Vibration Isolation Performance Of Beam And Panel Structures With Negative Stiffness Device

Vibration is a common physical phenomenon in engineering systems,which causes discomfort to human beings and many troubles such as fatigue and noise to precision instruments and civil structures.Therefore,the study of vibration isolation technology and its application in the industrial field is of great significance.Passive vibration isolation is widely used in vibration control due to its simple structure,easy operation,and no need for additional energy input.The nonlinear vibration isolator composed of positive and negative stiffness(NS)elements has the characteristics of high-static-low-dynamic(HSLD)stiffness,which can ensure high load-bearing capacity and have excellent vibration isolation performance.It has been widely studied by researchers at home and abroad.However,current research on passive vibration isolation mainly focuses on the vibration isolation problem of single degree-of-freedom vibration isolation systems under discrete concentrated loads,and the elastic vibration of the protected structur e itself is usually ignored.The study of vibration isolation of common flexible structures such as beams and plates in civil,mechanical,aviation,and aerospace fields has more important practical significance.Starting from the principle of low-frequency vibration isolation of nonlinear NS structures,this paper applies the concept of NS device to the problem of low-frequency vibration isolation for flexible continuum structures.According to the specific support conditions of the beam and plate structur es under different boundary conditions,different types of NS structure elements are considered and their dynamic modeling is carried out to explore the variation of the system’s natural frequency with the equivalent support stiffness and the impact of int roducing NS structure elements on the system’s natural characteristics.Subsequently,the nonlinear partial differential equation of the continuous system subjected to base displacement excitation is derived,and an analytical method is used to solve it.B y comparing the displacement transmission ratio results with those of the equivalent linear support system,the effect of the NS device on the low-frequency vibration isolation of the system is verified.The specific research contents are as follows:(1)The application of NS structure is explored in the vibration isolation of Euler-Bernoulli beam structures.Considering that both ends of the beam are supported by HSLD isolators,the rigid beam structure is first considered.The vibration response analysis is carried out considering the rigid body mode of the system.And then the beam is modeled as a flexible body,and the equation of motion and boundary conditions of the beam with elastic supports at both ends were obtained by using the Hamilton principle,and the mode is substituted into the boundary conditions for inherent characteristic analysis.The Galerkin method was used to analyze the isolation performance upon the based excitation,and the transmissibility is defined.The comparison results show that: if the NS element is connected in parallel with the positive stiffness mechanism at the support,the positive and NS will counteract each other and reduce low-order resonance frequency,which moves the low-order resonance peak to zero frequency but has little effect on the high-order resonance peak.The resonance peak is significantly reduced,showing the superior vibration isolation performance of the system.(2)The nonlinear vibration of a corner-supported rectangular thin panel with HSLD isolator supports is investigated.The dynamic model of the panel clamped at corners is established and the frequency equations are derived by employing the Rayleigh-Ritz procedure.The characteristic orthogonal polynomial series is introduced as the assumed modes and the equations of motions are obtained.The dynamic response of the system is analytically calculated for the first time by applying the complexification-averaging method.And the approximation solutions are verified with the numerical and finite element method.The isolation performance of the system is evaluated by the displacement transmissibility and the effects of the parameters are investigated for further design and a multi-objective optimization strategy is given.The comparison with the isolation performance of linear elastic-supported panel illustrates that introducing the HSLD isolators has a superior effect on reducing the peak transmissibility in the low-frequency band and provides a wide isolation range for the system.(3)A method is proposed for reducing the low-order natural frequencies of beam/plate structures with classical boundary conditions by adding several NS devices.This method effectively eliminates or weakens the influence of low-order resonances and achieves efficient vibration suppression in the low-frequency range.The assumed mode method was then used to analyze the thin plate structure with the added NS devices,and the natural characteristics of the system were obtained.The forced vibration equation was solved using the modal discretization partial differential equation.The research results show that as the NS increases,the low-order resonance frequency of the system gradually decreases to zero,and the modal order decrease changes with the number of negative stiffness devi ces added.This conclusion was then extended to other boundary-supported thin plate structures,and through comparison and verification of experimental and theoretical results,it was found that the additional NS support can achieve efficient and flexible passive control effects on the low-frequency vibration of flexible structures under suitable structural parameters and installation positions.(4)A novel pre-tensioned torsional NS device was designed for rotational systems.This device uses the interaction between pre-tensioned springs and connecting rods to transmit torsional NS,thus achieving the functions of transmitting motion and isolating vibration in the torsional direction.Static and dynamic analyses of the torsional structure were carried out,and the resonant response of the isolator installed under the axial components was analytically solved.The results show that the torsional NS device can offset the torsional stiffness of the shaft itself,reduce the natural frequency of the system,and th us isolate low-frequency vibration.Subsequently,the torsional NS structure was introduced into the vibration protection problem of a beam with one end free and the other end hinged-fixed,as well as a simply supported beam at both ends.Analysis of the natural characteristics and dynamic response was carried out.Comparison of the displacement transmissibility with an equivalent linear system without the NS device showed that the torsional NS unit reduces the first-order frequency of the system,enlarges the non-resonant region of the beam structure,expands the operating frequency band of the system,and this characteristic is not significantly affected by strong nonlinearity.