The geometric nonlinearity due to static and thermal load can significantly alter the vibration response of structures. This study presents a semi-analytical approach to illustrate the nonlinear vibration of clamped-clamped beams under static and thermal loads. The von Karman strain and Hamilton’s principle are employed to derive the nonlinear static equilibrium equation and nonlinear governing equation. The vibration equation’s coefficient is variable. The transfer-matrix method and local homogenization are used to solve the equation. The proposed method’s accuracy is validated by commercial software and literature. The numerical results indicate that uniform stress caused by thermal load only reduces the structural mode frequencies. The geometric nonlinearity of the structural static deformation affects both the mode frequencies and mode shapes. And the mode shapes cannot be approximated by harmonic functions. When the static deformation is significant, the structure’s local RMS response is substantially affected. The combined loads have a more significant impact on the acceleration response than the superposition of individual load effects.

This paper studies the yield behavior of a woven carbon-fiber-reinforced silicon-matrix (C/SiC) composite under dynamic tensile loading. Experiments were carried out to obtain the tensile properties of the C/SiC composite at a strain rate range of 2 × 10⁻⁵/s to 99.4/s. A strain-rate-dependent yield criterion based on the distortional strain energy density theory is established to describe the yield behavior. The interval uncertainty is considered for a more reliable yield prediction. Experimental results show that the yield stress, elastic modulus, and yield strain of the C/SiC composite grow with the increasing strain rate. The failure mode transitions from progressive crack extension to uneven fiber bundle breakage. The predicted results by the yield criterion match well with experimental data. Experimental results are enveloped within the uncertainty level of 45% in the critical distortional energy density, corresponding to an uncertainty of 14% and 11% in the yield stress and yield strain, respectively. With the support of the proposed strain-rate-dependent yield criterion, the yield behavior of the C/SiC composite under dynamic loading conditions can be predicted with reasonable accuracy.

The frequency-domain flutter analysis method requires a linear model as input; however, when a telescopic actuator is applied to morphing aircraft, traditional frequency-domain flutter analysis methods face challenges in addressing issues involving contact nonlinearity. To enable classical frequency-domain methods to handle this type of nonlinearity, this paper presents an equivalent linearization modeling method for morphing aircraft wing structures. The proposed modeling method uses rod elements as the equivalent linearization elements and avoids the need to handle node correspondence issues. The model is parameterized by the rod element’s elastic modulus, contact surface distance, and element length coefficient. Upon completion of the equivalent modeling, flutter analysis can be performed by the PK method. The proposed modeling method increases modeling efficiency while maintaining the accuracy of the model. A simulation study of a typical hypersonic telescopic wing structure is conducted. The effects of angle of attack and altitude on flutter characteristics are analyzed. The proposed modeling method effectively captures both the static and dynamic characteristics of the original structure. The flutter Mach number decreases with increasing extension length, and it increases with altitude and angle of attack. The flutter frequency decreases with increasing extension length, angle of attack, and altitude.