基础激励下Timoshenko梁冲击失效准则设计方法

A Design Method of Impact Failure Criteria for Timoshenko Beams Under Support Excitations

给出了基础激励下Timoshenko梁冲击失效准则设计方法,建立了基于Timoshenko梁的冲击动力学模型.通过求解系统运动方程并结合边界条件,给出了系统固有频率方程,给出了固有振型的计算方法.为了克服基础激励下冲击响应求解的困难,对Timoshenko梁的位移响应进行了假设,求解了系统的线位移和角位移冲击响应,进而得到了任意截面的内力,以及截面的最大von Mi⁃ses等效应力,基于von Mises屈服准则,给出了分别采用位移、速度和加速度确定失效准则的方法.典型算例的冲击响应计算结果表明,在20~5000 Hz频率范围内,算例中的Timoshenko梁存在3种失效模式,分别是根部、中部附近和末端发生屈服破坏.针对每种失效模式,分别给出了以最大可用位移幅值、速度幅值和加速度幅值表示的冲击失效准则.

A design method of impact failure criteria for Timoshenko beams under support exci⁃tations was established.The system motion equations were solved and combined with the boundary conditions to give the natural frequency equations and the mode shapes for the sys⁃tem.To overcome the difficulty of solving impact responses under support excitations,the pre⁃sumed displacement response of the Timoshenko beam was used to obtain the linear and angu⁃lar displacements of the system,and in turn the internal forces and maximum equivalent von Mises stresses on related cross sections.Based on the von Mises yield criterion,the method de⁃termining the failure criteria of displacement,velocity and acceleration was given.The calculat⁃ed impact responses of a typical example show that,there are 3 failure modes for the Timosh⁃enko beam within the frequency range of 20 Hz to 5000 Hz,i.e.,yield failures at the root,the middle and the end.For each failure mode,the impact failure criteria expressed with the maxi⁃mum available displacement amplitude,velocity amplitude and acceleration amplitude were giv⁃en.