2017
DOI: 10.1007/s00542-017-3681-5
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Investigation of free vibration response of smart sandwich micro-beam on Winkler–Pasternak substrate exposed to multi physical fields

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Cited by 9 publications
(2 citation statements)
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“…The first example is about the natural frequencies for a single‐layered macro isotropic beam, in absence of foundation. The results are presented in Table . The following specifications are used to obtain the results of this table: leftE=751em GPa ,ρ=27001em kg /normalm3,ν=0.33,hc=0.20.16emnormalm,L=10hcIt is noteworthy that the dimensionless frequency for this table is defined as Ω=ωLI0/A1, where ω is dimensional natural frequency.…”
Section: Numerical Results and Discussionmentioning
confidence: 99%
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“…The first example is about the natural frequencies for a single‐layered macro isotropic beam, in absence of foundation. The results are presented in Table . The following specifications are used to obtain the results of this table: leftE=751em GPa ,ρ=27001em kg /normalm3,ν=0.33,hc=0.20.16emnormalm,L=10hcIt is noteworthy that the dimensionless frequency for this table is defined as Ω=ωLI0/A1, where ω is dimensional natural frequency.…”
Section: Numerical Results and Discussionmentioning
confidence: 99%
“…The displacement field relations for each point of the micro sandwich beam along the x ‐ and z ‐axes according to the SSDBT are written for all three layers as follow: leftux,z,t=u0x,tzxw0x,t+fzϕx,t,leftwx,z,t=w0x,tThe rotation of the cross section about y ‐axis is shown by ϕ(x,t). Also, the shear strain function is as follow: fz=HπsinπzHThe non‐zero strain components based on the SSDBT are presented as follows: leftεxx=xu0x,tz2x2w0x,t+HπsinπzHxϕfalse(x,tfalse),leftγxz=cosπzHϕx,t…”
Section: Governing Equationsmentioning
confidence: 99%