Research On Multi-Physics Fields Coupled Vibrations Of Beam Structures

The multi-physics field coupled vibrations of beams are systematically investigated in this dissertation. The Green’s function method is applied and developed. Using the Green’s function method, the analytical solutions of the two fields (cracked field and elastic field, elastic field and thermal field, elastic fields and electric fields) and the three fields (elastic field, thermal field and electric field) coupled vibration problems are obtained. The influences of the coupling effects (cracks, thermoelastic effects, electroelastic effects and thermoelectroelastic effects) on the dynamic characteristics of the beam, temperature field characteristics and voltage characteristics are discussed in this dissertation.In Chapter 1, the background and significance of this work is illustrated. From the aspects of Green’s functions, the vibration of a cracked beam, the coupled thermoelastic vibration of a beam, the coupled electroelastic vibration of a piezoelectric beam and the coupled thermoelectroelastic vibration of a piezoelectric beam, some reviews on the past researches and the main problem in these aspects are presented, and then a brief statement on the research plan of this dissertation is given.The dynamic solutions for forced vibrations of Timoshenko beams in a systematical manner are sutdied in Chapter 2. Damping effects on the vibrations of the beam are taken into consideration by introducing two characteristic parameters. Laplace transform method is applied in the present study and corresponding Green’s functions are presented explicitly for beams with various boundaries. The present solutions can be readily reduced to those for others classical beam models by setting corresponding parameters to zero or infinite. Numerical calculations are performed to validate the present solutions and the effects of various important physical parameters are investigated.In Chapter 3, explicit expressions of the steady-state responses of a cracked Euler-Bernoulli beam submitted to a harmonic force are presented. The mechanical properties of cracked sections of the beam are characterized by local stiffness models available in literature. Fundamental dynamic response of a beam with one crack is obtained by means of Green’s function method. For a multi-cracked beam, transfer matrix method is employed to derive the steady-state response, which can be readily reduced to these for a single-cracked beam. Numerical calculations are performed to validate the present solutions, to compare the dynamical behaviors of the beam corresponding to various classical local compliance models and to study the influences of crack geometry (depth and location) on the mechanical behavior of beam. Furthermore, the interactions of two cracks in the beam are particularly studied. The present analytical results can serve as a valuable benchmark to the future numerical calculations and experimental studies.Chapter 4 focuses on obtaining the direct expressions of steady-state two dimension temperature and displacement responses for the coupled thermoelastic vibrations of Timoshenko beams subjected to both a harmonic concentrated heat flux and a harmonic uniform force. Coupling effects between temperature and displacement fields will be discussed conveniently through these analytical solutions, while these coupling effects are difficult to be obtained by the FEM and the other numerical methods. Damping effects on the transverse and rotational directions are taken into account in the vibration equations. Green’s functions and superposition principle are used in the present study to solve the coupled thermoelastic vibration equations of a beam. The Green’s functions for heat conduction equations and vibration equations are presented explicitly for the beams with various mechanical and thermal boundaries with the aid of eigenfunctions expansion method and Laplace transform technology. Numerical calculations are performed to validate the present solutions, and the influences of some important physical parameters on the coupling effects of the solutions are discussed as well.Chapter 5 mainly focuses on the closed-form solutions for the forced vibrations of cantilevered unimorph piezoelectric energy harvesters with tip mass and mass moment of inertia. Timoshenko beam assumption is used in this work to create the coupled electromechanical model of the piezoelectric energy harvester. Two damping effects, transverse and rotational damping, are taken into account. Green’s function method and Laplace transform technology are applied to solving the coupled electromechanical vibration system. The traditional case of a harmonic base excitation is considered and numerical calculations are performed to validate the present solutions by comparing the present solutions with the results in literature. The influences of shear effect and rotational inertia on the present solutions are discussed. The influence of load resistance on the electric power is studied, and the optimal load resistance is obtained. For the soft materials:PZT-5A & 5H, an optimum proposal is proposed to improve electricity generation performance of PZT-5A & 5H.A coupled piezothermoelastic model is created for the piezoelectric energy harvesters with a RLC circuit attached on the beam subjected to a harmonic uniform thermal load in Chapter 6. The direct expressions of steady-state two dimension temperature field, displacement and voltage responses of the coupled piezothermoelastic model are obtained. Coupling effects between temperature, displacement and voltage fields, which are difficult to be obtained by the FEM and the other numerical methods, are discussed conveniently through these analytical solutions. Structural viscoelasticity damping effect and viscous air damping effect are taken into account in the vibration equations. Green’s functions and superposition principle are used in the present study to solve the coupled piezothermoelastic vibration system. The Green’s functions for heat conduction equations and vibration equations are presented explicitly with the aid of eigenfunctions expansion method and Laplace transform technology. Numerical calculations are performed to validate the present solutions, and the influences of some important physical parameters on the coupling effects of the solutions of the coupled piezothermoelastic model are discussed as well.Finally, the research content, research methods and research results of this work are summarized, and a brief plan for future studies is given.