Dynamic response of single degree of freedom (duhamel program)

This program use Duhamel method to determine dynamic response of single degree of freedom system under any kind of impact load to mass or time history support acceleration then submit displacement, velocity, acceleration and supportive reaction at each time step as MATLAB output with two phase text and graph.

two different Examples, one for applide impact force to mass and that for applied time history acceleration to support are given which in these examples program outputs compared with the results from SAP2000 software.

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Elastic response spectrum

This program use Duhamel integration method to determine elastic response spectrums (include: displacement, velocity and acceleration spectrum) of a system under any timehistory ground acceleration then submit system response spectrum for displacement, velocity and acceleration as MATLAB output in three graph.

to test the program, we compare results of two examples with SeismoSignal program.

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Elastic response of shear buildings by MODAL analysis method

This program use MODAL analysis method using Jacobi iterative method for calculate eigenvalues and eigenvectors and then Duhamel integration method for numerical solution of equiblibrium equations of motion to determine elastic response of a multi story shear building under any timehistory ground acceleration then submit system response include; story displacements and story shears as MATLAB output in two phase, text and graph.

Finally, to test this program, two different Examples are given which in these examples program outputs compared with the results from SAP2000 software. Similarity of results shows that this program works without any deficiencies as well as this software

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Linear dynamic analyses of 2D frame

This program is able to analyze all types of 2D frames with all degrees of freedom under any kind of dynamic concentrated nodal loadings ( Fx(t), Fy(t) , Mz(t) ) using Modal analysis method and submit values of nodal displacements at each time step as MATLAB output. program can determine inertial properties with both Lumped and Consistent mass method. meantime the program have to use lumped method the writers used dynamic condensation method on both mass and stiffness matrixes to calculate eigen problems (eigen values and eigen vectors) without any disorder by Jacobi iterative method.

Finally, to test this program, one Example are given with both Lumped and Consistent mass. which in these example program outputs compared with the results from SAP2000 and ANSYS software (SAP for checking the program when it has to use lumped mass matrix method and Ansys for checking the program when it has to use consistent mass matrix). Similarity of results shows that this program works with the least deficiencies as well as these two softwares.

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