characteristic decompositions and interactions of rarefaction waves of 2 d euler equations abstract this paper is concerned with classical solutions to the interaction of two arbitrary planar rarefaction waves for the self similar euler equations in two space dimensions we develop the direct approach started in chen and zheng in press 3 to the problem to recover all the properties of the solutions obtained via the hodograph transformation of li and zheng 2009 14 the direct approach as opposed to the hodograph transformation is straightforward and avoids the common difficulties of the hodograph transformation associated with simple waves and boundaries the approach is made up of various characteristic decompositions of the self similar euler equations for the speed of sound and inclination angles of characteristics

an improved regularity result of semi hyperbolic patch problems for the 2 d isentropic euler equations abstract this paper investigates the regularity of a semi hyperbolic patch problem arising from the riemann problem for the 2 d isentropic euler equations we show that the solution is uniformly c 1 1 6 up to the sonic curve and the sonic curve is c 1 1 6 which improve the c 1 regularity of song et al 20 we introduce a novel set of change variables which allow us to establish higher regularity results based on the ideas of characteristic decomposition and the bootstrap method

existence of a global smooth solution for a degenerate goursat problem of gas dynamics the goursat problem of a mixed type equation p 0 is considered at the ends of its supports we have p 0 which means it is degenerate hyperbolic we prove the global existence of a smooth solution to the degenerate goursat problem up to a boundary where p 0 this problem comes from the expansion of a wedge of gas with constant velocity into vacuum in two dimensional pressure gradient equations in gas dynamics where p is the pressure and p 0 means vacuum

sensitivity analysis with plate and shell finite elements this paper addresses the problem of calculating sensitivity data by direct methods for isoparametric plate or shell elements sensitivity parameters of interest include intrinsic properties such as material modulus and plate thickness as well as geometry variables which influence the size and shape of a structure the sensitivity calculation therefore must consider the parametric mapping within an element as well as the influence of geometric variables on the orientation of an element in space the methods presented specialize directly to continuum elements in which the co ordinate transformation is omitted or to simple structural members situated arbitrarily in space numerical examples are presented which illustrate the accuracy of the proposed techniques and the effect of discretization error on computed sensitivities

direct update of dynamic mathematical models from modal test data two methods for the direct updating of mathematical models based on modal test data are described a set of minimum required constraints derived from eigendynamic and force equilibrium conditions are presented both methods generate mass and stiffness matrices fitted exactly to the given modal test data one method changes all coefficients of the mass respective to the stiffness matrix and lessens the solution effort by the algebraical elimination of the lagrangian multipliers the other method changes only those selected matrix coefficients requiring additional solutions for the numerical calculation of the lagrangian multipliers examples and comments on the applicability of the methods are given

on a regularity result for the transonic pressure gradient system in gas dynamics abstract this paper is concerned with the regularity of transonic flows originated from the two dimensional riemann problem to the pressure gradient system in gas dynamics it is verified that if the transonic solution of the pressure gradient system is c 3 in a neighborhood of a sonic point and is c in the subsonic sonic region then the solution is also c in the sonic supersonic region near the sonic point

semi hyperbolic patches of solutions to the two dimensional euler equations we construct semi hyperbolic patches of solutions in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves to the two dimensional euler equations this type of solution appears in the transonic flow over an airfoil and guderley reflection and is common in the numerical solutions of riemann problems

interaction of rarefaction waves of the two dimensional self similar euler equations we construct classical self similar solutions to the interaction of two arbitrary planar rarefaction waves for the polytropic euler equations in two space dimensions the binary interaction represents a major type of interaction in the two dimensional riemann problems and includes in particular the classical problem of the expansion of a wedge of gas into vacuum based on the hodograph transformation the method employed here involves the phase space analysis of a second order equation and the inversion back to or development onto the physical space

simple waves and a characteristic decomposition of the two dimensional compressible euler equations we present a characteristic decomposition of the potential flow equation in the self similar plane the decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adiabatic euler system this result is a generalization of the well known result on 2 d steady potential flow and a recent similar result on the pressure gradient system

