolmogorov fpk equation if the system is non linear the resulting fpk equation can be solved exactly only in a few special cases here an approximate expression is developed for the transition probability density function of a class of non linear systems by using this approximation the autocovariance and spectral density function for a certain first order system are obtained the approximate results so obtained are compared with those obtained by direct digital simulation

analytical formulation of dynamic stiffness abstract the dynamic stiffness matrix method enables one to model an infinite number of natural modes by means of a small number of unknowns the method has been extended to skeletal structures with uniform or non uniform straight or curved damped or undamped beam members for two dimensional structures if one of the dimensions can be eliminated by means of the kantorovich method the method still applies however for more complicated systems analytical formulation of the dynamic stiffness is tedious a computer assisted analytical method is introduced here for any structural members the differential governing equations of which are expressible in matrix polynomial form complex arithmetics are used to cater for all possible classification of the characteristic roots numerical examples are given and are compared with existing results

rigid ideals by deforming quadratic letterplace ideals abstract we compute the deformation space of quadratic letterplace ideals l 2 p of finite posets p when its hasse diagram is a rooted tree these deformations are unobstructed the deformed family has a polynomial ring as the base ring the ideal j 2 p defining the full family of deformations is a rigid ideal and we compute it explicitly in simple example cases j 2 p is the ideal of maximal minors of a generic matrix the pfaffians of a skew symmetric matrix and a ladder determinantal ideal

a finite element method for the statistics of non linear random vibration the transitional probability density function for the random response of a certain class of non linear system satisfies the fokker planck kolmogorov equation this paper concerns the numerical solution of the stationary form of this equation yielding the stationary probability density function of response the weighted residual statement for the problem is integrated by parts to yield the weak form of the equations which are then solved by the finite element method the method is applied to a duffing oscillator and good agreement is found with the exact result and the method is compared favourably with a galerkin solution method given by bhandari and sherrer 1 also the method is applied to the ship rolling problem and good agreement is found with an approximate analytical result due to roberts 2

analysis of non homogeneous timoshenko beams with generalized damping distributions abstract this paper presents a study on the effects of generalized damping distributions on non homogeneous timoshenko beams on the basis of some fundamentals of modal analysis for damped continuous systems applied to the particular case of the timoshenko beam model the eigenproblem is solved by applying a method combining a state space representation with a transfer matrix technique yielding closed form expressions for the eigenfunctions after validation by means of numerical examples using the finite element method response functions in both the time and the frequency domain are discussed and compared according to different damping distributions

bounds on the vibrational energy that can be harvested from random base motion abstract this paper is concerned with the development of upper bounds on the energy harvesting performance of a general multi degree of freedom nonlinear electromechanical system that is subjected to random base motion and secondary applied periodic forces the secondary forces are applied with the aim of enhancing the energy harvested from the base motion and they may constitute direct excitation or they may produce parametric terms in the equations of motion it is shown that when the base motion has white noise acceleration then the power input by the base is always s 0 m 2 where s0 is the single sided spectral density of the acceleration and m is the mass of the system this implies that although the secondary forces may enhance the energy harvested by causing a larger fraction of the power input from the base to be harvested rather than dissipated there is an upper limit on the power that can be harvested attention is then turned to narrow band excitation and it is found that in the absence of secondary forces a bound can be derived for a single degree of freedom system with linear damping and arbitrary nonlinear stiffness the upper bound on the power input by the base is m max s 2 where s is the single sided base acceleration spectrum the validity of this result for more general systems is found to be related to the properties of the first wiener kernel and this issue is explored analytically and by numerical simulation