Wei-Ren Chen

DYNAMIC STABILITY CHARACTERISTICS OF FUNCTIONALLY GRADED PLATES UNDER ARBITRARY PERIODIC LOADS

The dynamic instability of functionally graded material (FGM) plates under an arbitrary periodic load is studied. The properties of the functionally graded plates (FGPs) are assumed to vary continuously across the plate thickness according to a simple power law. With the derived Mathieu equations, the dynamic instability regions of the FGPs are determined by using the Bolotins method. The in-plane periodic load is taken to be a combination of periodic axial and bending stress in the example problems. The influences of the volume fraction index, layer thickness ratio, static and dynamic load on the dynamic instability of ceramic-FGM-metal plates are discussed. The results reveal that the excitation frequency, instability region and dynamic instability index of these plates are significantly affected by the static load, dynamic load, volume fraction index and layer thickness.

Stability of parametric vibrations of laminated composite plates

The dynamic stability of laminated composite plates subjected to arbitrary periodic loads is studied based on the first-order shear deformation plate theory. The in-plane load is taken to be a combination of periodic biaxial and bending stress. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to determine the regions of dynamic instability based on Bolotins method. Numerical results reveal that the dynamic instability is significantly affected by the modulus ratio, number of layer, static and dynamic load parameters. The effects of various important parameters on the instability region and dynamic instability index are investigated.

Closed-Form Solutions for Free Vibration Frequencies of Functionally Graded Euler-Bernoulli Beams

The bending vibration of a functionally graded Euler–Bernoulli beam is investigated by the transformed-section method. The material properties of the functionally graded beam (FGB) are assumed to vary across its thickness according to a simple power law. Closed-form solutions for free vibration frequencies of FGBs with classical boundary conditions are derived. Some analytical results are compared with numerical results found in the published literature to verify the accuracy of the model presented, and a good agreement between them is observed.

Effects of Locally Distributed Kelvin–Voigt Damping on Parametric Instability of Timoshenko Beams

The effect of partially distributed internal damping of the Kelvin–Voigt type on the parametric instability of a Timoshenko beam subjected to periodic axial loads is studied. To model the dynamic behavior of the beam, a coupled set of second-order linear ordinary differential equations with periodic coefficients is established by the finite element method. A quadratic eigenvalue equation is derived for a parametrically excited damped system to determine the instability regions of the beam of concern based on Bolotins method. The effects of internal damping, size and location of the damped segment, ratio of thickness to length and static load factor on the parametric instability of the beam are studied, along with the stabilizing effect of the Kelvin–Voigt damping on the primary parametric resonance presented. The results reveal that the beam with a larger damped segment positioned near the fixed end is dynamically more stable.

Hygrothermal Effects on Dynamic Instability of Hybrid Composite Plates

The dynamic characteristics of hybrid composite plates under an arbitrary periodic load in hygrothermal environments are investigated. The material properties of the plate are assumed to be dependent on the temperature and moisture. The governing equations of motion of the Mathieu-type are established based on the Galerkin method with reduced eigenfunction transforms. The periodic stress is taken to be a combination of the pulsating axial and bending stress in the example problems. Based on Bolotin’s method, the dynamic instability behaviors of hybrid composite plates are determined. The effects of layer thickness ratio, fiber volume fraction, temperature rise, moisture concentration and dynamic load on the instability regions of hybrid composite plates are studied, along with the dynamic instability index discussed. The results reveal that the layer thickness ratio and hygrothermal conditions have a significant impact on the dynamic instability of hybrid composite plates.

Vibration and Stability of Initially Stressed Hybrid Composite Plates in Hygrothermal Environments

Vibration and stability of hybrid composite plates with arbitrary initial stresses in hygrothermal environments are investigated. The governing equations, including the effects of moisture-caused, thermal, and initial stresses, are established based on the variational energy method. The influence of temperature and moisture on material properties of the hybrid composite plates is considered. The initial stress is taken to be a combination of a uniaxial load and pure bending. Example of an initially and hygrothermally stressed hybrid laminated plate with simply supported edges is solved. Effects of the layer thickness ratio, fiber volume fraction, initial stresses, temperature, and moisture concentration on the natural frequency and buckling load of hybrid composite plates are studied.