Dynamic response of sdof second order mechanical system. The most basic dynamic system is the massspring system. Dynamics of simple oscillators single degree of freedom systems cee 541. Notice that when the damping is 1 2, then there is the maximum response without having a peak in the response curve. Simple vibration problems with matlab and some help. Equivalent lateral force procedure gives base shear in terms of design spectrum and period of vibration. An sdof system is one whose motion is governed by a. The shock response spectrum srs models the peak response of. Dynamics of simple oscillators single degree of freedom. Structural dynamics final year structural engineering bsceng. Example of overhead water tank that can be modeled as sdof system 1.
Describes free vibration, the ode, natural frequency, and natural period. Simple vibration problems with matlab and some help from maple. Frequency response function 25 approach the solution to the equation using fourier. Frequency response function an overview sciencedirect. The peak response is the maximum of the absolute value of the response ratio, r max maxfj tjg. Sdof linear oscillator response to impulsive loads. Nonlinear analysis of sdof system under blast load 431 for personnel and valuable equipments. Structural dynamics final year structural engineering. The damped sdof system and the dynamic equilibrium equation for the system are introduced in part ii. Structural dynamics department of civil and environmental engineering duke university henri p. Chapter 2 sdof undamped oscillation the simplest form of vibration that we can study is the single degree of freedom system without damping or external forcing. Each display method is able to highlight a specific aspect of the frf. Apr 04, 20 this script illustrates how to plot frequency response of a single degree of freedom system using gnu octave.
Equation 1 is a nonhomogeneous, 2nd order differential equation. Meen 617 hd 6 numerical integration for time response. This script illustrates how to plot frequency response of a single degree of freedom system using gnu octave. When the variables in the time domain are transformed into the frequency domain, eq.
Instructional material complementing fema 451, design examples sdof dynamics 3 16 approximate periods of vibration asce 705 x t a c t h n t n a 0. Seismic response of single degree of freedom structural fuse. The srs method is thoroughly covered in reference 1. Then by comparing response parameters of the bsdof system i. Pdf dynamic response of a single degree of freedom sdof. Sdof base excitation cont particular solution sine term. The equation of motion of the sdof system is given by mx. T n necessarily r max happens after the end of the loading, and its value can be determined studying the free. Transient response of mdof systems with inerters to. Introduction to undamped free vibration of sdof 12. Part iv derives the equation of motion for the case of a damped sdof system subjected to earthquake shaking. The peakresponseis the maximum of the absolute value of the response ratio, rmax maxfjrtjg. The frequency response function of an sdof system can be displayed in a number of different ways, as shown in the preceding section. The motion of the system in the third figure can be described completely either by x and.
Looking for online definition of sdof or what sdof stands for. Free vibration of singledegreeoffreedom sdof systems. Empirical methods are essentially correlations with experimental data. Gnu octave frequency response of a sdof system youtube. Solving equation 9 gives the system response, expressed in terms of the relative displacement, relative velocity, and relative acceleration. Introduction the response to harmonic loading is one of the. Hd6 numerical integration of sdof 20 tribgroup tamu. We see that the steadystate response has a pure harmonic oscillation at a frequency w. Vibration and modal analysis basics home jefferson lab.
You can use any programming language, software tools excel, matlab, etc. Accuracy of response of singledegreeoffreedom systems to ground motion by robert m. Seismic response of single degree of freedom structural. In this chapter we will focus attention on the zero input response, i. Comparison of four numerical methods for calculating seismic. Ce634 structural dynamics spring 2020 develop a computer program for numerical evaluation of the response for a damped sdof system using the average acceleration method. Part 3 covers the resposne of damped sdof systems to persistent sinusoidal forcing. Tn necessarily rmax happens after the end of the loading, and its value can be determined studying the free. Jump to page 97 pdf count for ready to use formulas.
To obtain the time solution of any free sdof system damped or not, use the sdof calculator. The shock response spectrum srs models the peak response of a singledegreeoffreedom sdof system to a base acceleration, where the systems natural frequency is an independent variable. The second figure denotes a two rotor system whose motion can be specified in terms of. Sdof is listed in the worlds largest and most authoritative dictionary database of abbreviations and acronyms the free dictionary. Accuracy of response of singledegreeof freedom systems. Single degree of freedom systems linkedin slideshare. Observed response of linear sdof time, sec this slide from nonlin shows a series of response histories for a sdof system subjected to a sawtooth loading. Fundamentals of structural vibration school of civil and. This is known as a single degreeoffreedom sdof system as there is only one possible displacement.