updating finite element dynamic models using an element by element sensitivity methodology a sensitivity based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented the proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors the updating algorithm is derived from the unconstrained minimization of the squared 2 norms of the modal dynamic residuals via an iterative two step staggered procedure at each iteration the measured mode shapes are first expanded assuming that the model is error free then the model parameters are corrected assuming that the expanded mode shapes are exact the numerical algorithm is implemented in an element by element fashion and is capable of zooming on the detected error locations several simulation examples which demonstrate the potential of the proposed methodology are discussed i introduction e ven though the field of finite element analysis of structural dynamic problems has witnessed tremendous progress in the last two decades greater confidence is still placed in experimental data therefore the finite element model of a given structure is often updated to reflect the results of a particular experiment usually the computed eigenmodes are compared with the measured frequencies and mode shapes if both sets are not in agreement the finite element model is refined via a two step updating procedure which 1 locates the errors and 2 corrects them clearly the first step is the most challenging of the two once the location of the errors is known it is relatively easy to correct them especially if the error sources can be identified however locating and identifying these errors can be a difficult task for the following reasons in general only a few experimental modes are available and these may be contaminated with random and systematic measuring errors moreover only a subset of the degrees of freedom dof in the finite element model can be monitored and as for practical and economical reasons only a few sensors can be utilized

interaction of three and four rarefaction waves of the pressure gradient system abstract we study the two dimensional pressure gradient system a subsystem of the two dimensional compressible euler system we consider the problem of interaction of four rarefaction waves which is one case of two dimensional riemann problems it is known that when two planar waves interact there exists a smooth solution in the interaction region in this paper we establish the existence of a smooth solution in the hyperbolic domain of determinacy in which we encounter the interaction of simple and planar waves and shock prevention in simple waves

truss optimization on shape and sizing with frequency constraints an optimality criteria algorithm is presented for three dimentional truss structure optimization with multiple constraints on its natural frequencies both nodal coordinates and element cross sectional areas which are quite different in their natures are treated simultaneously in a unified design space for structural weight minimization first the optimality criterion is developed for a single constraint based on differentiation of the lagrangian function it states that at the optimum all of the variables should have equal efficiencies then the global sensitivity numbers are introduced to solve multiple constraints of frequencies avoiding computation of the lagrange multipliers finally upon the sensitivity analysis the most efficient variables are identified and modified in priority the optimal solution is achieved gradually from the initial design with a minimum weight increment four typical trusses are used to demonstrate the feasibility and validity of the proposed method

the structure of solutions near a sonic line in gas dynamics via the pressure gradient equation abstract a key issue in gas dynamics in two space dimensions is the regularity of solutions near a sonic curve we build a large class of regular solutions with given boundary conditions on the sonic line the modeling equation is the pressure gradient equation which is the same as euler system when the parameters of the gas are pushed to certain extreme we use a novel set of coordinates involving both the space time and state variables to split regular terms from singular terms in the analysis

on the two dimensional gas expansion for compressible euler equations we investigate the problem of two dimensional unsteady expansion of an inviscid polytropic gas which can be interpreted as the collapse of a wedge shaped dam containing water initially with a uniform velocity we model this problem by isentropic euler equations the flow is quasi stationary and using hodograph transform we describe it by a partial differential equation of second order in the state space if it is irrotational initially furthermore this equation is reduced to a linearly degenerate system of three partial differential equations with inhomogeneous source terms these properties are used to prove that the flow is globally smooth when a wedge of gas expands into a vacuum and to analyze that shocks may appear in the interaction of four planar rarefaction waves

on two dimensional gas expansion for pressure gradient equations of euler system abstract in this paper we establish the existence of global continuous solutions of gas expansion into a vacuum for the two dimensional pressure gradient equations in gas dynamics under irrotational condition by hodograph transformation the flow is governed by the equation p p 2 v p uu 2 p u p v p uv p p 2 u p vv 0 which can be further reduced to a inhomogeneous linearly degenerate system of three equations then the problem of the expansion of a wedge of gas into a vacuum is solved in the same way

