SIMPLY SUPPORTED BEAM Theory - SOLVE - The Virtual Lab ...

Free vibration of simply supported beamSIMPLY SUPPORTED BEAM TheoryLearning objectivesAfter completing this simulation experiment one should be able toModel a given real system to an equivalent simplified model of a simplysupported beam with suitable assumptions / idealisationsCalculate the stiffness of a real system which is assumed to be equivalent of asimply supported beamDetermine the mass of the system actively participating in dynamicsDetermine the natural frequency of a given system equated to a simplysupported beamDetermine the influence of material properties like Youngs modules (E) anddensity ( ) in dynamicsDetermine the influence of cross section, length of simply supported beam indynamicsSimply Supported BeamIntroductionA system is said to be a Simply Supported beam system if it has a hinged connection atone end and roller connection in other end.Roller supportHinged supportDetermining the natural frequency of any system helps us to find how the system willbehave when just disturbed and left, and to find what kind of excitation frequency to beavoided in the system. Vibration analysis of a Simply Supported beam system isimportant as it can explain and help us analyse a number of real life systems. Thefollowing few examples can be simplified to a simply supported beam, thereby helpingus make design changes accordingly for the most efficient systems.SOLVE the virtual lab@ NITK SurathkalMachine Dynamics and Vibration Lab

Free vibration of simply supported beamArchaeological wonders such as the ones shown below can be considered to be SimplySupported beams:Stone hengePartheonEven now in the construction of sky scrapers, transmission towers etc.. , the trusselements can be simply supported depending on their construction.In the design process of bridges too, simply supported beam analysis plays an importantrole.SOLVE the virtual lab@ NITK SurathkalMachine Dynamics and Vibration Lab

Free vibration of simply supported beamIn the automotive industry, the leaf spring suspension system analysis can be likened toa simply supported beam analysis. In machinery, there are a number of systems whichcan be analyzed taking the supports to be simply supported..Simply supported impact testerDetermining the natural frequency of any system helps us to find how the system willbehave when just disturbed and left (free vibration), and to find what kind of excitationfrequency to be avoided in the system.To understand the how determine the natural frequency of a simply supported beam,we need to understand and calculate the following parameters.Stiffness and mass of the Simply Supported beamWe can determine the stiffness of simply supported beam by a simple equation fromstrength of materials .WhereK = Stiffness of system. (N/m)E = Young s Modulus of the material. ( )I = Area moment of inertia. ( )L = Effective length of Simply Supported Beam (m)Assumptions made during modelling and analysis: The mass (M) of the whole system is considered to be lumped at the middle ofthe beam No energy consuming element (damping) is present in the system ie. undampedvibrationSOLVE the virtual lab@ NITK SurathkalMachine Dynamics and Vibration Lab