多自由度运动方程的建立分析课件.ppt

1、第九章第九章结构动力学多自由度运动方程的建立单自由度体系两种描述方法 单一的坐标 一个变形函数广义坐标主要有： 荷载的空间分布 荷载的时间历程 结构自身的动力特性刚度、质量及阻尼 自由度方向的位移幅值 广义坐标表示的一组位移模式的幅值 采用第一种方法111122223333( )( )( )IDSIDSIDSfffp tfffp tfffp tIDSf + f + f = p(t)111 112213 31SNNfk vk vk vk v221 122223 32SNNfk vk vk vkv1 12233SiiiiiNNfk vk vk vk vsf = kv ijk.21321222322

2、211113121121iiNiiiiiNiNiSiSSvvvkkkkkkkkkkkkkkkfff11111213112232222122123DiNDiND iiiiiiiiNfvcccccfcccvccfvccccc Df= cv ijc 11111213112232222122123IiNIiNIiiiiiiiiNfvmmmmmfmmmvmmfvmmmmm If = mv iim v+ cv+ kv = p(t)m iDSGf + f + f - f= p(t)11121311122322212212312iNiNiiiiiiiNGGGGGGGGGGGGiGGGGGGkkkkkfvfkk

3、kkkvvfkkkkk GGf= kvijGkGmv+cv+kv-k v=p(t)mv+cv+kv=p(t)mv+cv+kv = p(t)Gk = k - k 第十章第十章结构动力学结构特性矩阵的计算ijf11111221331NNvfpfpfpfp11121311112223222122123iNiNiiiiiiiiNfffffvpvpfffffvpfffffv=f psv = ffnTiii = 111U=pv=pv22T1U=pfp2T1U=vk v2Tv kv0Tp fp0sf = kvv=f pTvv0Asf = kv1k1kfTaaiaiaaa11W=p v=p v22TTbbab

4、bbab1W +W =p v +p v2 TTT1aabbabaabbab11W=W +W +W = p v + p v +p v22Tbbbb1W=pv2TTaabaaaba1W+ W=pv + pv2TTT2bbaababbaaba11W=W +W +W = p v + p v +p v22 TTabbap v =p v TTabbapv= pvTf = fTTabbap fp = p fpTk = k v=f psf = kv 231()13()2 ()xxxLL23()(1)xxxL232()3()2()xxxLL24()(1 )xxxLL 11223344( )( )( )( )(

5、)v xx vx vx vx v1234ababvvvvvv 113EaaWvpvk3( )( )( )xEI xx 11130( )( )( )LWvEI xxx dx1 310()()()LkE Ixxxd x0( )( )( )LijijkEI xxx dx ()( )()mnPiiiiiiiikkkk33()()v xx v 33( )( ) ( )( )( )Ifxm x v xm xx v 0( )( )LaaIpvfxv x dx13130()()()Lmm xxx dx0( ) ( )( )Liiijmm xxx dx0()()()Lijijcc xxx dx110( )( ,

6、 )( )Lptp x tx dx 0( )( , )( )Liiptp x tx dx1( )1xxL2( )xxL( , )( ) ( )p x txt0( )( )()()Liipttxx dx 1111ijGiijGifvNvflGGf= k v131EGaaGWfvkv1( ) ()dWN x de31110( )( )( )LdxdxWvN xdxdxdx13310( ) ( ) ( )LGkN xxx dx0( ) ( )( )LGijijkN xxx dx0tsttttsttsvfkkfkkvf.21321222322211113121121iiNiiiiiNiNiSiSSvvvkkkkkkkkkkkkkkkfff000ttttttttttttttvvvMc ck kpMc ck kvvv -1tt=-kk vv-1tttttst(k -k kk )v =fttstk v= f-1tttttk =k -k kk11110()()tsttttsttstttttttststttttttttttttttvfkkfkkvfvkk vkk kkvffkk kkvk vkkk kk ttttttttttM vc vk vp