transonic shock formation in a rarefaction riemann problem for the 2d compressible euler equations it is perhaps surprising for a shock wave to exist in the solution of a rarefaction riemann problem for the compressible euler equations in two space dimensions we present numerical evidence and generalized characteristic analysis to establish the existence of a shock wave in such a 2d riemann problem defined by the interaction of four rarefaction waves we consider both the customary configuration of waves at the right angle and also an oblique configuration for the rarefaction waves two distinct mechanisms for the formation of a shock wave are discovered as the angle between the waves is varied

global solution of an initial value problem for two dimensional compressible euler equations abstract this paper is concerned with the existence of global continuous solutions of the expansion of a wedge of gas into a vacuum for compressible euler equations by hodograph transformation we first prove that the flow is governed by a partial differential equation of second order which is further reduced to a system of two nonhomogeneous linearly degenerate equations in the phase space under an irrotationality condition then this conclusion is applied to solving the problem that a wedge of gas expands into a vacuum which is actually a goursat type problem for these two equations in the supersonic domain

dynamic condensation method for structural eigenvalue analysis an improved dynamic condensation approach is presented for accurate calculation of structural eigenproperties the approach is iterative the kept and reduced degrees of freedom in the approach are related through a condensation matrix that is used to form a condensed eigenvalue problem an initial condensation matrix can be defined in terms of the system submatrices the eigenproperties calculated in an iterative step are utilized to update the condensation matrix matrix inversions or gaussian eliminations are avoided in the updating process by employing the orthogonality of the eigenvectors the process of updating the condensation matrix and the eigenvalue problem is repeated until a desired convergence in the eigenvalues is achieved usually a few iterations are quite adequate iterations for both the lower as well as the higher modes can be performed as the condensation matrices for the two sets of modes are very simply related numerical examples are presented to show the applicability of the proposed approach several methods that have been used in practice to select the kept degrees of freedom for condensing are also evaluated numerically with respect to their effectiveness in providing accurate estimates of the eigenproperties with a minimum number of iterations

a complete global solution to the pressure gradient equation abstract we study the domain of existence of a solution to a riemann problem for the pressure gradient equation in two space dimensions the riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants the global existence of a smooth solution was established in dai and zhang z dai t zhang existence of a global smooth solution for a degenerate goursat problem of gas dynamics arch ration mech anal 155 2000 277 298 up to the free boundary of vacuum we prove that the vacuum boundary is the coordinate axes

stiffness matrix adjustment using mode data a procedure is introduced that uses in addition to mode data structural connectivity information to optimally adjust deficient stiffness matrices the adjustments performed are such that the percentage change to each stiffness coefficient is minimized the physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification the theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

axisymmetric solutions of the euler equations for polytropic gases we construct rigorously a three parameter family of self similar globally bounded and continuous weak solutions in two space dimensions for all positive time to the euler equations with axisymmetry for polytropic gases with a quadratic pressure density law we use the axisymmetry and self similarity assumptions to reduce the equations to a system of three ordinary differential equations from which we obtain detailed structures of solutions besides their existence these solutions exhibit familiar structures seen in hurricanes and tornadoes they all have finite local energy and vorticity with well defined initial and boundary values these solutions include the one parameter family of explicit solutions reported in a recent article of ours

the two dimensional riemann problem for chaplygin gas dynamics with three constant states abstract the riemann problem for two dimensional chaplygin gas is considered for the case with three constant states with the help of the generalized characteristic analysis method the riemann problem is classified into eight genuinely different cases the structures of the riemann problem solutions are analyzed and corresponding numerical solutions are illustrated using the numerical generalized characteristic analysis method we find that a delta shock wave appears and interacts with the simple waves in some cases

