## 1 Introduction  
Promoted by the realization of dwindling fossil fuel supplies and their adverse environmental impacts, more and more types of alternative fuels to fossil diesel have been investigated and used in compression ignition (CI) engines. It has been shown by many studies [1; 2; 3; 4] and small-scale applications [5; 6] that the use of biodiesel can be feasible as burning such fuels in a diesel engine can produce the desired power and an emission level similar to that of fossil diesel. It has also been observed that there are many significant differences in using biodiesel in terms of combustion behaviors, burning residuals, vibration and noise emissions, which might be attributed to their significant difference in physical and chemical properties [7; 8]. However, the majority of studies on biodiesel have mainly focused on its power performance, efficiency and emission performance, without fully investigating the potential effects on the vibro-acoustic emissions of engines caused by its significant differences in physical and chemical properties. Consequently, the impacts of the long-term use of biodiesel on structural failure, overall service lifespans and the associated maintenance activities of internal combustion (IC) engines are not yet fully understood. It has been found that there are many differences in the chemical components and combustion characteristics of biodiesel from various feed stocks [8]. To bring the service performance of biodieselclose to that of fossil diesel, that is, to fuel CI engines with biodiesel without modifying engines, appropriate additives and performance improvers are usually needed in the preparation of biodiesel. So far, the service performance, such as power performance, fuel economy and exhaust emission, has been generally selected as the optimization objective of biodiesel preparation. However, the noise, vibration and harshness (NVH) performance of an IC engine is rarely considered as the objective of fuel optimization design. This hinders the attempt at achieving service life extension and maintenance cost reduction through the optimization design of biodiesel. In order to investigate the differences in engine NVH performance fueled with biodiesel and fossil diesel, some preliminary experimental studies have been performed. [PERSON] et al. [8] proposed that, due to the high oxygen fraction, the combustion quality of biodiesel is better than that of conventional fossil diesel. The average engine vibration fueled with pure sunflower, canola and corn biodiesel decreased by 2.80%, 3.87% and 3.72% respectively when compared with fossil diesel. Smoother combustion with the usage of biodiesel means lowering the vibration emissions of the engine body. Biodiesel has a higher cetane value, which means that it is much easier to ignite after being injected into the combustion chamber. Advanced ignition or earlier premixed combustion can effectively shorten the ignition delay period, thus reducing the peak of pressure rise rate. It can be inferred that the burning of biodiesel may be helpful to reduce the dynamic responses of engines. However, as [PERSON] et al. [7] found, with an increase of the operating speed, especially at high-load conditions, a four-cylinder engine fueled with a blended fuel consisting of biodiesel and diesel with a blending ratio from 20% to 40% (biodiesel in blended fuel) shows much more intense vibration and noise emissions than the diesel under high-speed operating conditions. This phenomenon can hardly be explained just by the combustion characteristics of biodiesel, suggesting that vibration characteristics are determined by complex dynamic behaviors. It is essential to investigate the generating mechanism of dynamic responses and to study the causal relationship between the excitation sources and structural vibrations, thus achieving a more in-depth understanding of the vibrational characteristics of IC engines fueled with biodiesel.