Structural dynamics introduction this chapter provides an elementary introduction to timedependent problems. If the mass is given an initial displacement x and then released, the displacement oscillates about zero and gradually decreases with time. The acoustic equation of motion perturbation 1d equation of motion other coordinates equation of motion. Therefore, ft 0 in the equation of motion for forced vibration. Mcdonough departments of mechanical engineering and mathematics university of kentucky, lexington. Substituting equations 18, 19 and 20 into dalemberts equation 12, rearranging the order of the summations, factoring out the common. The course is intended to provide necessary knowledge to establish the equations of motion and for the determination of structural response from dynamic loads and experience in the modeling and calculation of dynamic response for simple structural systems. We will introduce the basic concepts using the singledegree of freedom springmass system. Evaluating structural response to the effects of dynamic loads for single degree and multi degree of freedom systems. Such a system is represented by a mass attached to the ground with a spring. Generalized coordinates, lagranges equations, and constraints.
Later the equations of motion also appeared in electrodynamics, when describing the motion of charged particles in electric and magnetic fields, the lorentz force is the general equation which serves as the definition of what is meant by an electric field and magnetic field. Sozen introduction this is a short presentation of the principles of structural dynamics applied to systems having several degrees of freedom for use by students in an earthquake engineering introductory course. Ch8a new direct time integration method for the equations of motion in structural dynamics. Explain and derive the equations of motion that govern the response of single and multiple degreeoffreedom structural systems.
Introduction to mdof systems 33 equations of motion. We will provide the basic equations necessary for structural. The value of describes the frequency at which the structure vibrates and is called the natu ral frequency. Structural dynamics department of civil and environmental engineering duke university henri p. University of florida structural dynamics ces 6108 spring 20 consolazio ces 6108.
Dynamics and vibrations matlab tutorial school of engineering brown university this tutorial is intended to provide a crashcourse on using a small subset of the features of matlab. Structural dynamics introduction to discuss the dynamics of a singledegreeof freedom spring. The motion can be described by a cosine function with a phase. Structural dynamics of earthquake engineering sciencedirect. Introduction to structural dynamics and aeroelasticity.
Structural dynamics aims at the following learning outcomes. A separate topic covers the analysis of linear elastic multipledegreeoffreedom mdof systems. Dynamics of simple oscillators single degree of freedom systems. Free vibration of undamped structures we will examine the case when there is no damping on the sdof system of figure 2.
Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic actions having high acceleration loading. Solving these second order equations is not difficult. Structural analysis iv chapter 5 structural dynamics 12 dr. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. The equation of motion is most important because structural response is computed as the solution. Structural analysis iv chapter 5 structural dynamics 31 dr. Motion a new paradigm in flexible multibody dynamics mbd 3 analysis engines dynamics analysis is usually carried out to provides the solution to nonlinear dynamics problems where material nonlinearity, geometric nonlinear effects or changes in boundary conditions occur due to dynamic events, such as a contact and variable external. Numerous case studies are given to provide the reader with a deeper insight into the practicalities of the area, and the solutions to these case studies are given in terms of realtime and. Explains mode shapes and frequencies and why they are important to structural dynamics. The equation tells us that any body that performs sinusoidal motion must have an acceleration that is. Introduction to structural dynamics of mdof systems.
Introduction to undamped free vibration of sdof 12. Prasad, assistant professor, civil engineering dept, nits 15. Dynamics of structures, theory and applications to earthquake engineering, second ed. It covers systems with both single and multiple degrees of freedom. A concise introduction to structural dynamics and earthquake engineering basic structural dynamics serves as a fundamental introduction to the topic of structural dynamics. Dalemberts method differential equation describing the motion is known as equation of motion. Inverse dynamics starting from the motion of the body determines the forces and moments causing the motion. Considers seismic and wind effects, modal analysis, numerical methods, structural idealization. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road. Dynamics of structures elementsofstructuraldynamics robertotomasi 11. Rather, they have different equations for different variations of the applied force with time.
The mass element signifies the mass and the inertial characteristics of the structural mass inertia force. Basic concepts on structural dynamics linkedin slideshare. We will include discussion of the stress analysis of the onedimensional bar, beam, truss, and plane frame. Instructional material complementing fema 451, design examples. Dynamics of mechanical systems, c105 mechanical and structural engineering and the edexcel hncd module mechanical science. We will introduce the basic concepts using the singledegreeoffreedom springmass system.
Dynamics of structures elements of structural dynamics. Prasad, assistant professor, civil engineering dept, nits 7. Write the equation of motion for a generalized single degreeoffreedom structure. He begins by describing dynamic systems and their representation for analytical purposes. Pdf a new direct time integration method for the equations. Structural dynamics of linear elastic singledegreeof. Dynamics tutorial natural vibrations one degree of freedom this work covers elements of the syllabus for the engineering council exam d225 dynamics of mechanical systems, c105 mechanical and structural engineering and the edexcel hncd module mechanical science. For example, consider the velocity and the acceleration. Fema 451b topic 3 notes slide 2 instructional material complementing fema 451, design examples sdof dynamics 3 2 structural dynamics equations of motion for sdof structures structural frequency and period of vibration behavior under dynamic load dynamic magnification and resonance effect of damping on behavior linear elastic response spectra. Covering single and multipledegreeoffreedom systems while providing an introduction to earthquake engineering, the book keeps the coverage succinct and on topic at a level that is appropriate for undergraduate and. Since the shape functions have not changed, the contributions of the first two terms to the element equations will not change. Structural dynamics final year structural engineering bsceng.
