Noise, vibration, and harshness is one of the main issues of heavy vehicles since their working conditions are very complex and tough. However, most previous works were focused on the optimization design methods of the engine mounting system and few works were reported to study those of the body mounting system. In practice, the body mounting system can significantly affect the noise, vibration, and harshness performance of the vehicle. An inappropriate body mounting system can produce unacceptable noise, vibration, and harshness performance and even result in serious accidents. To overcome this issue, an optimization design method for a body mounting system of a heavy vehicle is proposed to investigate the effect of the body mounting system on the noise, vibration, and harshness performance. Based on the geometrics of the vehicle body, the initial material parameters, shapes, and sizes of the rubber absorber of the body mounting system are determined by the vibration transmissibility ratio and static deformation ratio from an analytical method in the literature. The von Mises stresses of the initial rubber absorber cases from a static finite element analysis are used to select the optimal rubber absorber cases. A multibody dynamic method is proposed to validate the noise, vibration, and harshness performance of the optimal rubber absorber cases. The results show that the presented optimization design method for the body mounting system can be used to optimize the noise, vibration, and harshness performance of the heavy vehicles.
Purpose Modelling methods can be helpful for understanding vibrations of beam structures including cracks, as well as for early detection of crack. This study aims to provide an analytical modelling approach for a cantilever beam considering a slant vertical crack along its height. However, previous uniform crack methods cannot be used for describing this case. The results from the analytical, finite element (FE) and experimental methods are compared to verify the vibration problem. Design/methodology/approach A massless rotational spring model is adopted to describe the crack. An extended method based on the calculation method for a uniform vertical edge crack is proposed to obtain the stiffness of the slant case. The beam is divided into a series of independent thin slices along the beam height. An Euler–Bernoulli beam model is applied to formulate each slice. The crack in each slice is considered as a uniform one. The transfer matrix method in the literature is used to obtain the beam vibration frequencies and mode shapes. Influences of crack location and sizes on the natural frequencies for the cantilever beam, as well as the mode shapes, are analysed. An established FE model and test results in the listed references are used to validate the developed method. Findings The numerical results show that the rotational stiffness at the cracked section and the natural frequencies of the beam decrease by increasing the crack sizes; the natural frequencies for the beam are greatly influenced by the crack sizes and location; the first natural frequency decreases with the distance from the beam fixed end to the crack location; the value of the first natural frequency reaches a minimum value when the crack is at the beam fixed end; the value of the second natural frequency is a minimum value when the crack is at the beam middle; and the value of the third natural frequency is a minimum value when the crack is at the beam free end. Saltation is observed in some mode shapes at the crack location, especially for larger crack depths; but, the mode shapes of the beam are slightly influenced by the vertical crack. Originality/value This study gives a useful analytical modelling method for free vibration analysis for the cantilever beam with a vertical crack, which can overcome the disadvantages of the previous uniform crack methods.
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