- #1
lalala1plus1
Hello,
I am trying to derive the (Euler-Bernoulli) beam equation of a composite beam to determine the vibration and natural frequencies (up to 3 modes) of the beam.
The composite beam can be modeled as in the picture below:
In order to apply the general equation:
(EI)effw'''' = m'eff (d2w/dt2)
in which
(EI)eff : Effective Flexural Rigidity of the composite beam
m'eff : Effective mass per unit length of the composite beamI know that for pure layered composite beam (with n layers), we can simply add up the flexural rigidity and mass per unit length of each layer: (EI)eff,layered = Σ EnIn and m'eff,layered = Σ ρnbntn
However, for my case, I have 3 different materials laminated in parallel in the middle layer. Is there any way to get the effective EI and m' of this layer, so that I can add them with those from the top and bottom layer to find the total effective flexural rigidity and mass per unit length of the whole beam?
I am urgently looking forward for explanation, and if better, with literature suggestion, which I can read it in detail.
Thank you very much for the help!
I am trying to derive the (Euler-Bernoulli) beam equation of a composite beam to determine the vibration and natural frequencies (up to 3 modes) of the beam.
The composite beam can be modeled as in the picture below:
In order to apply the general equation:
(EI)effw'''' = m'eff (d2w/dt2)
in which
(EI)eff : Effective Flexural Rigidity of the composite beam
m'eff : Effective mass per unit length of the composite beamI know that for pure layered composite beam (with n layers), we can simply add up the flexural rigidity and mass per unit length of each layer: (EI)eff,layered = Σ EnIn and m'eff,layered = Σ ρnbntn
However, for my case, I have 3 different materials laminated in parallel in the middle layer. Is there any way to get the effective EI and m' of this layer, so that I can add them with those from the top and bottom layer to find the total effective flexural rigidity and mass per unit length of the whole beam?
I am urgently looking forward for explanation, and if better, with literature suggestion, which I can read it in detail.
Thank you very much for the help!