变截面耦合微悬臂双梁的基本振动特性

本文研究了连接部件的几何参数对变截面耦合微悬臂双梁振动特性的影响．首先，利用集总参数法建立了等效的两自由度系统耦合振动的解析模型；其次，利用分离变量法获得了耦合双梁自由振动的固有频率、振幅比和强迫振动的反共振频率；最后，通过比对解析解、有限元数值结果和实验数据，验证了解析预测的可靠性．研究结果表明，连接部件的宽度和初始偏转角的变化会对耦合双梁振动的特性产生较大的影响．     

PIEZOELECTRIC PROPERTIES OF SINGLE-STRAND DNA MOLECULAR BRUSH BIOLAYERS

The paper is devoted to investigations on nanomechanical behaviors of biochips in label-free biodetections.The chip consists of Si-layer,Ti-layer,Au-layer and single-strand DNA (ssDNA)molecular brush biolayer immobilized by self-assembly technology of thiol group.Unlike previous viewpoints,such as force-bending,entropy-bending and curvature electricity effect,etc., the piezoelectric effect of the biopolymer brush layer is viewed as the main factor that induces nanomechanical bending of biochips,and a classical macroscopic piezoelectric constitutive rela- tion is used to describe the piezoelectric effect.A new laminated cantilever beam model with a piezoelectric biolayer in continuum mechanics,the linearized Poisson-Boltzmann equation in statistical mechanics and the scaling method in polyelectrolyte brush theory are combined to es- tablish a relationship between the nanomechanical deflection of DNA chips and the factors such as nanoscopic structural features of ssDNA molecules,buffer salt concentration,macroscopic me- chanical/piezoelectric parameters of DNA chips etc.Curve fitting of experimental data shows that the sign of the piezoelectric constant of the biolayer may control the deflection direction of DNA chips during the packaging process.     

Thermal-induced snap-through buckling of simply-supported functionally graded beams

The instability of functionally graded material (FGM) structures is one of the major threats to their service safety in engineering applications. This paper aims to clarify a long-standing controversy on the thermal instability type of simply-supported FGM beams. First, based on the Euler-Bernoulli beam theory and von Kármán geometric nonlinearity, a nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang's two-variable method is formulated. Second, an approximate analytic solution to the nonlinear integro-differential boundary value problem under a thermal-induced inhomogeneous force boundary condition is obtained by using a semiinverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finally, based on the free energy theorem, it is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermore, the nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures.     

热载荷下粘弹性功能梯度材料薄板的准静态响应

由热粘弹性功能梯度材料的本构方程出发,利用Laplace变换,通过引进薄板的"结构函数"和"热函数",建立了各向同性薄板的数学模型.采用卷积双线性形式,给出了薄板准静态问题的简化Gurtin型泛函.在空域上和时域上分别采用Ritz法和Legendre插值法考察了温度变化和功能梯度对于薄板响应的影响.     

Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain

Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices. This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain. Firstly, Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam. Secondly, the related analytical solutions are obtained by combining the diffe...     

SURFACE STRESS PROPERTIES OF DNA-MICROCANTILEVER SYSTEMS

For the first time, the connection between surface stress and nanoscopic interac- tions of DNA adsorbed on microcantilever is established by combining Strey＇s mesoscopic liquid crystal theory and Stoney＇s formula. It is shown that surface stress depends not only on biomolec- ular interactions of DNA biofilm but also on mechanical properties of cantilever. Considering the correlativity between grafting density and chain length of DNA chain, we discuss the differences between DNA-microcantilever system and DNA solution system. The major theoretical achieve- ment of this model is to identify the main contributions to surface stress under different detection conditions. This provides guidelines for designing new biosensors with high sensitivity and improved reliability.     

A variational principle of perturbed motion on viscoelastic thin plates with applications

In this paper, in the light of the Boltzmann superposition principle in linear viscoelasticity, a mathematical model of perturbed motion on viscoelastic thin plates is established. The corresponding variational principle is obtained in a convolution bilinear form. For application the problems of free vibration, forced vibration and stability of a viscoelastic simply-supported rectangular thin plate are considered. The results show that numerical solutions agree well with analytical solutions. The project was supported by the National Natural Science Foundation of China (No. 19772027) and the Shanghai Municipal Development Foundation of Science and Technology (No. 98JC14032).