In this paper, first, the vibrational governing equations for the suspension system of a selected sports car were derived using Lagrange's Equations. Then, numerical solutions of the equations were obtained to find the characteristic roots of the oscillating system, and the natural frequencies, mode shapes, and mass and stiffness matrices were obtained and verified. Next, the responses to unit step and unit impulse inputs were obtained. The paper compares the effects of various values of the damping coefficient and spring stiffness in order to identify which combination causes better suspension system performance. In this regard, we obtained and compared the time histories and the overshoot values of vehicle unsprung and sprung mass velocities, unsprung mass displacement, and suspension travel for various values of suspension stiffness (KS
) and damping (CS
) in a quarter-car model. Results indicate that the impulse imparted to the wheel is not affected by the values of CS
and KS
. Increasing KS
will increase the maximum values of unsprung and sprung mass velocities and displacements, and increasing the value of CS
slightly reduces the maximum values. By increasing both KS
and CS
we will have a smaller maximum suspension travel value. Although lower values of CS
provide better ride quality, very low values are not effective. On the other hand, high values of CS
and KS
result in a stiffer suspension and the suspension will provide better handling and agility; the suspension should be designed with the best combination of design variables and operation parameters to provide optimum vibration performance. Finally, multi-objective optimization has been performed with the approach of choosing the best value for CS
and KS
and decreasing the maximum accelerations and displacements of unsprung and sprung masses, according to the TOPSIS method. Based on optimization results, the optimum range of KS
is between 130 000–170 000, and the most favorable is 150, and 500 is the optimal mode for CS
.
Through a combination of analytical, numerical, and experimental methods, we study a three-dimensional metamaterial with the ability to attenuate both airborne sound and mechanical vibrations, simultaneously, and in all directions. In addition, due to the auxetic nature of the design (i.e., having a negative Poisson's ratio), the metamaterial can shrink (or expand) in a relatively uniform manner, without buckling. We utilize an external load to cause a systematic shape change in the metamaterial and tune the attenuation frequency bands. The presented design principles can be utilized in many applications related to acoustic and elastic wave manipulation as well as acoustic devices.
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