IMPROVED ANALYSIS OF A PROPPED CANTILEVER UNDER LATERAL VIBRATION

Continuous systems are sometimes analysed as lumped masses connected by massless elements. This reduces the structure’s degree of freedom and therefore simplifies the analysis. However this over simplification introduces an error in the analysis and the results are therefore approximate. In this work sections of the vibrating beam were isolated and the equations of the forces causing vibration obtained using the Hamilton’s principle. These forces were applied to the nodes of an equivalent lumped mass beam and the stiffness modification needed for it to behave as a continuous beam obtained. The beam’s stiffness was modified using a set of stiffness modification factors to . It was observed that by applying these factors in the dynamic analysis of the beam using the Lagrange’s equation, we obtain the exact values of the fundamental frequency irrespective of the way the mass of the beam was lumped. From this work we observed that in order to obtain an accurate dynamic response from a lumped mass beam there is need to modify the stiffness composition of the system and no linear modification of the stiffness distribution of lumped mass beams can cause them to be dynamically equivalent to the continuous beams. This is so because the values of the modification factors obtained for each beam segment were not equal. The stiffness modification factors were obtained for elements at different sections of the beam

Ultra-Wide Bandgap in Two-Dimensional Metamaterial Embedded with Acoustic Black Hole Structures

This paper reports a type of metamaterial plate enabling in-plane ultra-wide vibration isolation in engineering equipment development. It is composed of periodic hexagonal lattice structures. The acoustic black hole (ABH) structures are embedded in each cell wall of the conventional hexagonal lattice, which results in the reduction of local stiffness in the cell wall and the local mass in the hexagonal corner. The lattice can be simplified as the form of lumped masses vibrating on springs, and two types of eigenstates can be obtained: the rotational eigenstates and the transverse eigenstates. The geometric nonlinearity of the ABH structure leads to unevenly distributed vibration modes, resulting in the ultra-wide bandgap. Experimental results prove the effective attenuation capacity. Compared with the traditional hexagonal lattice, the proposed design provides greater advantages in practical application.

Polyharmonic Vibrations of Human Middle Ear Implanted by Means of Nonlinear Coupler

This paper presents a possibility of quasi-periodic and chaotic vibrations in the human middle ear stimulated by an implant, which is fixed to the incus by means of a nonlinear coupler. The coupler represents a classical element made of titanium and shape memory alloy. A five-degrees-of-freedom model of lumped masses is used to represent the implanted middle ear for both normal and pathological ears. The model is engaged to numerically find the influence of the nonlinear coupler on stapes and implant dynamics. As a result, regions of parameters regarding the quasi-periodic, polyharmonic and irregular motion are identified as new contributions in ear bio-mechanics. The nonlinear coupler causes irregular motion, which is undesired for the middle ear. However, the use of the stiff coupler also ensures regular vibrations of the stapes for higher frequencies. As a consequence, the utility of the nonlinear coupler is proven.

Coupled Dynamics of Vehicle-Bridge Interaction System Using High Efficiency Method

Vehicle-bridge interaction is the core for a variety of applications, including vehicle vibration, bridge vibration, bridge structural health monitoring, weight-in-motion, bridge condition inspection, and load rating. These applications give rise to a great interest in pursuing a high-efficiency method that can tackle intensive computation in the context of vehicle-bridge interaction. This paper studies the accuracy and efficiency of discretizing the beam in space as lumped masses using the flexibility method and as finite elements using the stiffness method. Computational complexity analysis is carried out along with a numerical case study to compare the accuracy and efficiency of both methods against the analytical solutions. It is found that both methods result in a similar level of accuracy, but the flexibility method overperforms the stiffness method in terms of computational efficiency. This high efficiency algorithm and corresponding discretization schema are applied to study the dynamics of vehicle-bridge interaction. A system of coupled equations is solved directly for a simply supported single-span bridge and a four-degree-of-freedom vehicle modeling. Pavement roughness significantly influences dynamic load coefficient, suggesting preventative maintenance or timely maintenance of pavement surface on a bridge, to reduce pavement roughness, is of significant importance for bridge’s longevity and life-cycle cost benefit. For class A and B level pavement roughness, the dynamic load coefficient is simulated within 2.0, compatible with specifications of AASHTO standard, Australian standard, and Switzerland standard. However, the Chinese code underestimates the dynamic load coefficient for a bridge with a fundamental frequency of around 4 Hz. The proposed method is applicable to different types of bridges as well as train-bridge interaction.

