International Science Community Association Research Journal of Recent Sciences 2277 - 2502 3 1 2014 January 2 Calculating Free and Forced Vibrations of multi-story Shear Buildings by Modular method 83 90 EN Mohammad Aghaei 1 Department of Business Management, Branch, Shahid Beheshti University (SBU), Tehran, IRAN Amin Asadollahi 2 Department of Business Management, Science and Research Branch, Islamic Azad University, Tehran, IRAN RezaSalehi Nejad 3 Master of Executive Management Business Administration, Science and research Ayatollah Amoli Branch, Amol, Mazandaran, IRAN MahdiAzar Keyvan 4 MohammadiAlamoti Mostafa 5 Mohammadreza Zare 6 Khan Hamna 1 Jinnah University for Women, 5-C, Nazimabad, PAKISTAN Iqbal Munira 2 NarmeenShawoo Bawany 3 FaisalNadeem Saher 1 Civil Engineering and Earth Resources, University Malaysia Pahang, MALAYSIA, Nasly M.A. 2 Computer System and Software Engineering, University Malaysia Pahang, MALAYSIA TutyAsmawatyBintiAbdul Kadir 3 Department of Irrigation and Drainage Malaysia, Kuala Lumpur, MALAYSIA NasehirKhanE.M. Yahaya 4 Centre for Earth Resources Research and Management, University Malaysia Pahang, MALAYSIA WanMohdFaizalWan Ishak 5 MoradyGohareh Mehdy 1 Department of Industrial Engineering, Amirkabir University of Technology,424 Hafez Avenue, 1591634311, Tehran, IRAN Shams GharnehNaser 2 Aminnayeri Majid 3 Javad Heydarzadeh 1 Department of Accounting and Management, Kashan Branch, Islamic Azad University, Kashan, IRAN Hoseyn Jabbari 2 Hasan Ghodrati 3 Akhwanzada 1 Faculty of Technology, Universiti Malaysia Pahang, Gambang, 26300, Kuantan, MALAYSIA Salman Ahmad 2 Tahar Mat 3 Razman bin 4 M. Shirani 1 Department of Soil Science, Faculty of Agriculture, Armenian National Agrarian University, Yerevan, ARMENIA Mohammadi-Ghehsareh A. 2 Department of Soil Science, Faculty of Agriculture, Islamic Azad University (Khorasgan), Isfahan, IRAN Zare Ali 1 Najafzadeh Ali 2 E. AhmadiNaeim 3 Shahizare Behzad 4 Usman M. 1 Department of Statistics, University of Peshawar, Khyber Pakhtokhawa, PAKISTAN Iqbal M. 2 Department of Mathematics, Islamia College University, Peshawar, Khyber Pakhtokhawa, PAKISTAN QamarZ. 3 Shah S.I.A. 4 SeyyedMahdieh Mirmiran 1 Gilan University, IRAN RaoSohail Iqbal 1 Department of Computer Sciences, Government College University, Faisal Abad, PAKISTAN Majed Alshmari 2 College of Computer science and Information Technology, King Faisal University, Al Hasssa, SAUDI ARABIA Khan SherAfzal 3 Faculty of Sciences, Abdul Wali Khan University, Mardan, PAKISTAN AhmadZafar Nazir 4 Saeed Islam 5 MohseniRoozbahani Katayoon 1 Department of Communication, Faculty of Technical and Engineering, Islamic Azad UniversityShahr-E-Rey Branch, IRAN Ali Shahzadi 2 EhsanEsna Ashari 1 YoungResearchers and elite Club, Qazvin Branch, Islamic Azad University, Qazvi,IRAN > Research Article 2013 5 31 2014 January 2 The present study discretizes and calculates free and forced vibrations of a multi-story building by shear model. The present study shows that for free vibrations a dynamic system becomes a static system; as a result, static theories of linear structures can be used. Then, frequencies and modular forms are calculated. By contribution of Betti’s corresponding displacement theorem, orthogonal characteristic of modules is characterized. For forced vibrations, employment of module converts multi-degrees free engaged dynamic system to several independent single-degree free dynamic systems in each of which mass, spring stiffness and forced force for new system are linear combinations of mass, spring stiffness and forced force of engaged system. For example, frequencies, modular forms and forced displacement from transverse load to story such as hurricane force and acceleration imposed on building foundation, say earthquake, are manually calculated and compared by simulating with commercial-research software package, ANSYS. Results from ANSYS for forced vibrations are more accurate that results from approximate method of SAP 2000. Copyright@ International Science Community Association