solution of two dimensional riemann problems of gas dynamics by positive schemes the positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in x d liu and p d lax j fluid dynam 5 1996 pp 133 156 some numerical experiments presented there show how well the method works in this paper we use positive schemes to solve riemann problems for two dimensional gas dynamics

generalized dynamic reduction in finite element dynamic optimization on effectue une reconception automatisee des systemes structuraux non amortis pour des changements de frequences la methode met en jeu une perturbation non lineaire a partir de la conception de base des coordonnees generalisees sont introduites pour transformer le probleme original dans un sous espace de petite taille un schema de programmation mathematique non lineaire est applique dans le sous espace reduit

redesign of plates by large admissible perturbations the problem of structural redesign of plates for static deflection and modal dynamics objectives is formulated and solved by the method of large admissible perturbations the perturbation approach to redesign is first used to develop response equations for the objective plate design based on its specifications and the baseline plate design the equations of the objective state are strongly nonlinear implicit expressions of the variable plate thickness a large admissible perturbations algorithm is developed to solve the plate redesign problem and define the optimal objective state the latter is reached incrementally with a prediction correction scheme without repeated finite element analyses systematic numerical applications in redesign of a cantilever plate of 216 degrees of freedom are used to investigate the effects of number of extracted modes and redesign variables it is shown that the large admissible perturbations theory can be used efficiently to redesign plates for multiple specifications that require changes to the baseline design and its response of the order of 100 nomenclature cy admixture coefficient for participation of the j th mode to changes in the th mode e young s modulus k k global and generalized stiffness matrices ke stiffness matrix of element or group of elements related to property e

existence of smooth solutions to a one dimensional nonlinear degenerate variational wave equation abstract this paper is focused on a one dimensional nonlinear variational wave equation which is the euler lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts we establish the global existence of smooth solutions to its degenerate initial boundary value problem under relaxed conditions on the initial boundary data moreover we show that the solution is uniformly c 1 continuous up to the degenerate boundary and the degenerate curve is c 1 continuous for 0 1 2

frequency modification using newton s method and inverse iteration eigenvector updating an iterative procedure is proposed for determining structural changes necessary for modifying natural frequencies of a structure in a prescribed manner the procedure uses a newton s method approach to determine a structural change that satisfies the equation of motion of the modified structure the newton equation is the same as that derived from sensitivity analysis and from linear perturbation methods iterative application of this equation can be used to predict accurately the structural change for either large or small frequency modifications inverse iteration is used to update the structural eigenvector between newton iterations the application of this procedure to a finite element analysis is described natural frequency modification of a finite element structural model is shown to converge rapidly to accurate results

characteristic decomposition of compressible euler equations for a non ideal gas in two dimensions we consider a two dimensional compressible euler system for a non ideal gas and use the characteristic decomposition to establish that any pseudo steady isentropic irrotational flow adjacent to a constant state must be a simple wave further the constancy of the entropy and vorticity along the pseudo flow characteristics extends the foregoing conclusion to full euler system an attention is drawn to the fact that the result is also applicable to the shallow water system as it bears a close structural resemblance with the system under study these results are generalization of the well known theorem on reducible equations by courant and friedrichs supersonic flow and shock waves springer verlag new york 1999 and a recent result on compressible euler system for an ideal gas by li et al simple waves and a characteristic decomposition of the two dimensional compressible euler equations commun math phys 267 1 12 2006

characteristic decouplings and interactions of rarefaction waves of 2d euler equations abstract this paper is concerned with classical solutions for the interaction of two arbitrary planar rarefaction waves for the self similar euler equations in two space dimensions the approach is made up of various characteristic decompositions of the self similar euler equations for the speed of sound and inclination angles of characteristics reported in an earlier paper j li z yang y zheng characteristic decompositions and interactions of rarefaction waves of 2 d euler equations j differential equations 250 2011 782 798 here we report a new decomposition of the characteristics that decouples the two derivatives of the speed of sound along the two families of characteristics and we apply the decomposition to refine the global existence theory and convexity properties of the characteristics

