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- W2079557712 abstract "Scaling laws for vibrating beams and plates are investigated. It is shown how scaling laws can be derived directly from the equations of motion by non-dimensionalizing the variables of these. The scaling laws obtained from the classical equations (Bernoulli-Euler's beam and Lagrange's plate equations) are non-restrictive in the sense that they allow for independent scaling of the system variables. The scaling laws obtained from the advanced equations (Timoshenko's beam and Mindlin-Reissner-Uflyand's plate equation) are identical with the Newtonian scaling requirements. The non-restrictive plate scaling law is applied in an experimental study to predict natural frequencies of a plate from the measured natural frequencies of a model. Non-restrictive laws incorporating the effects of shear and rotatory inertia can be obtained by using the classical theory scaling laws together with approximate compensation factors obtained by assuming that, at higher modes, the compensation factors obtained for simply supported systems are applicable to systems having other boundary conditions." @default.
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- W2079557712 date "1972-01-01" @default.
- W2079557712 modified "2023-09-23" @default.
- W2079557712 title "An investigation of scaling laws for vibrating beams and plates with special attention to the effects of shear and rotatory inertia" @default.
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- W2079557712 doi "https://doi.org/10.1016/0022-460x(72)90766-3" @default.
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