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Nyquist plots are a classical means to visualize a complex vibration frequency response function. By graphing the real and imaginary parts of the response, the dynamic behavior in the vicinity of resonances is emphasized. This allows insight into how modes are coupling, and also provides a means to separate the modes. Mathematical models such as Nyquist analysis are often embedded in frequency analysis hardware. While this speeds data collection, it also removes this visually intuitive tool from the engineer’s consciousness. The behavior of a single degree of freedom system will be shown to be well described by a circle on its Nyquist plot. This observation allows simple visual examination of the response of a continuous system, and the determination of quantities such as modal natural frequencies, damping factors, and modes shapes. Vibration test data from an auto rickshaw chassis are used as an example application.

An experimental investigation of non-intrusive combustion sensing was performed using a tri-axial accelerometer mounted to the engine block of a small-bore high-speed 4-cylinder compression-ignition direct-injection (CIDI) engine. This study investigates potential techniques to extract combustion features from accelerometer signals to be used for cycle-to-cycle engine control. Selection of accelerometer location and vibration axis were performed by analyzing vibration signals for three different locations along the block for all three of the accelerometer axes. A magnitude squared coherence (MSC) statistical analysis was used to select the best location and axis. Based on previous work from the literature, the vibration signal filtering was optimized, and the filtered vibration signals were analyzed. It was found that the vibration signals correlate well with the second derivative of pressure during the initial stages of combustion.

The Hybrid Finite Element Analysis (HFEA) method is based on combining conventional Finite Element Analysis (FEA) with analytical solutions and energy methods for mid-frequency computations. The method is appropriate for computing the vibration of structures which are comprised by stiff load bearing components and flexible panels attached to them; and for considering structure-borne loadings with the excitations applied on the load bearing members. In such situations, the difficulty in using conventional FEA at higher frequencies originates from requiring a very large number of elements in order to capture the flexible wavelength of the panel members which are present in a structure. In the HFEA the conventional FEA model is modified by de-activating the bending behavior of the flexible panels in the FEA computations and introducing instead a large number of dynamic impedance elements for representing the omitted bending behavior of the panels.

High-Reynolds number turbulent boundary layers are an important source for inducing structural vibration. Small geometric features of a structure can generate significant turbulence that result in structural vibration. In this work we develop a new method to couple a high-fidelity fluid solver with a dynamic hybrid analytical-numerical formulation for the structure. The fluid solver uses the Large-Eddy Simulation closure for the unresolved turbulence. Specifically, a local and dynamic one-equation eddy viscosity model is employed. The fluid pressure fluctuation on the structure is mapped to the dynamic structural model. The plate where the flow excitation is applied is considered as part of a larger structure. A hybrid approach based on the Component Mode Synthesis (CMS) is used for developing the new hybrid formulation. The dynamic behavior of the plate which is excited by the flow is modeled using finite elements.

Recent stringent government regulations on emission control and fuel economy drive the vehicles and their associated components and systems to the direction of lighter weight. However, the achieved lightweight must not be obtained by sacrificing other important performance requirements such as manufacturability, strength, durability, reliability, safety, noise, vibration and harshness (NVH). Additionally, cost is always a dominating factor in the lightweight design of automotive products. Therefore, a successful lightweight design can only be accomplished by better understanding the performance requirements, the potentials and limitations of the designed products, and by balancing many conflicting design parameters. The combined knowledge-based design optimization procedures and, inevitably, some trial-and-error design iterations are the practical approaches that should be adopted in the lightweight design for the automotive applications.

The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration and the interior noise level of complex structural-acoustic systems by solving numerically governing differential equations with energy densities as primary variables. In this paper a complete simulation process for evaluating airborne noise in an automotive vehicle is presented and validated through extensive comparison to test data. The theoretical elements associated with the important paths of the noise transfer from the exterior of the vehicle to the interior acoustic space are discussed. The steps required for developing an EFEA model for a vehicle are presented. The model is developed based on the physical construction of the vehicle system and no test measurements are utilized for adjusting the numerical model.

