Free Vibration And Overall Stability Analysis Of The Rectangular Hard-sandwich Plate

Compared with the traditional structure, sandwich structure has higher strength and stiffness, good fatigue resistance, good seismic performance, insulate heat, insulate heat, etc. Can give full play to the superiority of the composite effects, and easy to design. Widely used in aerospace, transportation, buildings, etc. In the present research of the sandwich structure mainly based on the soft sandwich hypothesis, just linear theory mainly include:1. Reissner type theory;2. Hoff type theory;3. ⅡpycaKOB-DuQingHua type theory. But the entire sandwich layer is seen as soft sandwich in this three classic sandwich plate theories, ignore its in-plane stiffness and bending rigidity, namely the stress components in the sandwich layer are zero. But sandwich layer have large thickness relative to the surface, especially for sandwich layer with larger elastic modulus sandwich structure, the above three theories of soft sandwich hypothesis would have greater error. This article is to sandwich layer with larger elastic modulus sandwich structure, fixed the soft sandwich hypothesis of Reissner type theory and Hoff type theory, put forward the assumption of the hard sandwich interlayer board theory. Consider the sandwich layer’s in-plane stiffness and bending stiffness, namely the stress components in the sandwich layer are no longer for zero, get the following conclusion:1. Get the geometric equations and physical equations of hard-sandwich plate, established the basic equation of hard-sandwich plate free vibration and overall stability analysis by using Hamilton principle.2. Simplify the equation, got the analytical solution of some special boundary conditions. Change the sandwich layer’s elastic modulus, found that when the sandwich layer’s elastic modulus is greater one over ten than the surfaces’, hard sandwich hypothesis computing to the inherent frequency and critical load value than the results of soft sandwich hypothesis have increased significantly. In addition, we also calculated the other sandwich layer material parameters’effects on the sandwich board’s natural frequency and the overall instability.3. Based on the fixed Reissner type hard sandwich plate theory in this article, derived the stiffness matrix of the unit used the four nodes quadrilateral isoparametric unit. And based on MATLAB programming, solve the different boundary conditions hard sandwich rectangular interlayer board’s natural frequencies, the convergence of finite element solution by analytical solution.