two dimensional riemann problem for a hyperbolic system of conservation laws in three pieces abstract this paper studies the two dimensional riemann problem for a hyperbolic system of conservation laws with three constant initial data separated by x positive y positive and x negative axes using the generalized characteristic analysis method by considering the interactions of rarefaction waves shock waves and contact discontinuities 13 exact solutions and the corresponding criteria are obtained delta shock waves appear in some solutions moreover the numerical illustrations agree completely with the geometric structures of the exact solutions

on the existence of solutions to a one dimensional degenerate nonlinear wave equation abstract this paper is concerned with the degenerate initial boundary value problem to the one dimensional nonlinear wave equation u t t 1 u a u x x which arises in a number of various physical contexts the global existence of smooth solutions to the degenerate problem was established under relaxed conditions on the initial boundary data by the characteristic decomposition method moreover we show that the solution is uniformly c 1 continuous up to the degenerate boundary and the degenerate curve is c 1 continuous for 0 min a 1 a 1 1 a

closed form solution for minimum weight design with a frequency constraint displacements and cable tensions of a statically determinant cable network shown in fig 3 are calculated by the present method and a linear finite element method fem and results are compared the axial stiffness of the cables is 785 5 kgf a force of 1 kgf is imposed on node d from node e which moves along the line of jf f 0 z 1000 mm displacements of node d and cable tensions corresponding to the node e position are shown in table 1 when all cables are in tension x y 500 the model loses the statically determinant condition and the linear fem analysis results in a physically meaningless solution cables 2 and 3 are subjected to cpmpressive forces even in this case the present method yields a mechanically balanced configuration of the network in which cable 1 has a tension of 1 0 kgf equivalent to the magnitude of the applied force and is directed toward node e

structural optimization incorporating centrifugal and coriolis effects the problem of structural optimization in the presence of centrifugal and coriolis effects was studied for a rotating blade and for a rotating beam a finite element formulation was used and optimization was performed by applying nonlinear inverse perturbation centrifugal forces were modeled by the use of differential stiffness in a small displacement approximation and coriolis effects were obtained by employing coriolis finite element matrices the nonlinear inverse perturbation scheme was then modified to account for the mild geometric nonlinearities posed by differential stiffness and was also modified to incorporate the complex phase changes resulting from coriolis effects finally the method was applied to small and large changes in the fundamental bending frequency of two rotating systems satisfactory results were obtained ae be d e h k ke m m m p c

interaction of four rarefaction waves in the bi symmetric class of the two dimensional euler equations the global existence and structures of solutions to multi dimensional unsteady compressible euler equations are interesting and important open problems in this paper we construct global classical solutions to the interaction of four orthogonal planar rarefaction waves with two axes of symmetry for the euler equations in two space dimensions in the case where the initial rarefaction waves are large the bi symmetric initial data is a basic type of four wave two dimensional riemann problems the solutions in this case are continuous bounded and self similar and we characterize how large the rarefaction waves must be we use the methods of hodograph transformation characteristic decomposition and phase space analysis we resolve binary interactions of simple waves in the process

admissible large perturbations in structural redesign a new algorithm for structural redesign by perturbation is developed it allows for large changes between baseline and objective structures and can satisfy both modal and static displacement objectives it is faster and more accurate than previously developed perturbation resizing methods because it advances incrementally to the objective structure using large admissible perturbations the computer code developed is used as postprocessor to general or special purpose finite element codes to improve upon the design of structures with unacceptable modal and or static displacement response depending on the relation betweem the number of redesign goals allowable structural changes and admissibility constraints the desired redesign may be feasible either locally optimal or unique or may not exist in the latter case a minimum error inadmissible design is produced several numerical examples are used to study the effects of definition and relaxation of the redesign admissible domain and demonstrate the accuracy of the new redesign algorithm an offshore tower with repeated eigen values and 192 degrees of freedom is also redesigned subject to frequency static displacement goals and admissibility constraints 22 refs