The hybrid FEA method combines the conventional FEA method with the energy FEA (EFEA) for computing the structural vibration in vehicle structures when the excitation is applied on the load bearing stiff structural members. Conventional FEA models are employed for modeling the behavior of the stiff members in the vehicle. In order to account for the effect of the flexible members in the FEA analysis, appropriate damping and spring/mass elements are introduced at the connections between stiff and flexible members. Computing properly the values of these damping and spring/mass elements is important for the overall accuracy of the computations. Utilizing in these computations the analytical solutions for the driving point impedance of infinite or semi-infinite members introduces significant approximations.

Simulation of reach movements is an essential component for proactive ergonomic analysis in digital human modeling and for numerous applications in vehicle design. Most studies on reach kinematics described human movements in static conditions. Earlier studies of reach performance in vibration environments focused mainly on fingertip deviation without considering multi-body dynamics. However, for the proper assessment of reach performance under whole-body vibration exposure, a multi-body biodynamic model needs to be developed. This study analyzes three dimensional reach kinematics of the upper extremity during in-vehicle operations, using a multi-segmental model of the upper body in the vibratory environment. The goals are to identify the characteristics of upper body reach movements and to investigate vibration-induced changes in joint kinematics. Thirteen subjects reached to four target directions in the right hemisphere.

Exposure of a driver to vehicle vibration is known to disrupt manual performances, and more specifically affect the speed and accuracy of reaching tasks associated with vehicle operation. The effects of whole body vibration (WBV) can be analyzed as a function of the vibration characteristics of each body link. This information can then be used to identify movement strategies and predict biodynamic responses. Conceptual principles derived from the understanding of human behavior in a vibratory environment can then be used for the design of controls or interfaces adapted for vehicle operation in this context. The transfer functions of individual upper body links were estimated to investigate their biodynamic properties as a function of vehicle vibration frequency and spatial location of targets to be reached. In the present study, fourteen seated participants performed pointing movements to eight targets distributed in the right hemisphere.

The Energy Boundary Element Analysis (EBEA) has been utilized in the past for computing the exterior acoustic field at high frequencies (above ∼400Hz) around vehicle structures and numerical results have been compared successfully to test data [1, 2 and 3]. The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration of complex structures at high frequencies and validations have been presented in previous publications [4, 5]. In this paper the EBEA is utilized for computing the acoustic field around a vehicle structure due to external acoustic noise sources. The computed exterior acoustic field comprises the excitation for the EFEA analysis. Appropriate loading functions have been developed for representing the exterior acoustic loading in the EFEA simulations, and a formulation has been developed for considering the acoustic treatment applied on the interior side of structural panels.

A comprehensive formulation is presented for the dynamics of a rotating flexible crankshaft coupled with the dynamics of an engine block through a finite difference elastohydrodynamic main bearing lubrication algorithm. The coupling is based on detailed equilibrium conditions at the bearings. The component mode synthesis is employed for modeling the crankshaft and block dynamic behavior. A specialized algorithm for coupling the rigid and flexible body dynamics of the crankshaft within the framework of the component mode synthesis has been developed. A finite difference lubrication algorithm is used for computing the oil film elastohydrodynamic characteristics. A computationally accurate and efficient mapping algorithm has been developed for transferring information between a high - density computational grid for the elastohydrodynamic bearing solver and a low - density structural grid utilized in computing the crankshaft and block structural dynamic response.

The internal combustion (IC) engine is an important source of vibration in many vehicles, and understanding its dynamic response to demands from both the vehicle operator and the terrain is essential to proper engine and mount design and optimization. Development of an engineering tool for understanding this dynamic response and the resulting forces transmitted from the engine block to the supporting structure is a priority in both commercial and military engine applications. Ideally, engine dynamics and vibration would be directly simulated through effective and efficient analytical and computational models of both the internal engine component dynamics as well as engine block vibrations. The present analytical study was undertaken to produce a comprehensive and efficient rigid-body engine dynamics and vibration model which predicts engine block motion, engine mount load transmission, as well as instantaneous engine crankshaft rotational speed.

