Wuhan University of Technology-Chapter5Responseto impulsiveloading5.1 General nature of impulsive loading5.2 Sine-wave impulse5.3 Rectangular impulse5.4 Triangular impulse5.5 Shock or response spectra5.6 Approximateanalysis of impulsive-load response6-1
6-1 Wuhan University of Technology 5.1 General nature of impulsive loading 5.2 Sine-wave impulse 5.3 Rectangular impulse 5.4 Triangular impulse 5.5 Shock or response spectra 5.6 Approximate analysis of impulsive-load response Chapter 5 Response to impulsive loading
Wuhan University of Technology5.1 General nature of impulsive loading The general solution must also include thetP(t)particularsolutionwhichdependsupontheformofdynamicloading..Suchaload consists of a singleprincipalimpulseofarbitraryform,asillustratedinFig51.Impulsiveorshockloadsfrequentlyareofgreatimportanceinthedesignofcertainclasses of structural systems, e.g., vehiclessuchastrucksorautomobilesortravelingcranes.Dampinghasmuchlessimportanceincontrollingthemaximumresponseofastructuretoimpulsiveloadsthanforperiodicorharmonicloadsbecausethemaximum response to a particular impulsive load will be reached in a veryshorttime,beforethedampingforcescanabsorbmuchenergyfromthestructure..For this reason only the undamped response to impulsive loads will beconsidered in this chapter.6-2
6-2 Wuhan University of Technology 5.1 General nature of impulsive loading • The general solution must also include the particular solution which depends upon the form of dynamic loading. • Such a load consists of a single principal impulse of arbitrary form, as illustrated in Fig. 51. Impulsive or shock loads frequently are of great importance in the design of certain classes of structural systems, e.g., vehicles such as trucks or automobiles or traveling cranes. • Damping has much less importance in controlling the maximum response of a structure to impulsive loads than for periodic or harmonic loads because the maximum response to a particular impulsive load will be reached in a very short time, before the damping forces can absorb much energy from the structure. • For this reason only the undamped response to impulsive loads will be considered in this chapter
Wuhan University of Technology> Suddenly Applied Constant Load[0,t<0Fp(t)F,(t) :t>0Fpot>0:POFpo sin o(t -t)dty(t) =(l-cosot)= y(1-cosot)二moJomoFPO=F,SStatic displacement under the load FpY stmo?6-3
6-3 Wuhan University of Technology Suddenly Applied Constant Load 0 0, 0 ( ) , 0 p P t F t F t t>0： 0 0 2 0 1 ( ) sin ( ) (1 cos ) (1 cos ) t P P st F y t F td t y t m m 0 2 P st P F y F m Static displacement under the load FP FP(t) t FP0
Wuhan Universityof Technology2元T03元wtJ(t);质点围绕静力平衡位置作简谐振动[y(t)]maxβ==2Y st突加荷载所引起的最大位移比相应的静位移增大1倍6-4
6-4 Wuhan University of Technology max [ ( )] 2 st y t y 突加荷载所引起的最大位移比相应的静位移增大1倍 yst y(t) ωt 0 π 2π 3π 质点围绕静力平衡位置作简谐振动
Wuhan University of Technology> Suddenly Applied Load with a Limited DurationFp(t)当t<00,Fpo当o<t<u0,当t>uu阶段I(0<t≤u)：此阶段的荷载情况与突加荷载相同y(t) = ys, (1 -cos ot)6-5
6-5 Wuhan University of Technology Suddenly Applied Load with a Limited Duration 0 0, 0 () , 0, p P t Ft F 当当0<t<u 当t>u 阶段I(0≤t≤u)：此阶段的荷载情况与突加荷载相同 FP(t) t P u (1 cos ) st y ty t