Vibration Characteristic Analysis And Control Research Of Fractional Viscoelastic Beams

Viscoelastic beam structures have been widely used in aerospace,ship and vehicle engineering due to its excellent vibration reduction performance.Compared with the integer-order model,the fractional-order model can describe the mechanical properties of viscoelastic materials in a wide frequency range with fewer parameters.It is of great significance to study the vibration of viscoelastic beam structures based on the fractional calculus theory.Due to the urgent demand for active vibration reduction of viscoelastic beam structures,the application of intelligent materials in viscoelastic beam structures has received much attention.In this paper,the vibration analysis method of viscoelastic beam structures based on fractional calculus theory,the transmission characteristics of structural vibration wave based on wave vector method,fractional dynamic models of viscoelastic sandwich beams and local vibration control strategies of a piezoelectric sandwich beam are studied.Specific studies are as follows:(1)For the difficulty in solving the fractional-order dynamic equations of viscoelastic uniform beam structures with complex support boundaries and piecewise uniform beam structures,the wave vector method is extended to structural vibration analysis process of viscoelastic beam structures.The wave vector method obtains a steady-state analytical solution of the equation by matrix operations in frequency domain,which is easy to achieve iterative calculations.The effects of model and structural parameters on the vibration wave transmission characteristics under different interfaces are analyzed based on the wave vector method,which can better explain the flow of vibration energy on the structure,and provide a theoretical basis for the study of vibration wave transmission characteristics of non-uniform beam structures.This study provides a method for solving the fractional-order dynamic equations of viscoelastic beam structures.(2)Since there are few methods for vibration analysis and analysis of vibration wave transmission characteristics of viscoelastic non-uniform beam structures,especially for vibration analysis under fractional-order models,the wave vector method is extended to the vibration analysis and the analysis of vibration wave transmission characteristics of non-uniform beam structures.The dynamic responses and characteristics of continuous variable cross-section beams,acoustic black hole structures and axial non-uniform beams with different fractional-order models are obtained.The effects of the three non-uniform structures on vibration wave transmission characteristics of are analyzed,and the results enrich the vibration wave transmission theory of structures under fractional-order models,and provide a theoretical basis for the design of energy converging structures and the research of structural energy recovery.(3)For viscoelastic materials are used in sandwich beams,the fractional calculus theory is introduced into the modeling of sandwich beams.Currently,there are few studies on the vibration analysis and fractional-order models of film-covered sandwich beams.In this paper,a fractionalorder dynamic model is established based on the fractional-order constitutive equation and the equilibrium condition of forces.To improve the accuracy of the RKU model,a fractional-order dynamic model of a constrained damping sandwich beam is established.The fractional-order model has fewer parameters than the integer-order mode with same description accuracy,and it can degenerate to the general integer-order model,which is a more generalized model.The introduction of fractional calculus theory brings difficulties in solving the dynamic equations of sandwich beams.Therefore,the wave vector method is extended to the vibration analysis process of viscoelastic sandwich beams described by fractional-order models,and the effects of beam structure parameters on the dynamic characteristics of sandwich beam are analyzed.(4)Local vibration control methods for a film-covered sandwich beam under fractional-order models are proposed.Currently,most of the vibration control methods for sandwich beam structures are global vibration control methods,while there are few local vibration control methods,especially the local vibration control method under fractional-order models.For the vibration control problem in the local region of the film-covered sandwich beam,an optimization control method based on particle swarm optimization(PSO)algorithm and a vibration wave feedback local control algorithm based on wave vector method are proposed.The local vibration control method does not require real-time feedback calculation and it achieves the local vibration control effect by adjusting the transmission amount and direction of vibration energy.To obtain better control performance in the local area of the beam,PSO algorithm is used to optimize the parameters of piezoelectric sheets.The effects of various parameters on the local area control performance are discussed,and the variation trend of piezoelectric sheet parameters is analyzed.To compare the control effect of local control method under steady-state response,a linear quadratic regulator(LQR)control method is designed based on fractional-order state equation.The results show that both the local control method and the optimal control method can achieve the local vibration control,but the optimal control method needs a large voltage;Compared with LQR method,the local control method has better control effect in high frequency range.