Belt drives have long been utilized in engine applications to power accessories such as alternators, pumps, compressors and fans. The first belt drives consisted of one or more V-belts powering fixed-centered pulleys and were pre-tensioned by statically adjusting the pulley center separation distances. In recent years, such drives have been replaced by a single, flat, ‘serpentine belt’ tensioned by an ‘automatic tensioner.’ The automatic tensioner consists of a spring-loaded, dry friction damped, tensioner arm that contacts the belt through an idler pulley. The tensioner's major function is to maintain constant belt tension in the presence of changing engine speeds and accessory loads. The engine crankshaft supplies both the requisite power to drive the accessories as well as the (unwanted) dynamic excitation that can adversely affect the accessories and the noise and vibration performance of the belt.

High-fidelity overall vehicle simulations require efficient computational routines for the various vehicle subsystems. Typically, these simulations blend theoretical dynamic system models with empirical results to produce computer models which execute efficiently. Provided that the internal combustion engine is a dominant source of vehicle vibration, knowledge of its dynamic characteristics throughout its operating envelope is essential to effectively predict vehicle response. The present experimental study was undertaken to determine the rigid body modal content of engine block vibration of a modern, heavy-duty Diesel engine. Experiments were conducted on an in-line six-cylinder Diesel engine (nominally rated at 470 BHP) which is used in both commercial Class-VIII trucks, and on/off-road military applications. The engine was mounted on multi-axis force transducers in a dynamometer test cell in the standard three-point configuration.

An engine system finite-element model is developed and experimentally evaluated for predicting the structural vibration and radiated noise of the running engine. Combustion and inertial loads from a rigid-body dynamic analysis of the crank-piston motion are applied as operating loads in the model. Comparisons are made with measurements of the structural vibration and radiated noise of a running engine. The comparisons show that the accuracy of the model in predicting structural vibration and radiated noise is generally adequate.

In this work, we discuss statistical energy methods for predicting mid-frequency vibration transmission between two spring-coupled substructures with parameter uncertainties. We adopt a parameter-based approach, which allows us to relax certain assumptions associated with a classical Statistical Energy Analysis (SEA) approximation. We consider both a numerical method and an analytical method. The latter is called a Parameter-based Statistical Energy Method (PSEM). An example of two elastic bars coupled by a single spring or multiple springs is examined. The power transmitted from the excited substructure to the other substructure is calculated and compared for the various methods.

A solution is proposed to the upcrossing problem for a stress of a special form encountered in probabilistic torsional vibration analysis of marine Diesel engine shafting systems. For the case that two engine criticals occur at the same engine speed, the stress is modeled as a cyclostationary random process with two frequencies. An equivalent stationary process is defined, requiring that its envelope process has the same upcrossing rate as the envelope of the original cyclostationary random process. It is assumed that both processes have the same probability of upcrossing a specific threshold in a given time interval. Numerical implementation shows the applicability and efficiency of the method.

Designing trucks for good ride characteristics is a challenge to the engineer, given the many design constraints imposed by requirements for transport productivity and efficiency. The objective of this lecture is to explain why trucks ride as they do, and the basic mechanisms involved. The response of primary interest is the vibration to which the driver is exposed in the cab. Whole-body vibration tolerance curves give an indication of how those vibrations are perceived at the seat; however, ride studies have shown that visual and hand/foot vibrations are also important to the perception of ride in trucks. The ride environment of the truck driver is the product of the applied excitation and the response properties of the truck. The major excitation sources are road roughness, the rotating tire/wheel assemblies, the driveline, and the engine.