Unfortunately, there are mistakes in Eqs. (20–23). The corrected equations are given here:

$$\begin{aligned} c_{NL,A} & = c_{L} \cdot (0.8 \cdot v_{\hbox{max} ,A} \cdot \cos \theta )^{{1 - \bar{\alpha }}} \\ & = \overline{\xi } \cdot \omega_{1} \cdot m_{tot} \cdot \left( {\frac{N + 1}{n}} \right) \cdot \frac{1}{{\cos^{2} \theta }} \cdot \left( {M \cdot 0.8 \cdot \frac{{S_{a} }}{{\omega_{1} }} \cdot \frac{12N}{{(2 + 5N + 5N^{2} )}} \cdot \cos \theta } \right)^{{1 - \bar{\alpha }}} \\ \end{aligned}$$
(20)
$$c_{NL,B} = c_{L} \cdot \left( {0.8 \cdot v_{\hbox{max} ,B} \cdot \cos \theta } \right)^{{1 - \bar{\alpha }}} = \overline{\xi } \cdot \omega_{1} \cdot m_{tot} \cdot \left( {\frac{N + 1}{n}} \right) \cdot \frac{1}{{\cos^{2} \theta }} \cdot \left( {M \cdot 0.8 \cdot \frac{{S_{a} }}{{\omega_{1} }} \cdot \frac{2}{N + 1} \cdot \cos \theta } \right)^{{1 - \bar{\alpha }}}$$
(21)

where the factor \(\cos \theta\) is applied to \(v_{\hbox{max} ,A}\) and \(v_{\hbox{max} ,B}\) to obtain the velocity along the inclined direction of the damper.

$$F_{NL,A} = c_{NL,A} \cdot v_{\hbox{max} ,A}^{{\bar{\alpha }}} = 0.8^{{1 - \bar{\alpha }}} \cdot \overline{\xi } \cdot m_{tot} \cdot \frac{1}{n \cdot \cos \theta } \cdot M \cdot S_{a} \left( {T_{1} ,\overline{\xi } } \right) \cdot \frac{{12N\left( {N + 1} \right)}}{{(2 + 5N + 5N^{2} )}}$$
(22)
$$F_{NL,B} = c_{NL,B} \cdot v_{\hbox{max} ,B}^{{\bar{\alpha }}} = 2 \cdot 0.8^{{1 - \bar{\alpha }}} \cdot \overline{\xi } \cdot m_{tot} \cdot \frac{1}{n \cdot \cos \theta } \cdot M \cdot S_{a} \left( {T_{1} ,\overline{\xi } } \right)$$
(23)