استفاده از روش گام به گام باقيمانده وزني زماني در حل مساله ارتعاش اجباري عضو يك بعدي با مقطع متغير

چكيده انگليسي :

Implementation of the time weighted residual method in solution of forced vibration problems in one dimensional members with variable section Mohammad Hamed Nilforoushan Mh1993nn@gmail com Date of Submission 2019 06 07 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Dr Bashir Movahedian b movahedian@cc iut ac ir Dr Nima Noormohammadi noormohammadi@cc iut ac ir Abstract In this thesis a method for solving the scalar wave propagation problem in a one dimensional member withvariable cross section is developed based on the step by step time weighted residual method The most importantadvantage of this method is solving problems without need for subdivision of the member which rises from itsmeshless composure There will also be total continuity of displacement and stress throughout the entire member The idea of the step by step method is to use pre integration relationships along with equilibrium equations Inthis method the initial conditions are satisfied precisely and the equilibrium equation is satisfied by using a time weighted residual method Another feature of this method is to store the information of each time step on thecoefficients of the base functions in such a way that the solution advances in time without the need to selectinternal points within the member only by using an explicit relation for the coefficients of successive time steps In this method base scalar functions are used to estimate the spatial equation of differential equations withnon stable coefficients Also in the time domain assuming linear variation of acceleration first the velocity anddisplacement functions are determined for the nth interval by the pre integration For this purpose the formulationof the proposed method has been developed first by considering the axial stiffness and then considering theflexural stiffness In this method the acceleration field is expressed as a combination of a non spatial functionand two series of exponential functions Then the equation is obtained by inserting the displacement field obtainedfrom the pre integration relations in the equilibrium equation with non constant coefficients and its approximatedsatisfaction In the following a function called the stimulation function is introduced which by putting it equal tothe increment of displacement at the end of each time step the unknown coefficients of the basis functions areobtained Boundary conditions are also met at the end of each step at the two boundary points Given the fact thatin the step by step method the initial conditions of the time step n 1 are determined from the velocity anddisplacement values at the end of the nth time interval in the final step it is necessary to reconnect the correctioncoefficients to advance the solution in time the equation is placed on the displacement field at the beginning ofthe n 1 interval and the end of the nth time step In another part of the thesis using an approximated equilibration method and modifying the step by steptechnique of the former part a new idea for the axial wave propagation problem will be raised which will removethe need to use the stimulation functions It s all about The basis of the work is the creation of suitable foundationsfor applying the boundary conditions of the two ends of the member using approximate approximations of thehomogeneous face of the differential equation in the form of a weighted integral in the location Keywords Variable Section Step by Step Time Solution Scaler wave propagationEquation Differential Equation With Non Constant Coefficients Exponential basisFunctions Chebyshev basis Function

نيلفروشان دردشتي، محمد حامد

استفاده از روش گام به گام باقيمانده وزني زماني در حل مساله ارتعاش اجباري عضو يك بعدي با مقطع متغير

مقطع متعير , روش گام به گام زماني , معادله انتشار موج اسكالر , معادله ديفرانسيل با ضرايب غير ثابت , توابع پايه نمايي , توابع پايه چبي شف