solution existence of the optimization problem of truss structures with frequency constraints a basic theory is presented for determining the solution existence of frequency optimization problems for truss structures this theory says that the natural frequencies remain unchanged when a truss is modified uniformly and that the natural frequency constraint is usually the key constraint in determining the solution existence of a truss dynamic optimization problem based on this theory a practical method is presented in which only the first order derivatives of certain eigenvalues with respect to design variables are used to determine whether or not a specific natural frequency constraint is achievable if there is a solution for a given frequency constraint a solution existence result can be obtained very quickly using the method otherwise the extreme value of the corresponding natural frequency or a small confined range of design variables which contains the extreme value can be obtained numerical examples are presented to illustrate the feasibility and efficiency of the proposed method

self similar solutions for the triple point paradox in gasdynamics we present numerical solutions of a two dimensional riemann problem for the com pressible euler equations that describes the mach reflection of weak shock waves high resolution finite volume schemes are used to solve the equations formulated in self similar variables we use extreme local grid refinement to resolve the solution in the neighborhood of an apparent but math ematically inadmissible shock triple point the solutions contain a complex structure instead of three shocks meeting in a single standard triple point there is a sequence of triple points and tiny supersonic patches behind the leading triple point formed by the reflection of weak shocks and ex pansion waves between the sonic line and the mach shock an expansion fan originates at each triple point resolving the von neumann triple point paradox

an iterative method for finite dimensional structural optimization problems with repeated eigenvalues a numerical method for solving finite dimensional structural optimization problems with constraints on natural frequency and on buckling is formulated the method treats nondifferentiable repeated eigenvalues that have been shown to systematically arise in structural optimization recent results on differentiability of eigenvalues are used to develop a generalized gradient projection method for structural optimization the algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues the method is used to solve buckling and vibration optimization problems in which repeated eigenvalues occur

redesigning the dynamics of structural systems the critical link between two powerful modeling techniques component mode synthesis and large admissible perturbation theory is established this new redesign process allows structural systems that are composed of several substructures to be redesigned the process is developed in three steps first the analytical first order perturbation relationships between the structural system eigenvalues and the eigenvalues of each independent substructure are developed second a transformation matrix is developed for each perturbation relationship then combined to form the ultimate structural transformation matrix third a minimization problem is defined that uses the ultimate transformation matrix as a set of constraint equations the result of this minimization is a set of changes to the substructure eigenvalues that approximately affect the objective changes to the structural system eigenvalues the success of the redesign process is demonstrated by an isolated platform example the changes in the substructure eigenvalues are predicted via the redesign process then substituted back into the full nonlinear equations for the structural system and the results are discussed this work forms the basis for future redesign developments when other static and dynamic objectives are to be achieved for structural systems

improvement of a large analytical model using test data a method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure the method directly identifies without iteration a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements an application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure the resulting changes in the model are judged to be small compared to expectations of error in the analysis thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics in addition it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure nomenclature analytical matrix matrix of changes identity matrix full improved stiffness and mass matrices n x n full analytical k m matrices n x n partitions of ka ma corresponding to test coordinates partitions of ka ma corresponding to coupling elements partitions of ka ma corresponding to unmea sured coordinates number of measured modes number of degrees of freedom in the model measures of changes eqs 15 17 matrix norm sum of the squares of all the elements rectangular modal matrix normalized n x m th mode th column of measured and unmeasured partitions of diagonal matrix of measured natural frequencies m xm natural frequency of th mode 12 17 sum of the squares of all elements of matrix

