Vibration Analysis Of Multi-span Lattice Sandwich Beams Using Assumed Mode Method

Multi-span beams are widely used in the practical engineering fields.As a result,researches on the multi-span beams have attracted considerable attention.So far,analytical method is common in calculating the vibration of multi-span structures.However,the calculating process would be more complex with the increasing number of spans.If this analytical method is used to calculate vibration characteristics of composite structures,like sandwich structures,it would be more difficult.Sandwich structures attracted much attention on aviation,spaceflight and high-speed train recently.Meanwhile,sandwich structures are used for multi-span structures in practical engineering on a regular basis.In this paper,the assumed mode method is used for calculating vibration characteristics of multi-span Timoshenko beams and multi-span lattice sandwich beams.The main contents of this dissertation are as follow:(1)When the assumed mode method is used to express vibration mode functions of multi-span beams,the assumed modes of the transverse displacements of multi-span beams are assumed as those of uniform beams modified by the interpolation functions,which are satisfied boundary conditions.There are two methods for assumed modes of the rotation angles,which are expressed by trigonometric series and a uniform beam's assumed mode of rotation angle modified by the interpolation functions respectively.(2)The equation of motion of the multi-span Timoshenko beam is established by the Hamilton's principle and assumed mode method.The natural frequencies of structures and the vibration respond of mid-point at structures with the external transverse single pulse excitation are studied.Compared with literature and finite element results from Ansys software,the correctness of assumed mode method in this paper can be verified.Additionally,the natural frequencies of three-span Timoshenko beams are calculated using two different assumed modes of the rotation angles respectively.The method which is more accurate and simpler would be selected by comparing with results from Ansys.The influences of the length-thickness ratio,the disorder degree and the span number on the free vibration of the structure are also analyzed.In this paper,the length-thickness ratio is the ratio of total length of structure to diameter of cross section.The disorder degree is the ratio of middle-span's length to total length of three-span Timoshenko beam.In order to eliminate different influences of disordered structure,the effect of the span number on the vibration analysis of the ordered multi-span Timoshenko beams with equal spans are studied.The results show that changes of these parameters have regular effects on the vibration characteristics of multi-span Timoshenko beams.Furthermore,some laws of equal frequencies of symmetrical three-and four-span beams are found,e.g.,the same even order frequencies of different three-span beams are equal under specific disorder degree.In addition to that,the multi-span Euler-Bernoulli beams are also calculated by the assumed mode method.(3)Based on the analysis of multi-span Timoshenko beams,this assumed mode method is used for calculating vibration characteristics of complex multi-span lattice sandwich beam in depth.In this paper,typical multi-span pyramidal and Kagome sandwich beams are calculated.Then this method is also used for other types of multi-span lattice sandwich beams.For the vibration analysis of multi-span lattice sandwich beam,the core is equivalent to the uniform layer,and the equivalent density and the shear stiffness of the core layer are calculated.The shear deformation of the core is considered.The sheets of the lattice sandwich structure are thin plates,so the bending deformation is only considered.The assumed mode method and the Hamilton principle are also used to solve the vibration characteristics of the structure.The natural frequencies and mode shapes of structure obtained by theoretical solution are compared by the results from ANSYS software.(4)The natural frequencies and the free vibration response at the mid-point of three-span pyramidal and Kagome sandwich beams with different truss radius,truss inclination angle and sheet thickness are calculated.The effects of the above variables on the vibration characteristics of the structure are analysed.At the same time,the influences of the elastic modulus and damping on the vibration characteristics of the three-span pyramid lattice sandwich beam are also studied.