Exact Dynamic Characteristic Analysis of Steel-Concrete Composite Continuous Beams

The free vibration characteristics of steel-concrete composite continuous beams (SCCCBs) are analyzed based on the Euler–Bernoulli beam theory. A modified dynamic direct stiffness method has been developed, which can be used to analyze the SCCCBs with some lumped masses and elastic boundary conditions. The results obtained by the proposed method are exact due to the elimination of approximated displacement and force fields in derivation. The proposed method is verified by comparing its results with those obtained by ANSYS software and laboratory tests. Then, the influencing factors on the reduction of natural frequency are analyzed and discussed in detail using the proposed method. The results show that stronger interfacial interaction results in higher values of natural frequency as well as larger steel subbeam and thinner concrete slab. The smaller the natural frequency of the SCCCBs is, the more significant effect the interfacial interaction on the natural frequency is. The reduction of natural frequency is not affected by the different numbers of spans but the equal single-span length and various ratios of the side span to the main span but equal total length, but it is influenced by the extra single-span length and different ratios of the side span to the main span but equal main span length. And it is only affected by bending stiffness. Furthermore, the reasonable ratio of the side span to the main span is 0.9∼1.0.

Estimation of Design Parameters of the Crank-Connecting Rod Mechanism of Engines for Mobile Agricultural Machines

An accurate choice of the design model of the crank-connecting rod mechanism of piston internal combustion engines affects the accuracy of the calculation results and their complexity. At present, most of scientists and technicians choose a two-mass design model to analyze the operation of the crankconnecting rod mechanism. The model considers only the rotational and reciprocating movements of two masses, which are connected by a rigid weightless rod. This model significantly simplifies the calculations, neglects the elastic deformations of the parts of the crank-connecting rod mechanism, and eliminates the need for compiling the equations of dynamics in partial derivatives. However, the model has a number of drawbacks. The calculation results obtained using the two-mass model exhibit significant errors, which mainly depend on the design features of the connecting rod assembly. The paper discusses multi-mass design models, where the connecting rod assembly can comprise several lumped masses located along its length. In this case, the plane-parallel motion of these masses is added. The masses have weightless and absolutely rigid bonds. Forces and moments acting on the piston assembly and the crank are calculated according to the equations compiled. Comparison of the calculation results with the results obtained for a two-mass model can be used to determine errors and choose a design model that provides the required accuracy. The considered design model is of interest to engineers and technicians engaged in the design and calculation of the crank-connecting rod mechanism of piston internal combustion engines.

Seismic Responses of NPP Structures Considering the Effects of Lead Rubber Bearing

Abstract-This study investigates the effects of Lead Rubber Bearings (LRBs) on Floor Response Spectra (FRS) of Nuclear Power Plant (NPP) structures. Three main structures in the Advanced Power Reactor 1400 (APR1400) NPP including the reactor containment building, an internal structure, and an auxiliary building were numerically developed in SAP2000. The structures were modeled using beam stick elements, and lumped masses were assigned to beam element nodes. All equivalent section properties of beam elements were calculated based on the designed cross-sections of the structures. A series of 40 ground motions with response spectra scaled to match the NRC 1.60 spectrum were utilized in numerical time-history analyses. Finally, a thorough comparison of FRS was conducted at different elevations of the structures, considering both with and without LRB. Numerical results showed that the FRS of base-isolated structures at higher elevations was significantly reduced compared to non-isolated structures. However, at lower elevations, the FRS was higher for the base-isolated structures compared to the non-isolated ones. Additionally, at a low-frequency range, roughly smaller than 3 Hz, the FRS of base-isolated structures was always greater than that of the non-isolated ones.

Dynamic Analysis of Encastre Beams by Modification of the System’s Stiffness Distribution

Numerical and energy methods are used to dynamically analyze beams and complex structures. Hamilton’s principle gives exact results but cannot be easily applied in frames and complex structures. Lagrange’s equations can easily be applied in complex structures by lumping the continuous masses at selected nodes. However, this would alter the mass distribution of the system, thus introducing errors in the results of the dynamic analysis. This error can be corrected by making a corresponding modification in the systems’ stiffness matrix. This was achieved by simulating a beam with uniformly distributed mass with the force equilibrium equations. The lumped mass structures were simulated with the equations of motion. The continuous systems were analyzed using the Hamilton’s principle and the vector of nodal forces {P} causing vibration obtained. The nodal forces and displacements were then substituted into the equations of motion to obtain the modified stiffness values as functions of a set of stiffness modification factors. When the stiffness distribution of the system was modified by means of these stiffness modification factors, it was possible to predict accurately the natural fundamental frequencies of the lumped mass encastre beam irrespective of the position or number of lumped masses.

Sources of Excitation and Models for Cylindrical Gear Dynamics: A Review

In this paper, a review of the evolution of the study of cylindrical gear dynamics is presented. After a brief historical introduction to the field, the first attempts to describe the complex interactions in those systems are analyzed introducing the dynamic factor and the first methodologies used to compute it. Next, the sources of excitation in geared systems are analyzed in detail and the models of the various contributions are discussed. Then, the paper focuses on the use of those sources in several dynamic models which are wildly different in terms of scope, applicability, complexity and methodology employed, ranging from simple analytical models, to lumped masses models up to multibody and finite element models. Finally, an outlook to the future evolution of the field is given and conclusions are drawn.