Nonlinear dynamic analysis of thermally deformed beams subjected to uniform loading resting on nonlinear viscoelastic foundation. (English) Zbl 1490.74053
Summary: The purpose of this article is to examine the dynamic behavior of shear deformation beams subjected to high-speed thermal and mechanical loadings. The structure’s theoretical equations are derived by employing the first-order shear deformation theory and nonlinear strain-displacement relationships. Loading is accomplished in two different time stages. Initially, the beam is subjected to stress and strain due to fast surface heating. We explore the circumstances that result in dynamic bending or buckling. After that, the bent beam is abruptly exposed to consistent pressure over time. For this reason, two-parameter mechanical loading is proposed. The first parameter indicates the final loading amount, while the second specifies the loading rate. As a consequence of this load, heat-induced displacements are decreased. Additionally, it is investigated whether mechanical loading results in snap-through in the structure based on the Budiansky criterion. The transient heat conduction equation is solved analytically, and the temperature profile is obtained over time. The nonlinear dynamic partial differential equations are then solved by the Chebyshev collocation, Newmark, and Newton-Raphson numerical methods. Moreover, the effect of a nonlinear viscoelastic foundation on the beam response is examined in this research. After demonstrating validation, some novel outcomes are provided to characterize the system’s response in various situations.
MSC:
| 74H60 | Dynamical bifurcation of solutions to dynamical problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74F05 | Thermal effects in solid mechanics |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
dynamic bending; dynamic buckling; dynamic snap-through; Chebyshev collocation method; Newmark method; Newton-Raphson methodReferences:
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