structural redesign for forced response with proportional damping by large admissible perturbations a method to solve redesign inverse design problems of complex structures with forced response amplitude constraints is developed the assumption is made that a structure is excited by harmonic external forces at a given frequency the problem is to find optimum values of structural characteristics in order to achieve a desired level of forced response at one or several locations on the structure the method of large admissible perturbations leap is used the main advantage of leap is that a solution of the inverse problem can be found automatically without trial and error or repetitive finite element analyses using this method algorithms with modal dynamic constraints and static displacement constraints have been developed and tested in the past in this paper the redesign problem with forced response amplitude constraints is formulated the method consists of two distinctive parts first the general perturbation equations are derived they provide relations between the original structure s1 which is known and has undesired forced response amplitudes and the unknown objective structure s2 second the redesign problem is solved by an incremental prediction correction scheme which permits large changes in redesign structural damping is considered in the form of rayleigh damping under this formulation the damping matrix can be diagonalized by use of the real mode shapes of the undamped structure which leads to the derivation of an exact perturbation equation with no loss of accuracy modal dynamic and static constraints may also be imposed simultaneously by the designer the algorithm produces accurate results for large changes in response amplitude without additional finite element analyses the number of extracted modes and the increment size control the accuracy of the results and the computational time the importance of the choice of the objective function is discussed and examples are presented

extending sensitivity based updating to lightly damped structures the sensitivity based element by element sb ebe method is extended for updating the finite element models of lightly damped structures using experimentally measured complex modes the new updating method proceeds in two steps first the measured mode shapes are expanded and the mass and stiffness matrices are corrected to minimize a set of dynamic residuals next a damping matrix is constructed to absorb the remainder of these dynamic residuals as the mass and stiffness matrices are corrected before the computation of the damping matrix the extension is used for the updating of lightly damped structures the new sb ebe method is illustrated with two examples that highlight its potential for refining the finite element models of lightly damped structures

structural model correlation using large admissible perturbations incognate space a nonlinear perturbation method is developed to solve the problem of correlating a finite element model to a structure for which an incomplete set of natural frequencies and mode shapes and or some static deflections have been measured

direct coupled load verification of modified structural component an analytical vefification method for structural dynamics subject to partial design change is proposed the method can predict time domain structural dynamic responses after the changes are implemented incorporated with the entire structural characteristics including the unchanged portion by using small numbers of modal parameters of the original structure and the modified component the concise computation of the degrees of freedom of the modal representation which are formulated to retain the residual flexibility in the equation of motion can correctly provide changed effects the representation of the component mode synthesis and the force equilibrium between the changed component and the main structure are utilized to develop the algorithm which yields the modal mass stiffness conversion in the component modes applying this method to the spacecraft redesign without the physical property information of the launch vehicle or repetition of coupled load analysis the established algorithm can improve the prediction of the coupled spacecraft and launch vehicle structural dynamics a reanalysis can be implemented using a limited number of available modal parameters from the coupled analysis for the original structure demonstrations applied to simple beam and spacecraft launch vehicle models presented show the effectiveness of the method

on a degenerate mixed type boundary value problem to the 2 d steady euler equation abstract this paper is concerned with the structure of sonic supersonic solutions near sonic curves arising from the transonic channel flow problems in gas dynamics given two smooth curves one of which is a sonic curve and the other is a characteristic curve we construct a local classical supersonic solution for the two dimensional steady euler equations in the angular region a novel set of dependent and independent variables are introduced to transform the euler equations into a linear system with explicitly singularity regularity structures we use the iteration method to establish the existence and uniqueness of smooth solutions for the new system and then express the solution in terms of the original variables

interactions between two rarefaction waves for the pressure gradient equations in the gas dynamics in this paper we consider the interactions of forward and backward centered rarefaction waves for pressure gradient equations for the goursat problem developed on the domain of interactions using characteristic analysis it is proved that there never appears vacuum in this field when there is no vacuum on characteristic boundary with the help of uniform a priori estimate the existence and uniqueness of smooth solution is obtained the results of interactions between two rarefaction waves are presented moreover the numerical illustrations agree completely with the theoretical analysis

interaction of four rarefaction waves in the bi symmetric class of the pressure gradient system abstract the global existence and structure of solutions to multi dimensional pressure gradient system has some open problems in this paper we construct global classical solutions to the interaction of four planar rarefaction waves with two axes of symmetry for the pressure gradient system in two space dimensions the bi symmetric initial data is a basic type of four wave two dimensional riemann problems the solutions in this case are continuous bounded and self similar