For the case of structural dynamics in civil engineering, the equations of motion are usually presented in the form of second order differential equations. Dynamics of simple oscillators single degree of freedom systems 7 2 free response of simple oscillators using equation 21 to describe the free response of a simple. The oscillations may be periodic such as the motion of a pendulum or random such. Introduction to dynamics of structures 2 washington university in st. Mar 03, 2015 this video is an introduction to undamped free vibration of single degree of freedom systems. The two main chapters deal with linear analysis of single sdof and multidegreeoffreedom mdof systems, under free vibration and in response to a variety. This book covers structural dynamics from a theoretical and algorithmic approach. The main contents include basic theory of dynamics, establishment of equation of motion, single degree of freedom systems, multidegree of freedom systems, distributedparameter systems, stochastic structural vibrations, research projects of structural dynamics, and structural dynamics of marine pipeline and risers. Oct 07, 2014 introduction to structural dynamics of mdof systems. Dynamics of simple oscillators single degree of freedom. It covers systems with both single and multiple degreesoffreedom.
Dynamics of structures lecture 1 overview of structural dynamics and vibrational equation of motion technical report pdf available february 2015 with 482 reads how we measure reads. Introduction to dynamics of structures 5 washington university in st. The equation of motion newtons law for a fluid element is. Instructional material complementing fema 451, design examples sdof dynamics 3 2 structural dynamics equations of motion for sdof structures structural frequency and period of vibration behavior under dynamic load dynamic magnification and resonance effect of damping on behavior linear elastic response spectra. Select the most appropriate method and solve an equation or set of equations of motion for a structural system. Overview of structural dynamics structuremembers,joints,strength,stiffness,ductility structureaction forcesresponse stresses,displacements forces. Derivation of the beam equation of motion using hamiltons principle 442. Statespace formulation for structural dynamics jose luis. Structural dynamics final year structural engineering. Dynamics of a springmass system the standard form of the equation is. Structural dynamics of linear elastic singledegreeoffreedom. We need only evaluate the residual term produced by the acceleration term in the motion equation. Statespace formulation for structural dynamics by jose luis mendoza zabala.
The spring element signifies the potential energy of and the stiffness characteristics elastic restoring force, k x of the structural system. Now can just alter our previous function and take account of the revised equations for the amplitude equation 5. If you complete the whole of this tutorial, you will be able to use matlab to integrate equations of motion. The above equation is a secondorder linear differential equation whose solution for the displacement consists of a homogeneous solution and a particular solution. Announcements sept 01 welcome to cee511 structural dynamics nov 25 final exam. The effectof gravity should therefore not be taken into account in the equation of motion of the system. Martin williams presents this short, accessible introduction to the area of structural dynamics. The vibration of the structure can also be described by the natural period. The number of independent displacement components that must be considered to represent the effects of all significant inertia forces of a structure. This set of slides covers the fundamental concepts of structural dynamics of linear elastic singledegreeoffreedom sdof structures. Describes free vibration, the ode, natural frequency, and natural period. Gavin where q jt are generalized forces, collocated with the generalized coordinates, q jt. Nov 21, 2016 basic concepts of structural dynamics 11212016 6dr. Explicit solution explicit dynamics focus on local response and wave propagation well suited to simulate short dynamic events implicit solution structural dynamics, aka mechanical focus more on global response suitable for static analysis, slower process or linear dynamics such as modal, harmonic dynamics.
Multiple degrees of freedom structural dynamics 2 l. Structural dynamics of linear elastic singledegreeoffreedom sdof systems. Holmes wind loading of structures 2001 multidegree of freedom structures lect. The single degree of freedom, or sdof, system is a useful concept in structural dynamics. Equations of motion equations of motion set of mathematical equations which describe the forces and movements of a body. This video is an introduction to undamped free vibration of single degree of freedom systems. It consists of a mass m connected to ground via a spring with stiffness k and a damper with damping coefficient c. Thus, noting that the displacement, velocity and acceleration are all functions of time, we have the fundamental equation of motion. Static gravity,dynamic timevarying,lateralwind,seismic harmonic,random structuraldynamics responseofstructuredeflection,drift,stressesdueto applicationofdynamicforces. The objective of this experiment is to introduce students to principles in structural dynamics through the use of an instructional shake table. Dynamics of simple oscillators single degree of freedom systems cee 541. From equation the natural frequency, is determined by the stiffness and mass of the structure. Gavin fall, 2018 this document describes free and forced dynamic responses of simple oscillators somtimes called single degree of freedom sdof systems. The study of the single degree of freedom dof system is the foundation of structural dynamics.
1465 893 719 616 5 1150 925 824 40 1514 664 1072 874 1120 56 722 399 43 1467 14 1223 19 1138 1177 880 436 810 906 180 482 801 1033 812 869 771 547 840 1241 462 192 1179