Mdof and continuous systems dynamic response to general dynamic loading and transient response formulation of equation of. Singledegreeoffreedom linear oscillator sdof for many dynamic systems the relationship between restoring force and deflection is approximately linear for small deviations about some reference. The purpose of this tutorial is to present some additional notes. Abstractionmodeling idealize the actual structure to a simpli. Gavin fall, 2018 this document describes free and forced dynamic responses of simple oscillators somtimes called single degree of freedom sdof systems. For a nonlinear sdof with hysteretic behavior, once the yield point is exceeded, the spring force is no longer. Accuracy of response of singledegreeof freedom systems to. This document describes free and forced dynamic responses of simple oscillators somtimes called single degree of freedom sdof systems.
Vandiver introduces the single degree of freedom sdof system, finding the eom with respect to the static equilibrium position, sdof system response to initial conditions, phase angle in free decay, natural frequencies, and damping ratios. The prototype single degree of freedom system is a. The problem is now just like any other sdof system with a harmonic excitation 2 22 sin 2. Sdof system a single geometrical coordinate often called a degreeoffreedom is adequate to represent the motion of the system a handy approximation for most of the complex engineering systems 2. Different response parameters were calculated under the scaled record through nonlinear time history analysis. Moreover, many other forces can be represented as an infinite. Most manufacturers of seismometers attempt to achieve this level of damping. Results of the analysis are used to determine the dependence of the timevarying meansquare response of the primary mdof system on the key system parameters such as primary system damping.
Note that w d will equal w n when the damping of the system is zero i. Idealize pushover curve and determine properties of. Forced vibration of singledegreeoffreedom sdof systems. San andres 20 4 and initial conditions 0 t yuut oo. This type of excitation is common to many system involving rotating and reciprocating motion. Sdof harmonically forced vibration purdue university. Forced response of a sdof system how much energy is leaving before next force input. Introduction to the single degree of freedom sdof system. For many structures, mainly metallic ones, it gives a simple. The amplitude of the steadystate response is 0 22 2 2 amplitude 12 p nn f xt k ww ww note that 0 f k is the static deflection, i.
French, university of tennessee at martin approved for public release. Nonlinear seismic response of stiffening sdof systems. Returns a plot with the response of a sdof system to an impulse of magnitude fo newton seconds. Mar 03, 2015 this video is an introduction to undamped free vibration of single degree of freedom systems. Empirical or analytical methods semiempirical methods numerical methods. Dynamics of simple oscillators single degree of freedom systems. Derivation derive the dynamic governing equation of the simpli. Each of these quantities are measured with respect to the fixed base of the structure. Structural dynamics of linear elastic singledegreeof.
This chapter introduces the response of single degreeoffreedom sdof systems to shock loading. Response of a damped system under harmonic force the equation of motion is written in the form. Mdof system capacity curve esdof system capacity spectrum by computing the yield displacement and yield force and also post yield stiffness ratio, one can conduct inelastic sdof analysis using the acceleration timeseries to find the target spectral displacement d 0n. Simple vibration problems with matlab and some help from maple original version by stephen kuchnicki december 7, 2009. The derivation of the equation of motion for a damped sdof system subjected to a time dependent force history is described in part iii. Frequency response function an overview sciencedirect topics. This video is an introduction to undamped free vibration of single degree of freedom systems. Modal superposition analysis uses design response spectrum as basic ground motion input. The time solutions for the free sdof system is presented below for each of the three case scenarios. In the case of random vibration, the vibratory response of the system is also random. Distribution is unlimited prepared for headquarters, u. Part 1 of this document describes some useful trigonometric identities.
Derivation derive the dynamic governing equation of. Solution of the expression gives a complete description of the response of the structure as a function of time derivation of eom 1. Sep 26, 2010 what is a single degree of freedom sdof system. Part 2 shows how damped sdof systems vibrate freely after being released from an initial displacement with some initial velocity. Equivalent sdof systems to simulate mdof system behavior.