Nonlinear dynamics of a third-order reduced model of thermomechanically coupled plate under different thermal excitations

Settimi, Valeria; Saetta, Eduardo; Rega, Giuseppe

doi:10.1007/s11012-019-01117-w

Cited by 7 publications

(3 citation statements)

References 35 publications

(58 reference statements)

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“…Among the few works, Refs. [26,27] should be mentioned, where the nonlinear thermoelastic dynamics is analyzed in referring to Third-order Shear Deformation Theory (TSDT).…”

Section: Introductionmentioning

confidence: 99%

Simplified Approach to Nonlinear Vibration Analysis of Variable Stiffness Plates

González

Vescovini

2023

J. Compos. Sci.

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A formulation for the analysis of the nonlinear vibrations of Variable Stiffness (VS) plates is presented. Third-order Shear Deformation Theory (TSDT) is employed in conjunction with a mixed variational formulation. The solution is sought via Ritz approximation for the spatial dependency, while time dependency is handled via Differential Quadrature (DQ) and Harmonic Balance (HB) methods. The main advantage of the framework is the reduced computational time, which is of particular interest to explore the large design space offered by variable stiffness configurations. The results are validated against reference solutions from the literature. Exemplary parametric studies are presented to demonstrate the potential of the approach as a powerful means for exploring the nonlinear vibration response of VS plates.

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“…Among the few works, Refs. [26,27] should be mentioned, where the nonlinear thermoelastic dynamics is analyzed in referring to Third-order Shear Deformation Theory (TSDT).…”

Section: Introductionmentioning

confidence: 99%

Simplified Approach to Nonlinear Vibration Analysis of Variable Stiffness Plates

González

Vescovini

2023

J. Compos. Sci.

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“…With the increased significance of multiphysics phenomena occurring in many technological contexts, linear and nonlinear dynamic responses of materials and structures in thermal environments become a research topic of significant interest recently [1,2]. Temperature becomes a significant factor that may change the dynamic characteristics and responses of some essential structure elements, for example, beam [3], shells [4], pipes [5], and cables [6].…”

Section: Introductionmentioning

confidence: 99%

Temperature Effects on Dynamic Properties of Suspended Cables Subjected to Dual Harmonic Excitations

Zhao

Zheng

Lin

et al. 2021

Shock and Vibration

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The paper aims at studying the influences of temperature on the suspended cables’ dynamical behaviors subjected to dual harmonic excitations in thermal environments. Significantly, the quadratic nonlinearity and the corresponding secondary resonances are considered. By introducing a tension variation factor, the nonlinear vibration equations of motion could be obtained based on the condensation model. By using Galerkin’s procedure, the continuous model of the nonlinear system is reduced to a set of infinite models with quadratic and cubic nonlinearities. By using the multiple scales method, the resultant reduced model is solved and the stability analysis is also presented in two simultaneous resonance cases. Nonlinear dynamical behaviors with thermal effects are presented using bifurcation diagrams, time-history curves, phase portraits, frequency spectrums, and Poincaré sections. The numerical results show that thermal effects induce different scenarios. The sensitivities of linear (natural frequency) and nonlinear (quadratic and cubic) coefficients to temperature variations are different. The temperature may increase or decrease the response amplitudes depending on the excitation amplitude and the sag-to-span ratio. The inflection point is shifted and exhibited at a smaller or larger excitation amplitude in thermal environments. The resonant range between two Pitchfork bifurcations seems to be reduced when the temperature is decreasing. The response amplitude is very sensitive to temperature, and even an opposite spring behavior may be exhibited due to warming/cooling conditions. However, the periodic motions seem independent of temperature variations.

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“…Nonlinear dynamics of thermoelastic laminated plate vibrations has been studied by Settimi et al [8]. The plate model has been derived on the basis of von Karman plate theory and nonlinear temperature distribution along the beam thickness.…”

mentioning

confidence: 99%

Recent advances in nonlinear dynamics and vibrations: special issue of meccanica

2020

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Nonlinear dynamics of a third-order reduced model of thermomechanically coupled plate under different thermal excitations

Cited by 7 publications

References 35 publications

Simplified Approach to Nonlinear Vibration Analysis of Variable Stiffness Plates

Simplified Approach to Nonlinear Vibration Analysis of Variable Stiffness Plates

Temperature Effects on Dynamic Properties of Suspended Cables Subjected to Dual Harmonic Excitations

Recent advances in nonlinear dynamics and vibrations: special issue of meccanica

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