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Abstract
This paper presents a comparative analysis of linear and non‐linear problems of plate dynamics. By expressing the internal friction coefficient of the material by power polynomial γ= γ0 + γ1ϵ0 + γ2ϵ0 2+…, we assume γ= γ0 = const for a linear problem. When at least two polynomial terms are taken, a non‐linear problem is obtained. The calculations of resonance amplitudes of a rectangular plate yielded 3 per cent error: a linear problem yields a higher resonance amplitude. Using the Ritz method and the theory of complex numbers made the calculations. Similar methods of calculation can be used in solving the dynamic problems of thin‐walled vehicle structures.
Highlights
Most parts of a vehicle body consist of a light frame covered with thin-walled shells and plates
Though the dynamic problems of shells and plates have been discussed in many papers, some issues require special consideration [1, 2, 6, 8,9,10,11, 13]
The dissipation of oscillational energy in material is usually expressed by the logarithmic decrement δ (ε 0 ) or the internal friction coefficient γ = γ (ε 0 ), in which ε 0 is the amplitude of deformation
Summary
Most parts of a vehicle body consist of a light frame covered with thin-walled shells and plates. Assuming δ (ε 0 ) = const , we get a linear problem and the calculations are simplified to a large extent. Formulation of the problem ( ) The function of the oscillation form w0 x, y can be expressed as follows: w0 (x, y) = a1Φ1(x, y) + a2Φ 2 (x, y) + ... By applying methods of approximating functions, the experimentally determined relationship γ = γ (ε 0 ) can be expressed by the power polynomial γ γ. Hamilton’s principle applied to a system of forces, including inelastic forces, can be expressed by a variation equation as follows: τ2 d S = δ ∫ T − (1 + iγ )V + W d t = 0 , (1). Let us consider the first type of oscillation of the plate supported around the periphery
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